Shyam visited Ram during his brief vacation. In the mornings they both would go for yoga. In the evenings they would play
tennis. To have more fun, they indulge only in one activity per day, i.e. either they went for yoga or played tennis each day.
There were days when they were lazy and stayed home all day long. There were 24 mornings when they did nothing, 14
evenings when they stayed at home, and a total of 22 days when they did yoga or played tennis. For how many days Shyam
stayed with Ram?

In a class of 120 students numbered 1 to 120, all even numbered students opt for Physics, those whose numbers are divisible by 5 opt for Chemistry and those whose numbers are divisible by 7 opt for Math. How many opt for none of the three subjects?

A´ is defined as the complement of A, as in, set of all elements that are part of the universal set but not in A. How many of the following have to be true?
i. n(A∪B)′ = n(A′∩B′)
ii. If A∩B = 0, then A′∪B′ is equal to the universal set
iii. If A∪B = universal set, then A′∩B′ should be the null set.
iv. If A⊂B then A′∪B′ = (A∩B)′

n a survey of 100 people, it was found that 60 people read the India Today, 55 read the Outlook and 10 read neither of the two magazines. How many people read both the magazines?

Answer the question on the basis of the information given below.

Mr. Suzuki, a car dealer, sold cars of only two brands, A and B, in the previous year. This year, he introduced a new brand, C. The number of cars of cars of brand A and brand B sold in the previous year were in the ratio 3:2, and the ratio of the number of cars sold in the previous year to that sold in this year is 2:3 for brand A and 2:5 for brand B. Further, the number of cars of brand C sold this year forms 81% of the total number of cars sold this year. What is the percentage increase in the total number of cars sold this year when compared to the total number of cars sold in the previous year?

Answer the question on the basis of the information given below.

Mr. Suzuki, a car dealer, sold cars of only two brands, A and B, in the previous year. This year, he introduced a new brand, C. The number of cars of cars of brand A and brand B sold in the previous year were in the ratio 3:2, and the ratio of the number of cars sold in the previous year to that sold in this year is 2:3 for brand A and 2:5 for brand B. Further, the number of cars of brand C sold this year forms 81% of the total number of cars sold this year. In the next year, Mr. Suzuki wants to increase the total sales by 80%, compared to the total sales this year, by keeping the sales of each of A, B and C at the same level as that in this year and introducing a new brand D. By what percent will the number of cars of brand D (to be sold next year) be more than the total number of cars sold last year?

Answer the question on the basis of the information given below.

Mr. Suzuki, a car dealer, sold cars of only two brands, A and B, in the previous year. This year, he introduced a new brand, C. The number of cars of cars of brand A and brand B sold in the previous year were in the ratio 3:2, and the ratio of the number of cars sold in the previous year to that sold in this year is 2:3 for brand A and 2:5 for brand B. Further, the number of cars of brand C sold this year forms 81% of the total number of cars sold this year. If total of 380 cars were sold this year, and the sales of C this year were nil, instead of 81% of total sales, then how many cars of brand A were sold in the previous year?

S1 = {2, 4, 6, 8, ……………….. 800}
S2 = {3, 6, 9, 12, ……………… 900}
If S3 = S1∪ S2, then what will be the 105th element of S3 if all its elements are arranged in increasing order?

Read the information given below and answer the question that follow. In order to study the breakfast habits of the people in the city of Longkong, a survey of 400 families was conducted. Of these 400 families, 156 had cereals, 288 had eggs and 300 had toast. It was found that 212 families had egg and toast and 104 had cereal and toast, and 128 had egg and cereal and 84 had all three. In a class of 50 students, 28 like pop music, and 20 like classical music. If 10 students like one of the two kinds of music, find the number of the students who like both kinds of music?

For constructing the working class consumer price index number of a particular town, the following weights corresponding to different group of items were assigned: Food-55, Fuel-15, Clothing -10, Rent -8 and Miscellaneous-12.
It is known that the rise in food prices is double that of fuel and the rise in miscellaneous group prices is double that of rent. In October 2006, the increased D.A. by a factory of that town by 182% fully compensated for the rise in prices of food and rent but did not compensate for anything else. Another factory of the same locality increased D.A. by 46.5%, which compensated for the rise in fuel and miscellaneous groups.
Which is the correct combination of the rise in prices of food, fuel, rent and miscellaneous groups?

This question is based on the information given below.

The following table provides partial details about the comparison of the increase in the number of applicants among four streams in education viz. Engineering, Medical Science, Commerce and Arts in the year 2008 as compared to the year 2007. The increase in the number of applicants in the Commerce stream in 2008 as compared to 2007 is 70000 and the average number of applicants in the four streams in 2008 is 400000. Assume that these are the only four streams in the education system. In the given table, the number 20000 under the title ‘Commerce’ means that the increase in the number of applicants in the Commerce stream in 2008 as compared to the year 2007 is 20000 less than the corresponding increase in the Engineering stream. All the other data in the table should be interpreted similarly. Which of the following is not true?

This question is based on the information given below.

The following table provides partial details about the comparison of the increase in the number of applicants among four streams in education viz. Engineering, Medical Science, Commerce and Arts in the year 2008 as compared to the year 2007. The increase in the number of applicants in the Commerce stream in 2008 as compared to 2007 is 70000 and the average number of applicants in the four streams in 2008 is 400000. Assume that these are the only four streams in the education system. In the given table, the number 20000 under the title ‘Commerce’ means that the increase in the number of applicants in the Commerce stream in 2008 as compared to the year 2007 is 20000 less than the corresponding increase in the Engineering stream. All the other data in the table should be interpreted similarly. The total number of applicants in the four given streams in 2007 was

This question is based on the information given below.

The following table provides partial details about the comparison of the increase in the number of applicants among four streams in education viz. Engineering, Medical Science, Commerce and Arts in the year 2008 as compared to the year 2007. The increase in the number of applicants in the Commerce stream in 2008 as compared to 2007 is 70000 and the average number of applicants in the four streams in 2008 is 400000. Assume that these are the only four streams in the education system. In the given table, the number 20000 under the title ‘Commerce’ means that the increase in the number of applicants in the Commerce stream in 2008 as compared to the year 2007 is 20000 less than the corresponding increase in the Engineering stream. All the other data in the table should be interpreted similarly. The total increase in the number of applicants in the Arts stream in 2008 as compared to 2007 as a percentage (approximate) of the total number of applicants in the four given streams in 2007 is

Read the information given below and answer the question that follow:

Ghoshbabu is staying at Ghosh Housing Society, Aghosh Colony, Dighoshpur, Calcutta. In Ghosh Housing Society 6 persons read daily Ganashakti and 4 read Anand Bazar Patrika; In his colony there is no person who reads both. Total number of persons who read these two newspapers in Aghosh Colony and Dighoshpur is 52 and 200 respectively. Number of persons who read Ganashakti in Aghosh Colony and Dighoshpur is 33 and 121 respectively; while the persons who read Anand Bazar Patrika in Aghosh Colony and Dighoshpur are 32 and 117 respectively. Number of persons in Dighoshpur who read only Ganashakti is

Read the information given below and answer the question that follow:

Out of 10,000 persons surveyed, 3,700 liked city A, 4,000 liked city B, and 5,000 liked city C. 700 persons liked city A and B, 1,200 liked A and C, and 1,000 liked city B and C. Each person liked at least one city. Find the number of persons who liked all the three cities. Answer options :

Read the information given below and answer the question that follow:

Ghoshbabu is staying at Ghosh Housing Society, Aghosh Colony, Dighoshpur, Calcutta. In Ghosh Housing Society 6 persons read daily Ganashakti and 4 read Anand Bazar Patrika; In his colony there is no person who reads both. Total number of persons who read these two newspapers in Aghosh Colony and Dighoshpur is 52 and 200 respectively. Number of persons who read Ganashakti in Aghosh Colony and Dighoshpur is 33 and 121 respectively; while the persons who read Anand Bazar Patrika in Aghosh Colony and Dighoshpur are 32 and 117 respectively. Number of persons in Aghosh Colony who read only one newspaper

Read the information given below and answer the question that follow:

There are three different cable channels namely Ahead, Luck and Bang. In a survey it was found that 85% of viewers respond to Bang, 20% to Luck, and 30% to Ahead. 20% of viewers respond to exactly two channels and 5% to none. What percentage of the viewers responded to all three?

There are three different cable channels namely Ahead, Luck and Bang. In a survey it was found that 85% of viewers respond to Bang, 20% to Luck, and 30% to Ahead. 20% of viewers respond to exactly two channels and 5% to none. Assuming 20% respond to Ahead and Bang and 16% respond to Bang and Luck, what is the percentage of viewers who watch only Luck?

There are three different cable channels namely Ahead, Luck and Bang. In a survey it was found that 85% of viewers respond to Bang, 20% to Luck, and 30% to Ahead. 20% of viewers respond to exactly two channels and 5% to none. In a locality, two-thirds of the people have cable-TV, one-fifth have VCR, and one-tenth have both, what is the fraction of people having either cable -TV or VCR?

A survey of 200 people in a community who watched at least one of the three channels — BBC, CNN and DD — showed that 80% of the people watched DD, 22% watched BBC, and 15% watched CNN. What is the maximum percentage of people who can watch all the three channels?

A survey of 200 people in a community who watched at least one of the three channels — BBC, CNN and DD — showed that 80% of the people watched DD, 22% watched BBC, and 15% watched CNN. If 5% of the people watched DD and CNN, 10% watched DD and BBC, then what per cent of the people watched BBC and CNN only?

A shop sells three type of products i.e. Pen, Pencil & Notebook. On a survey for checking the sales of each product of the shop he found that the no. of people who bought only pen, only pencil, & only notebook are in A.P. in no particular order. Similarly, the number of people who bought exactly two of the three products are in A.P. too.
It was also found that the no. of people who bought all the products is 1/20th of the number of people who bought pencil only which in turn is equal to half of the number of people who bought notebook only. The number of people that bought both pen & pencil is 15, whereas that of those who bought pencil & notebook is 19. The number of people who bought notebook are 120, which is more than the no. of people who bought pen (which is a 2 digit no above 50). What is the total no people that visits the shop?

In a political survey, 78% of the politicians favour at least one proposal. 50% of them are in favour of proposal A, 30% are in favour of proposal B and 20% are in favour of proposal C. 5% are in favour of all three proposals. What is the percentage of people favouring more than one proposal?

Of the 200 candidates who were interviewed for a position at a call center, 100 had a two-wheeler, 70 had a credit card and 140 had a mobile phone. 40 of them had both, a two-wheeler and a credit card, 30 had both, a credit card and a mobile phone and 60 had both, a two wheeler and mobile phone and 10 had all three. How many candidates had none of the three?

Let ‘f’ be a function from set A to set B for a set, XCB define f^–1 (X) = {x ∈ A : f(x) ∈ X}{Then which of the following is necessarily true for a subset U of X?

A and B are two sets (e.g. A = mothers, B = women). The elements that could belong to both the sets (e.g. women who are mothers) is given by the set C = A.B. The elements which could belong to either A or B, or both, is indicated by the set D = A ∪ B.
A set that does not contain any elements is known as null set, represented by ϕ (for example, if none of the women in the set B is a mother, then C = A.B. is a null set, or C = ϕ).
Let ‘V’ signify the set of all vertebrates; ‘M’ the set all mammals; ‘D’ dogs, ‘F’ fish; ‘A’ alsatian and ‘P’, a dog named Pluto. Given that X = M.D is such that X = D, which of the following is true?

A and B are two sets (e.g. A = mothers, B = women). The elements that could belong to both the sets (e.g. women who are mothers) is given by the set C = A.B. The elements which could belong to either A or B, or both, is indicated by the set D = A ∪ B.
A set that does not contain any elements is known as null set, represented by ϕ (for example, if none of the women in the set B is a mother, then C = A.B. is a null set, or C = ϕ).
Let ‘V’ signify the set of all vertebrates; ‘M’ the set all mammals; ‘D’ dogs, ‘F’ fish; ‘A’ alsatian and ‘P’, a dog named Pluto. If Y = F.(D.V), is not a null set, it implies that:

A and B are two sets (e.g. A = mothers, B = women). The elements that could belong to both the sets (e.g. women who are mothers) is given by the set C = A.B. The elements which could belong to either A or B, or both, is indicated by the set D = A ∪ B.
A set that does not contain any elements is known as null set, represented by ϕ (for example, if none of the women in the set B is a mother, then C = A.B. is a null set, or C = ϕ).
Let ‘V’ signify the set of all vertebrates; ‘M’ the set all mammals; ‘D’ dogs, ‘F’ fish; ‘A’ alsatian and ‘P’, a dog named Pluto. If Z = (P.D) ∪ M, then

A and B are two sets (e.g. A = mothers, B = women). The elements that could belong to both the sets (e.g. women who are mothers) is given by the set C = A.B. The elements which could belong to either A or B, or both, is indicated by the set D = A ∪ B.
A set that does not contain any elements is known as null set, represented by ϕ (for example, if none of the women in the set B is a mother, then C = A.B. is a null set, or C = ϕ).
Let ‘V’ signify the set of all vertebrates; ‘M’ the set all mammals; ‘D’ dogs, ‘F’ fish; ‘A’ alsatian and ‘P’, a dog named Pluto. If P.A = ϕ and P ∪ A = D, then which of the following is true?

Let T be the set of integers {3, 11, 19, 27 …..451, 459, 467} and S be a subset of T such that the sum of no two elements of S is 470. The maximum possible number of elements in S is

How many even integers n, where 100≤n≤200 , are divisible neither by seven nor by nine?

Two binary operations ⊕ and * are defined over the set {a, e, f, g, h} as per the following tables: Thus, according to the first table f ⊕ g = a, while according to the second table g*h = f, and so on. Also, let f² = f * f, g³ = g * g * g, and so on. What is the smallest positive integer n such that gⁿ = e?

Two binary operations ⊕ and * are defined over the set {a, e, f, g, h} as per the following tables: Thus, according to the first table f ⊕ g = a, while according to the second table g*h = f, and so on. Also, let f² = f * f, g³ = g * g * g, and so on. Upon simplification, f ⊕ [f * {f ⊕ (f * f)}] equals

Two binary operations ⊕ and * are defined over the set {a, e, f, g, h} as per the following tables: Thus, according to the first table f ⊕ g = a, while according to the second table g*h = f, and so on. Also, let f² = f * f, g³ = g * g * g, and so on. Upon simplification {a¹⁰ * (f¹⁰ ⊕ g⁹)} ⊕ e⁸ equals

A survey on a sample of 25 new cars being sold at a local auto dealer was conducted to see which of the three popular options — air-conditioning, radio and power windows – were already installed. The survey found
15 had air conditioning
2 had air conditioning and power windows but no radios
12 had radio
6 had air-conditioning and radio but no power windows
11 had power windows
4 had radio and power windows
3 had all three options.
What is the number of cars that had none of the options?

70 per cent of the employees in a multinational corporation have VCD players, 75 per cent have microwave ovens, 80 per cent have ACs and 85 per cent have washing machines. At least what percentage of employees has all four gadgets?

A shop sells three type of products i.e. Pen, Pencil & Notebook. On a survey for checking the sales of each product of the shop he found that the no. of people who bought only pen, only pencil, & only notebook are in A.P. in no particular order. Similarly, the number of people who bought exactly two of the three products are in A.P. too.
It was also found that the no. of people who bought all the products is 1/20th of the number of people who bought pencil only which in turn is equal to half of the number of people who bought notebook only. The number of people that bought both pen & pencil is 15, whereas that of those who bought pencil & notebook is 19. The number of people who bought notebook are 120, which is more than the no. of people who bought pen (which is a 2 digit no above 50). How many people bought both pen and notebook?

At the birthday party of Sherry, a baby boy, 40 persons chose to kiss him and 25 chose to shake hands with him. 10 persons chose to both kiss him and shake hands with him. How many persons turned out at the party?

In an examination 43% passed in Math, 52% passed in Physics and 52% passed in Chemistry. Only 8% students passed in all the three. 14% passed in Math and Physics and 21% passed in Math and Chemistry and 20% passed in Physics and Chemistry. Number of students who took the exam is 200.
Let Set P, Set C and Set M denotes the students who passed in Physics, Chemistry and Math respectively. Then How many students passed in Math only?

In an examination 43% passed in Math, 52% passed in Physics and 52% passed in Chemistry. Only 8% students passed in all the three. 14% passed in Math and Physics and 21% passed in Math and Chemistry and 20% passed in Physics and Chemistry. Number of students who took the exam is 200.
Let Set P, Set C and Set M denotes the students who passed in Physics, Chemistry and Math respectively. Then Find the ratio of students passing in Math only to the students passing in Chemistry only?

In an examination 43% passed in Math, 52% passed in Physics and 52% passed in Chemistry. Only 8% students passed in all the three. 14% passed in Math and Physics and 21% passed in Math and Chemistry and 20% passed in Physics and Chemistry. Number of students who took the exam is 200.
Let Set P, Set C and Set M denotes the students who passed in Physics, Chemistry and Math respectively. Then What is the ratio of the number of students passing in Physics only to the students passing in either Physics or Chemistry or both?

In an examination 43% passed in Math, 52% passed in Physics and 52% passed in Chemistry. Only 8% students passed in all the three. 14% passed in Math and Physics and 21% passed in Math and Chemistry and 20% passed in Physics and Chemistry. Number of students who took the exam is 200.
Let Set P, Set C and Set M denotes the students who passed in Physics, Chemistry and Math respectively. Then A student is declared pass in the exam only if he/she clears at least two subjects. The number of students who were declared passed in this exam is?

In the Mindworkzz club all the members participate either in the Tambola or the Fete. 320 participate in the Fete, 350 participate in the Tambola and 220 participate in both. How many members does the club have?

Last year, there were 3 sections in the Catalyst, a mock CAT paper. Out of them 33 students cleared the cut-off in Section 1, 34 students cleared the cut-off in Section 2 and 32 cleared the cut-off in Section 3. 10 students cleared the cut-off in Section 1 and Section 2, 9 cleared the cut-off in Section 2 and Section 3, 8 cleared the cut-off in Section 1 and Section 3. The number of people who cleared each section alone was equal and was 21 for each section. How many cleared all the three sections?

Last year, there were 3 sections in the Catalyst, a mock CAT paper. Out of them 33 students cleared the cut-off in Section 1, 34 students cleared the cut-off in Section 2 and 32 cleared the cut-off in Section 3. 10 students cleared the cut-off in Section 1 and Section 2, 9 cleared the cut-off in Section 2 and Section 3, 8 cleared the cut-off in Section 1 and Section 3. The number of people who cleared each section alone was equal and was 21 for each section. How many cleared only one of the three sections?

Last year, there were 3 sections in the Catalyst, a mock CAT paper. Out of them 33 students cleared the cut-off in Section 1, 34 students cleared the cut-off in Section 2 and 32 cleared the cut-off in Section 3. 10 students cleared the cut-off in Section 1 and Section 2, 9 cleared the cut-off in Section 2 and Section 3, 8 cleared the cut-off in Section 1 and Section 3. The number of people who cleared each section alone was equal and was 21 for each section. The ratio of the number of students clearing the cut-off in one or more of the sections to the number of students clearing the cutoff in Section 1 alone is?

In the Indian athletic squad sent to the Olympics, 21 athletes were in the triathlon team; 26 were in the pentathlon team; and 29 were in the marathon team. 14 athletes can take part in triathlon and pentathlon; 12 can take part in marathon and triathlon; 15 can take part in pentathlon and marathon; and 8 can take part in all the three games. How many players are there in all?

In the Indian athletic squad sent to the Olympics, 21 athletes were in the triathlon team; 26 were in the pentathlon team; and 29 were in the marathon team. 14 athletes can take part in triathlon and pentathlon; 12 can take part in marathon and triathlon; 15 can take part in pentathlon and marathon; and 8 can take part in all the three games. How many were in the marathon team only?

In a test in which 120 students appeared, 90 passed in History, 65 passed in Sociology and 75 passed in Political Science. 30 students passed in only one subject and 55 students in only two. 5 students passed no subjects. How many students passed in all the three subjects?

In a test in which 120 students appeared, 90 passed in History, 65 passed in Sociology and 75 passed in Political Science. 30 students passed in only one subject and 55 students in only two. 5 students passed no subjects. Find the number of students who passed in at least two subjects.

5% of the passengers who boarded Guwahati- New Delhi Rajdhani Express on 20th February, 2002 do not like coffee, tea and ice cream and 10% like all the three. 20% like coffee and tea, 25% like ice cream and coffee and 25% like ice cream and tea. 55% like coffee, 50% like tea and 50% like ice cream. The number of passengers who like only coffee is greater than the passengers who like only ice cream by

5% of the passengers who boarded Guwahati- New Delhi Rajdhani Express on 20th February, 2002 do not like coffee, tea and ice cream and 10% like all the three. 20% like coffee and tea, 25% like ice cream and coffee and 25% like ice cream and tea. 55% like coffee, 50% like tea and 50% like ice cream. The percentage of passengers who like both tea and ice cream but not coffee is

5% of the passengers who boarded Guwahati- New Delhi Rajdhani Express on 20th February, 2002 do not like coffee, tea and ice cream and 10% like all the three. 20% like coffee and tea, 25% like ice cream and coffee and 25% like ice cream and tea. 55% like coffee, 50% like tea and 50% like ice cream. The percentage of passengers who like at least 2 of the 3 products is

5% of the passengers who boarded Guwahati- New Delhi Rajdhani Express on 20th February, 2002 do not like coffee, tea and ice cream and 10% like all the three. 20% like coffee and tea, 25% like ice cream and coffee and 25% like ice cream and tea. 55% like coffee, 50% like tea and 50% like ice cream. If the number of passengers is 180, then the number of passengers who like ice cream only is

In a survey among students at all the IIMs, it was found that 48% preferred coffee, 54% liked tea and 64% smoked. Of the total, 28% liked coffee and tea, 32% smoked and drank tea and 30% smoked and drank coffee. Only 6% did none of these. If the total number of students is 2000 then find The ratio of the number of students who like only coffee to the number who like only tea is

In a survey among students at all the IIMs, it was found that 48% preferred coffee, 54% liked tea and 64% smoked. Of the total, 28% liked coffee and tea, 32% smoked and drank tea and 30% smoked and drank coffee. Only 6% did none of these. If the total number of students is 2000 then find Number of students who like coffee and smoking but not tea is

In a survey among students at all the IIMs, it was found that 48% preferred coffee, 54% liked tea and 64% smoked. Of the total, 28% liked coffee and tea, 32% smoked and drank tea and 30% smoked and drank coffee. Only 6% did none of these. If the total number of students is 2000 then find The percentage of those who like coffee or tea but not smoking among those who like at least one of these is

In a survey among students at all the IIMs, it was found that 48% preferred coffee, 54% liked tea and 64% smoked. Of the total, 28% liked coffee and tea, 32% smoked and drank tea and 30% smoked and drank coffee. Only 6% did none of these. If the total number of students is 2000 then find The percentage of those who like at least one of these is

In a survey among students at all the IIMs, it was found that 48% preferred coffee, 54% liked tea and 64% smoked. Of the total, 28% liked coffee and tea, 32% smoked and drank tea and 30% smoked and drank coffee. Only 6% did none of these. If the total number of students is 2000 then find The two items having the ratio 1:2 are

In a survey among students at all the IIMs, it was found that 48% preferred coffee, 54% liked tea and 64% smoked. Of the total, 28% liked coffee and tea, 32% smoked and drank tea and 30% smoked and drank coffee. Only 6% did none of these. If the total number of students is 2000 then find The number of persons who like coffee and smoking only and the number who like tea only bear a ratio

In a survey among students at all the IIMs, it was found that 48% preferred coffee, 54% liked tea and 64% smoked. Of the total, 28% liked coffee and tea, 32% smoked and drank tea and 30% smoked and drank coffee. Only 6% did none of these. If the total number of students is 2000 then find Percentage of those who like tea and smoking but not coffee is

30 monkeys went to a picnic. 25 monkeys chose to irritate cows while 20 chose to irritate buffaloes. How many chose to irritate both buffaloes and cows?

In the CBSE Board Exams last year, 53% passed in Biology, 61% passed in English, 60% in Social Studies, 24% in Biology & English, 35% in English & Social Studies, 27% in Biology and Social Studies and 5% in none. Percentage of passes in all subjects is

Set P comprises all multiples of 4 less than 500. Set Q comprises all odd multiples of 7 less than 500, Set R comprises all multiples of 6 less than 500. How many
elements are present in P U Q U R?

In the CBSE Board Exams last year, 53% passed in Biology, 61% passed in English, 60% in Social Studies, 24% in Biology & English, 35% in English & Social Studies, 27% in Biology and Social Studies and 5% in none. If the number of students in the class is 300, what will be the% change in the number of passes in only two subjects, if the original number of students is 200?

In the CBSE Board Exams last year, 53% passed in Biology, 61% passed in English, 60% in Social Studies, 24% in Biology & English, 35% in English & Social Studies, 27% in Biology and Social Studies and 5% in none. What is the ratio of percentage of passes in Biology and Social Studies but not English in relation to the percentage of passes in Social Studies and English but not Biology?

How many of the following statements have to be true?
I)No year can have 5 Sundays in the month of May and 5 Thursdays in the month of June.
II)If Fb 14 of a certain year is a Friday, May 14 of the same year cannot be a Thursday
iii. If a year has 53 Sundays, it can have 5 Mondays in the month of May.

In the Quiz held last year, participants were free to choose their respective areas from which they were asked questions. Out of 880 participants, 224 chose Mythology, 240 chose Science and 336 chose Sports, 64 chose both Sports and Science, 80 chose Mythology and Sports, 40 chose Mythology and Science and 24 chose all the three areas. Of those participating, the percentage who choose only one area is

In the Quiz held last year, participants were free to choose their respective areas from which they were asked questions. Out of 880 participants, 224 chose Mythology, 240 chose Science and 336 chose Sports, 64 chose both Sports and Science, 80 chose Mythology and Sports, 40 chose Mythology and Science and 24 chose all the three areas. Number of participants who chose at least two areas is

In the Quiz held last year, participants were free to choose their respective areas from which they were asked questions. Out of 880 participants, 224 chose Mythology, 240 chose Science and 336 chose Sports, 64 chose both Sports and Science, 80 chose Mythology and Sports, 40 chose Mythology and Science and 24 chose all the three areas. Which of the following areas shows a ratio of 1:8?

In the Quiz held last year, participants were free to choose their respective areas from which they were asked questions. Out of 880 participants, 224 chose Mythology, 240 chose Science and 336 chose Sports, 64 chose both Sports and Science, 80 chose Mythology and Sports, 40 chose Mythology and Science and 24 chose all the three areas. The ratio of students choosing Sports & Science but not Mythology to Science but not Mythology & Sports is

The table here gives the distribution of students according to professional courses. What is the percentage of Math students over English students?

The table here gives the distribution of students according to professional courses. The average number of females in all the courses is (count people doing full-time MBA and CA as a separate course)

The table here gives the distribution of students according to professional courses. The ratio of the number of girls to the number of boys is

The table here gives the distribution of students according to professional courses. The percentage increase in students of full-time MBA only over CA only is

The table here gives the distribution of students according to professional courses. The number of students doing full-time MBA or CA is

A newspaper agent sells The TOI, HT and IN in equal numbers to 302 persons. Seven get HT & IN, twelve get The TOI & IN, nine get The TOI & HT and three get all the three newspapers. The details are given in the Venn diagram: How many get only one paper?

A newspaper agent sells The TOI, HT and IN in equal numbers to 302 persons. Seven get HT & IN, twelve get The TOI & IN, nine get The TOI & HT and three get all the three newspapers. The details are given in the Venn diagram: What percent get The TOI and The HT but not The IN

A newspaper agent sells The TOI, HT and IN in equal numbers to 302 persons. Seven get HT & IN, twelve get The TOI & IN, nine get The TOI & HT and three get all the three newspapers. The details are given in the Venn diagram: The number of persons buying The TOI and The HT only, The TOI and The IN only and The HT and The IN only are in the ratio of

A newspaper agent sells The TOI, HT and IN in equal numbers to 302 persons. Seven get HT & IN, twelve get The TOI & IN, nine get The TOI & HT and three get all the three newspapers. The details are given in the Venn diagram: The difference between the number reading The HT and The IN only and HT only is

A group of 78 people watch Zee TV, Star Plus or Sony. Of these, 36 watch Zee TV, 48 watch Star Plus and 32 watch Sony. If 14 people watch both Zee TV and Star Plus, 20 people watch both Star Plus and Sony, and 12 people watch both Sony and Zee TV find the ratio of the number of people who watch only Zee TV to the number of people who watch only Sony.

The following data was observed from a study of car complaints received from 180 respondents at Colonel Verma’s car care workshop, viz., engine problem, transmission problem or mileage problem. Of those surveyed, there was no one who faced exactly two of these problems. There were 90 respondents who faced engine problems, 120 who faced transmission problems and 150 who faced mileage problems. How many of them faced all the three problems?

The following data was observed from a study of car complaints received from 180 respondents at Colonel Verma’s car care workshop, viz., engine problem, transmission problem or mileage problem. Of those surveyed, there was no one who faced exactly two of these problems. There were 90 respondents who faced engine problems, 120 who faced transmission problems and 150 who faced mileage problems. How many of them faced either transmission problems or engine problems?

At the Rosary Public School, there are 870 students in the senior secondary classes. The school is widely known for its science education and there is the facility for students to do practical training in any of the 4 sciences – viz: Physics, Chemistry, Biology or Social Sciences. Some students in the school however have no interest in the sciences and hence do not undertake practical training in any of the four sciences. While considering the popularity of various choices for opting for practical training for one or more of the choices offered, Mr. Arvindaksham, the school principal noticed something quite extraordinary. He noticed that for every student in the school who opts for practical training in at least M sciences, there are exactly three students who opt for practical training in at least (M – 1) sciences, for M = 2, 3 and 4. He also found that the number of students who opt for all four sciences was half the number of students who opt for none. Can you help him with the answer to “How many students in the school opt for exactly three sciences?”

A bakery sells three kinds of pastries—pineappple, chocolate and black forest. On a particular day, the bakery owner sold the following number of pastries: 90 pineapple, 120 chocolate and 150 black forest. If none of the customers bought more than two pastries of each type, what is the minimum number of customers that must have visited the bakery that day?

Gauri Apartment housing society organised annual games, consisting of three games – viz: snooker, badminton and tennis. In all, 510 people were members in the apartments’ society and they were invited to participate in the games — each person participating in as many games as he/she feels like. While viewing the statistics of the performance. Mr Capoor realised the following acts. The number of people who participated in at least two games was 52% more than those who participated in exactly one game. The number of people participating in 1, 2 or 3 games respectively was at least equal to 1. Being a numerically inclined person, he further noticed an interesting thing — the number of people who did not participate in any of the three games was the minimum possible integral value with these conditions. What was the maximum number of people who participated in exactly three games?

A school has 180 students in its senior section where foreign languages are offered to students as part of their syllabus. The foreign languages offered are: French, German and Chinese and the numbers of people studying each of these subjects are 80, 90 and 100 respectively. The number of students who study more than one of the three subjects is 50% more than the number of students who study all the three subjects. There are no students in the school who study none of the three subjects. Then how many students study all three foreign languages?

In the second year, the Hampard Business School students are offered a choice of the specialisations they wish to study from amongst only three specialisations —Marketing, Finance and HR. The number of students who have specialised in only Marketing, only Finance and only HR are all numbers in an Arithmetic Progression— in no particular order. Similarly, the number of students specialising in exactly two of the three types of subjects are also numbers that form an Arithmetic Progression.
The number of students specialising in all three subjects is one-twentieth of the number of students specialising in only Finance which in turn is half of the number of students studying only HR. The number of students studying both Marketing and Finance is 15, whereas the number of students studying both Finance and HR is 19. The number of students studying HR is 120, which is more than the number of students studying Marketing (which is a 2 digit number above 50). It is known that there are exactly 4 students who opt for none of these specialisations and opt only for general subjects. What is the total number of students in the batch?

In the second year, the Hampard Business School students are offered a choice of the specialisations they wish to study from amongst only three specialisations —Marketing, Finance and HR. The number of students who have specialised in only Marketing, only Finance and only HR are all numbers in an Arithmetic Progression— in no particular order. Similarly, the number of students specialising in exactly two of the three types of subjects are also numbers that form an Arithmetic Progression.
The number of students specialising in all three subjects is one-twentieth of the number of students specialising in only Finance which in turn is half of the number of students studying only HR. The number of students studying both Marketing and Finance is 15, whereas the number of students studying both Finance and HR is 19. The number of students studying HR is 120, which is more than the number of students studying Marketing (which is a 2 digit number above 50). It is known that there are exactly 4 students who opt for none of these specialisations and opt only for general subjects. What is the number of students specialising in both Marketing and HR?

In the Pattbhiraman family, a clan of 192 individuals, each person has at least one of the three Pattabhiraman characteristics—Blue eyes, Blonde hair, and sharp mind.
It is also known that:
(i) The number of family members who have only blue eyes is equal to the number of family members who have only sharp minds and this number is also equal to twice the number of family members who have blue eyes and sharp minds but not blonde hair.
(ii) The number of family members who have exactly two of the three features is 50.
(iii) The number of family members who have blonde hair is 62.
(iv) Among those who have blonde hair, 26 family members have at least two of the three characteristics. If the number of family members who have blue eyes is the maximum amongst the three characteristics, then what is the maximum possible number of family members who have both sharp minds and blonde hair but do not have blue eyes?

In the Pattbhiraman family, a clan of 192 individuals, each person has at least one of the three Pattabhiraman characteristics—Blue eyes, Blonde hair, and sharp mind.
It is also known that:
(i) The number of family members who have only blue eyes is equal to the number of family members who have only sharp minds and this number is also equal to twice the number of family members who have blue eyes and sharp minds but not blonde hair.
(ii) The number of family members who have exactly two of the three features is 50.
(iii) The number of family members who have blonde hair is 62.
(iv) Among those who have blonde hair, 26 family members have at least two of the three characteristics. Which additional piece of information is required to find the exact number of family members who have blonde hair and blue eyes but not sharp minds?

In a class of 97 students, each student plays at least one of the three games – Hockey, Cricket and Football. If 47 play Hockey, 53 play Cricket, 72 play Football and 15 play all the three games, what is the number of students who play exactly two games?

In a referendum about three proposals, 78% of the people were against at least one of the proposals, 50% of the people were against 1st proposal, 30% of the people were against 2nd proposal, and 20% of the people were against 3rd proposal. If 5% of the people were against all the three proposals, what percentage of people were against more than one of the three proposals?

In a recent survey conducted by Cable TV Association among the people who watch DD, Zee, and Star TV, it is found that 80% of the people watched DD, 22% watched Star TV, and 15% watched Zee. What is the maximum percentage of people who can watch all the three channels?

Eighty thousand students appeared in the last year’s CAT consisting of three sections QA, DI, and EU. Twenty-four thousand students passed in QA; 31,000 students passed in DI; 35,000 students passed in EU. Further, 49,000 students passed in at least one of QA and DI; 59,000 students passed in at least one of DI and EU; 54,000 students passed in at least one of QA and EU. Calls for IIMs are sent to only those students who passed in all the three sections in CAT. If only 2000 students got the IIM calls, then what is the number of students who failed in all the three papers (either you can pass or fail)?

Consider a universal set U = {1, 2, 3, 4…..10}
Set P = {x | x is a prime number}
Set (E) = {2, 4, 6, 8, 10}
Set (O) = { 1, 3, 5, 7, 9}
Set (C) = {x | x is a composite number} How many elements does P’ or Pc has, or find
n(P’)

Consider a universal set U = {1, 2, 3, 4…..10}
Set P = {x | x is a prime number}
Set (E) = {2, 4, 6, 8, 10}
Set (O) = { 1, 3, 5, 7, 9}
Set (C) = {x | x is a composite number} Find the number of elements in E – C,

Consider a universal set U = {1, 2, 3, 4…..10}
Set P = {x | x is a prime number}
Set (E) = {2, 4, 6, 8, 10}
Set (O) = { 1, 3, 5, 7, 9}
Set (C) = {x | x is a composite number} Find the number of elements in P U O

Consider a universal set U = {1, 2, 3, 4…..10}
Set P = {x | x is a prime number}
Set (E) = {2, 4, 6, 8, 10}
Set (O) = { 1, 3, 5, 7, 9}
Set (C) = {x | x is a composite number} Find the number of elements in P n O

Consider a universal set U = {1, 2, 3, 4…..10}
Set P = {x | x is a prime number}
Set (E) = {2, 4, 6, 8, 10}
Set (O) = { 1, 3, 5, 7, 9}
Set (C) = {x | x is a composite number} Find the number of elements in power set of set E

If in Praxis Business school 40 students like chocolate while 30 like cake, if there are 10 students
who like both and an equal number of students who like none of them. Find the total number of students at Praxis Business School.

If in Praxis Business school 40 students like chocolate while 30 like cake, if there are 10 students
who like both and an equal number of students who like none of them. What percentage of students do not like cake?

If in Praxis Business school 40 students like chocolate while 30 like cake, if there are 10 students
who like both and an equal number of students who like none of them. A dinner party is to be f xed for a group of
100 persons. In this party, 50 persons do not
prefer fish, 60 prefer chicken and 10 do not
prefer either chicken or fish. The number of
persons who prefer both fish and chicken is.

If in Praxis Business school 40 students like chocolate while 30 like cake, if there are 10 students
who like both and an equal number of students who like none of them. In an examination, 62% of the candidates failed in English, 42% in Mathematics and
20% in both. The number of those who passed in both the subjects is.

If in Praxis Business school 40 students like chocolate while 30 like cake, if there are 10 students
who like both and an equal number of students who like none of them. In a market research project, 20% opted for ‘Nirma’ detergent whereas 60% opted for ‘Surf blue’ detergent. The remaining individuals were not certain. If the difference between those who opted for ‘Surf blue’ and those who were uncertain was 720, how many respondents were covered in the survey

If in Praxis Business school 40 students like chocolate while 30 like cake, if there are 10 students
who like both and an equal number of students who like none of them. If X and Y are two sets such that (X È Y) has 60 elements, X has 38 elements and Y has 42
elements, how many elements does (X Ç Y) have?

If in Praxis Business school 40 students like chocolate while 30 like cake, if there are 10 students
who like both and an equal number of students who like none of them. In a B School there are 15 teachers who teach
marketing or finance. Of these, 8 teach finance
and 4 teach both marketing and finance. How
many teach marketing but not finance?

If in Praxis Business school 40 students like chocolate while 30 like cake, if there are 10 students
who like both and an equal number of students who like none of them. In a school 50 students play cricket, 70 play football while 30 play none of the games, If
total number of students are 100 then how many of them Play only cricket

In a school 80 students like chocolate, 40 like coffee if the number of students doesn’t like any of them is equal to the number of students who like both of them then what is
the total number of students in the school?

If in Praxis Business school 40 students like chocolate while 30 like cake, if there are 10 students
who like both and an equal number of students who like none of them. There are 200 students in a B school, 120 have been taken in project of finance, 50 in project of marketing and 30 in both the marketing and finance. Find the number of students
worked on marketing but not on finance

If in Praxis Business school 40 students like chocolate while 30 like cake, if there are 10 students
who like both and an equal number of students who like none of them. In a school there are 100 students 60 of them don’t like Chocolate and 50 don’t like Biscuit
and 10 of them like none then how many of them like both?

An Airline Company has divided the potential market into three categories through a market
survey for the purpose of implementing a Customer Relationship Management Programme. The
rectangle given in the diagram below represents Economy Class passengers. The circle represents
working Executives and the triangle represents the Indians. A signature hotel is launching a service for Executives who travel Economy Class but
are not Indians. Which segments should it concentrate in the diagram above?

An Airline Company has divided the potential market into three categories through a market
survey for the purpose of implementing a Customer Relationship Management Programme. The
rectangle given in the diagram below represents Economy Class passengers. The circle represents
working Executives and the triangle represents the Indians. A travel agency wishes to target passengers who are Executives and travel by Economy

Class. Which segments in the diagram should it aim?

An Airline Company has divided the potential market into three categories through a market
survey for the purpose of implementing a Customer Relationship Management Programme. The
rectangle given in the diagram below represents Economy Class passengers. The circle represents
working Executives and the triangle represents the Indians. The Airline Company wishes to target Economy Class, non-Executive passengers
for In-flight Duty Free Shopping. Which area must it focus on?

In the diagram below, the circle stands for educated‘, square stands for hard working‘, triangle for urban

people ‘and rectangle for honest‘. The different regions of the diagram are numbered from 1 to 12. Study the

diagram carefully and answer the questions: Uneducated urban hard-working an honest people are indicated by:

In the diagram below, the circle stands for educated‘, square stands for hard working‘, triangle for urban

people ‘and rectangle for honest‘. The different regions of the diagram are numbered from 1 to 12. Study the

diagram carefully and answer the questions: Non-urban educated people who are neither hard-working nor honest are indicated by:

The Venn diagram given below shows the estimated readership of 3 daily newspapers (X, Y & Z) in a city. The total readership and advertising cost
for eac h of th e papers is as below : The total population of the city is estimated to be 14 million. The common readership (in lakhs) is
indicated I the given Venn diagram. The number of people (in Lakhs) who read at least one newspaper is

A survey was conducted of 100 people whether
they have read recent issues of ‘Golmal’, a monthly
magazine. Summarized in formation is presented
below:
Only September:18
September but not August: 23
September and July: 8
September: 28
July: 48
July and August: 10
None of the three months: 24 What is the number of surveyed people who have read exactly for two consecutive
months?

A survey was conducted of 100 people whether
they have read recent issues of ‘Golmal’, a monthly
magazine. Summarized in formation is presented
below:
Only September:18
September but not August: 23
September and July: 8
September: 28
July: 48
July and August: 10
None of the three months: 24 In 2002, according to a news poll, 36% of the voters had leaning towards party “Y”. In 2004, this gure rose to 46%. But in another survey the percentage was down to 40%. Therefore, the party “Z” is likely to win the next election. Which of the following, if true, would seriously weaken the above conclusion?

TT School of Management is a management
institute involved in teaching, training and
research. Currently it has 37 faculty members.
They are involved in three jobs: teaching, training
and research. Each faculty member working with
TT School of Management has to be involved in
atleast one of the three jobs mentioned above:
A maximum number of faculty members are
involved in training. Among them, a number
of faculty members are having additional
involvement in the research. The number of faculty members in research
alone is double the number of faculty members
involved in all the three jobs. The number of faculty members involved in
teaching alone is less than the number of
faculty members involved in research alone. Ten faculty member involved in the teaching
are also involved in at least one more job. After some time, the faculty members who were involved in all the three tasks were
asked to withdraw from one task. As a result, one of the faculty member each opted out of teaching and research, while remaining ones involved in all the three tasks opted out of training. Which one of the following statements, then necessarily follows:

TT School of Management is a management
institute involved in teaching, training and
research. Currently it has 37 faculty members.
They are involved in three jobs: teaching, training
and research. Each faculty member working with
TT School of Management has to be involved in
atleast one of the three jobs mentioned above:
A maximum number of faculty members are
involved in training. Among them, a number
of faculty members are having additional
involvement in the research. The number of faculty members in research
alone is double the number of faculty members
involved in all the three jobs. The number of faculty members involved in
teaching alone is less than the number of
faculty members involved in research alone. Ten faculty member involved in the teaching
are also involved in at least one more job. Based on the information given above, the minimum number of faculty members
involved in both training and teaching, but not in research is:

TT School of Management is a management
institute involved in teaching, training and
research. Currently it has 37 faculty members.
They are involved in three jobs: teaching, training
and research. Each faculty member working with
TT School of Management has to be involved in
atleast one of the three jobs mentioned above:
A maximum number of faculty members are
involved in training. Among them, a number
of faculty members are having additional
involvement in the research. The number of faculty members in research
alone is double the number of faculty members
involved in all the three jobs. The number of faculty members involved in
teaching alone is less than the number of
faculty members involved in research alone. Ten faculty member involved in the teaching
are also involved in at least one more job. A survey shows that 61 %, 46% and 29% of the people watched “3 idiots”, “Rajneeti” and “Avatar” respectively. 25% people watched exactly two of the three movies and 3% watched none. What percentage of people watched all the three movies?

A professor keeps data on students tabulated by
performance and sex of the student. The data is
kept on a computer disk, but unfortunately some
of it is lost because of a virus. Only the following
could be recovered: Panic buttons were pressed but to no avail. An
expert committee was formed, which decided
that the following facts were self-evident: Half
the students were either excellent or good. 40% of
the students were females. One third of the male
students were average. How many students are both female and excellent?

A professor keeps data on students tabulated by
performance and sex of the student. The data is
kept on a computer disk, but unfortunately some
of it is lost because of a virus. Only the following
could be recovered: Panic buttons were pressed but to no avail. An
expert committee was formed, which decided
that the following facts were self-evident: Half
the students were either excellent or good. 40% of
the students were females. One third of the male
students were average. What proportion of good students are male?

A professor keeps data on students tabulated by
performance and sex of the student. The data is
kept on a computer disk, but unfortunately some
of it is lost because of a virus. Only the following
could be recovered: Panic buttons were pressed but to no avail. An
expert committee was formed, which decided
that the following facts were self-evident: Half
the students were either excellent or good. 40% of
the students were females. One third of the male
students were average. What proportion of female students are good?

A professor keeps data on students tabulated by
performance and sex of the student. The data is
kept on a computer disk, but unfortunately some
of it is lost because of a virus. Only the following
could be recovered: Panic buttons were pressed but to no avail. An
expert committee was formed, which decided
that the following facts were self-evident: Half
the students were either excellent or good. 40% of
the students were females. One third of the male
students were average. How many students are both male and good?

A professor keeps data on students tabulated by
performance and sex of the student. The data is
kept on a computer disk, but unfortunately some
of it is lost because of a virus. Only the following
could be recovered: Panic buttons were pressed but to no avail. An
expert committee was formed, which decided
that the following facts were self-evident: Half
the students were either excellent or good. 40% of
the students were females. One third of the male
students were average. Among average students, what is the ratio of male to female?

New Age Consultants have three consultants
Gyani, Medha and Buddhi, The sum of the
number of projects handled by Gyani and Buddhi
individually is equal to the number of projects in
which Medha is involved. All three consultants are
involved together in 6 projects. Gyani works with
Medha in 14 projects. Buddhi has 2 projects with
Medha but without Gyani, and 3 projects with
Gyani but without Medha. The total number of
projects for New Age Consultants is one less than
twice the number of projects in which more than
one consultant is involved. What is the number of projects in which Gyani alone is involved?

Help Distress (HD) is an NGO involved in providing
assistance to people suffering from natural
disasters. Currently, it has 37 volunteers. They
are involved in three projects: Tsunami Relief (TR)
in Tamil Nadu, Flood Relief (FR) in Maharashtra,
and Earthquake (ER) in Gujarat. Each volunteer
working with Help Distress has to be involved in
at least one relief work project.
A Maximum number of volunteers are involved
in the FR project. Among them, the number of
volunteers involved in FR project alone is equal to
the volunteers having additional involvement in
the ER project.
The number of volunteers involved in the ER
project alone is double the number of volunteers
involved in all the three projects.
17 volunteers are involved in the TR project.
The number of volunteers involved in the TR project
alone is one less than the number of volunteers
involved in ER project alone.
Ten volunteers involved in the TR project are also
involved in at least one more project.
[ Based on the information given above, the minimum number of volunteers involved in
both FR and TR projects, but not in the ER project is:

Help Distress (HD) is an NGO involved in providing
assistance to people suffering from natural
disasters. Currently, it has 37 volunteers. They
are involved in three projects: Tsunami Relief (TR)
in Tamil Nadu, Flood Relief (FR) in Maharashtra,
and Earthquake (ER) in Gujarat. Each volunteer
working with Help Distress has to be involved in
at least one relief work project.
A Maximum number of volunteers are involved
in the FR project. Among them, the number of
volunteers involved in FR project alone is equal to
the volunteers having additional involvement in
the ER project.
The number of volunteers involved in the ER
project alone is double the number of volunteers
involved in all the three projects.
17 volunteers are involved in the TR project.
The number of volunteers involved in the TR project
alone is one less than the number of volunteers
involved in ER project alone.
Ten volunteers involved in the TR project are also
involved in at least one more project.
[ Which of the following additional information would enable to find the exact number of
volunteers involved in various projects?

Help Distress (HD) is an NGO involved in providing
assistance to people suffering from natural
disasters. Currently, it has 37 volunteers. They
are involved in three projects: Tsunami Relief (TR)
in Tamil Nadu, Flood Relief (FR) in Maharashtra,
and Earthquake (ER) in Gujarat. Each volunteer
working with Help Distress has to be involved in
at least one relief work project.
A Maximum number of volunteers are involved
in the FR project. Among them, the number of
volunteers involved in FR project alone is equal to
the volunteers having additional involvement in
the ER project.
The number of volunteers involved in the ER
project alone is double the number of volunteers
involved in all the three projects.
17 volunteers are involved in the TR project.
The number of volunteers involved in the TR project
alone is one less than the number of volunteers
involved in ER project alone.
Ten volunteers involved in the TR project are also
involved in at least one more project.
After some time, the volunteers who were involved in all the three projects were asked
to withdraw from one project. As a result, one of the volunteers opted out of the TR project, and one opted out of the ER project, while the remaining ones involved in all the three projects opted out of the FR project. Which of the following statements, then, necessarily follows?

Help Distress (HD) is an NGO involved in providing
assistance to people suffering from natural
disasters. Currently, it has 37 volunteers. They
are involved in three projects: Tsunami Relief (TR)
in Tamil Nadu, Flood Relief (FR) in Maharashtra,
and Earthquake (ER) in Gujarat. Each volunteer
working with Help Distress has to be involved in
at least one relief work project.
A Maximum number of volunteers are involved
in the FR project. Among them, the number of
volunteers involved in FR project alone is equal to
the volunteers having additional involvement in
the ER project.
The number of volunteers involved in the ER
project alone is double the number of volunteers
involved in all the three projects.
17 volunteers are involved in the TR project.
The number of volunteers involved in the TR project
alone is one less than the number of volunteers
involved in ER project alone.
Ten volunteers involved in the TR project are also
involved in at least one more project.
After the withdrawal of volunteers, as indicated in Question 42, some new
volunteers joined the NGO. Each one of them was allotted only one project in a manner
such that, the number of volunteers working in one project alone for each of the three
projects became identical. At that point, it was also found that the number of volunteers
involved in FR and ER projects was the same as the number of volunteers involved in TR
and ER projects. Which of the projects now has the highest number of volunteers?

The proportion of male students and the proportion of
vegetarian students in a school are given below. The school
has a total of 800 students, 80% of whom are in the Secondary
Section and rest equally divided between Class 11 and 12. What is the percentage of vegetarian students in Class 12?

The proportion of male students and the proportion of
vegetarian students in a school are given below. The school
has a total of 800 students, 80% of whom are in the Secondary
Section and rest equally divided between Class 11 and 12. In Class 12, twenty five per cent of vegetarians are male. What is the difference between the
number of female vegetarians and male non vegetarians?

The proportion of male students and the proportion of
vegetarian students in a school are given below. The school
has a total of 800 students, 80% of whom are in the Secondary
Section and rest equally divided between Class 11 and 12. What is the percentage of male students in the secondary section?

The proportion of male students and the proportion of
vegetarian students in a school are given below. The school
has a total of 800 students, 80% of whom are in the Secondary
Section and rest equally divided between Class 11 and 12. In the Secondary Section, 50 % of the students are vegetarian males. Which of the following
statements is correct?

In Praxis Business School Kolkata 60 1st year students participated either in Marketing quiz
(MQ) or in Finance quiz (FQ) some information is as follows-
No girl student participated in both MQ and FQ
40 % students are girls out of which 75% has work
experience.
60 % students have work experience of which one
third participated in only MQ.
The number of boys students with work experience
participated in only MQ is 8.
8 number of girl students participated in only MQ
12 fresher students (without work experience)
participated in only FQ. What is the maximum percentage of boys participated in only FQ?

In Praxis Business School Kolkata 60 1st year students participated either in Marketing quiz
(MQ) or in Finance quiz (FQ) some information is as follows-
No girl student participated in both MQ and FQ
40 % students are girls out of which 75% has work
experience.
60 % students have work experience of which one
third participated in only MQ.
The number of boys students with work experience
participated in only MQ is 8.
8 number of girl students participated in only MQ
12 fresher students (without work experience)
participated in only FQ. If K is the ratio of students participated in only MQ to that participated in only FQ then
find the range of K

In Praxis Business School Kolkata 60 1st year students participated either in Marketing quiz
(MQ) or in Finance quiz (FQ) some information is as follows-
No girl student participated in both MQ and FQ
40 % students are girls out of which 75% has work
experience.
60 % students have work experience of which one
third participated in only MQ.
The number of boys students with work experience
participated in only MQ is 8.
8 number of girl students participated in only MQ
12 fresher students (without work experience)
participated in only FQ. Find the minimum and maximum number of students who participated in only MQ.

In Praxis Business School Kolkata 60 1st year students participated either in Marketing quiz
(MQ) or in Finance quiz (FQ) some information is as follows-
No girl student participated in both MQ and FQ
40 % students are girls out of which 75% has work
experience.
60 % students have work experience of which one
third participated in only MQ.
The number of boys students with work experience
participated in only MQ is 8.
8 number of girl students participated in only MQ
12 fresher students (without work experience)
participated in only FQ. What could be the number of fresher boys participated only in FQ

In Praxis Business School Kolkata 60 1st year students participated either in Marketing quiz
(MQ) or in Finance quiz (FQ) some information is as follows-
No girl student participated in both MQ and FQ
40 % students are girls out of which 75% has work
experience.
60 % students have work experience of which one
third participated in only MQ.
The number of boys students with work experience
participated in only MQ is 8.
8 number of girl students participated in only MQ
12 fresher students (without work experience)
participated in only FQ. What could be the ratio of number of boys with work experience to the number of girls
without work experience participated in only FQ?

In a society 60 family read Times Of India (TOI), 70
read Hindustan Times HT), and 40 read Telegraph
(Tel). 10 family read both HT and Tel but not TOI,
18 family read HT & TOI, number of family who
read only TOI & Tel but not HT is 10 less than
the number of family who read all the three news
paper. What could be the total number of family in the society assuming that each family read
at least one news paper?

In a society 60 family read Times Of India (TOI), 70
read Hindustan Times HT), and 40 read Telegraph
(Tel). 10 family read both HT and Tel but not TOI,
18 family read HT & TOI, number of family who
read only TOI & Tel but not HT is 10 less than
the number of family who read all the three news
paper. If number of family who read both TOI and HT but not Tel is more than the number of family who read both TOI and Tel but not HT then what could be the number of family who read only Tel?

In a society 60 family read Times Of India (TOI), 70
read Hindustan Times HT), and 40 read Telegraph
(Tel). 10 family read both HT and Tel but not TOI,
18 family read HT & TOI, number of family who
read only TOI & Tel but not HT is 10 less than
the number of family who read all the three news
paper. If on a particular day HT was not available
so those who read only HT shifted to either
TOI or Tel such that number of family who
read only TOI and only Tel, become equal
then find the ratio of number of families who
shifted to TOI to the number of family who
shifted to Tel.

In a society 60 family read Times Of India (TOI), 70
read Hindustan Times HT), and 40 read Telegraph
(Tel). 10 family read both HT and Tel but not TOI,
18 family read HT & TOI, number of family who
read only TOI & Tel but not HT is 10 less than
the number of family who read all the three news
paper. If T, H and L is the number of family who read only TOI, HT and Tel respectively then which
one of the following is correct relation

In a society 60 family read Times Of India (TOI), 70
read Hindustan Times HT), and 40 read Telegraph
(Tel). 10 family read both HT and Tel but not TOI,
18 family read HT & TOI, number of family who
read only TOI & Tel but not HT is 10 less than
the number of family who read all the three news
paper. If P is the number of family who read exactly two news paper then which of the following
is true about P.

In Praxis Business School Kolkata, 8 friends A, B,
C, D, E, F, G & H have interest in one or more of
the three subjects Marketing, Finance and HR. No
two students like the same set of subjects. Further
known facts are as follows –
A like all the three subjects.
Pair of students (B, C) , (D, E) (G- H) (B, D) and (F,
G) have no common subjects i.e B and C have not
common subjects and so on.
F likes only HR.
H like none of the subjects.per. Which of the following pair of students don’t like Mkt.

In Praxis Business School Kolkata, 8 friends A, B,
C, D, E, F, G & H have interest in one or more of
the three subjects Marketing, Finance and HR. No
two students like the same set of subjects. Further
known facts are as follows –
A like all the three subjects.
Pair of students (B, C) , (D, E) (G- H) (B, D) and (F,
G) have no common subjects i.e B and C have not
common subjects and so on.
F likes only HR.
H like none of the subjects.per. Which of the following could be students who like Finance?

In Praxis Business School Kolkata, 8 friends A, B,
C, D, E, F, G & H have interest in one or more of
the three subjects Marketing, Finance and HR. No
two students like the same set of subjects. Further
known facts are as follows –
A like all the three subjects.
Pair of students (B, C) , (D, E) (G- H) (B, D) and (F,
G) have no common subjects i.e B and C have not
common subjects and so on.
F likes only HR.
H like none of the subjects.per. Which of the following student passed in exactly two subjects?

In Praxis Business School Kolkata, 8 friends A, B,
C, D, E, F, G & H have interest in one or more of
the three subjects Marketing, Finance and HR. No
two students like the same set of subjects. Further
known facts are as follows –
A like all the three subjects.
Pair of students (B, C) , (D, E) (G- H) (B, D) and (F,
G) have no common subjects i.e B and C have not
common subjects and so on.
F likes only HR.
H like none of the subjects.per. Which of the following statement require to find liking and disliking of each and every
subjects.
(I)There is 1 student who don’t like a single subject. (ii)B and E have a common subject in liking. (III)D and C have a common subject in liking.

In Praxis Business School Kolkata, 8 friends A, B,
C, D, E, F, G & H have interest in one or more of
the three subjects Marketing, Finance and HR. No
two students like the same set of subjects. Further
known facts are as follows –
A like all the three subjects.
Pair of students (B, C) , (D, E) (G- H) (B, D) and (F,
G) have no common subjects i.e B and C have not
common subjects and so on.
F likes only HR.
H like none of the subjects.per. If G don’t like Mktany more and F likes Mkt and no other change happen then which of
the following is set of students like same subject?

In a school students at Pioneer career Kolkata
wrote Mock test which has three subjects DI, VA
and QA, here is the result of these students.
80 students cleared cut off in DI, 70 in VA and 60
in QA.
Only 40 students cleared all the three subjects.
10 students failed to clear cut off even in one
subjects.
50 students cleared cut off in VA and QA.
5 students cleared in cut off in only QA. What is the minimum number of students who appeared in the Mock test.

In a school students at Pioneer career Kolkata
wrote Mock test which has three subjects DI, VA
and QA, here is the result of these students.
80 students cleared cut off in DI, 70 in VA and 60
in QA.
Only 40 students cleared all the three subjects.
10 students failed to clear cut off even in one
subjects.
50 students cleared cut off in VA and QA.
5 students cleared in cut off in only QA. If number of students who didn’t clear cut off in at least two subjects is maximum possible
then find the number of students who failed in exactly one subject?

In a school students at Pioneer career Kolkata
wrote Mock test which has three subjects DI, VA
and QA, here is the result of these students.
80 students cleared cut off in DI, 70 in VA and 60
in QA.
Only 40 students cleared all the three subjects.
10 students failed to clear cut off even in one
subjects.
50 students cleared cut off in VA and QA.
5 students cleared in cut off in only QA. What is the ratio of number of students who didn’t clear cut off DI, but cleared cut off
in QA to the number of students who didn’t clear cut off in exactly 1 subject.

In a school students at Pioneer career Kolkata
wrote Mock test which has three subjects DI, VA
and QA, here is the result of these students.
80 students cleared cut off in DI, 70 in VA and 60
in QA.
Only 40 students cleared all the three subjects.
10 students failed to clear cut off even in one
subjects.
50 students cleared cut off in VA and QA.
5 students cleared in cut off in only QA. What is the maximum number of students who didn’t clear cut off in QA

Out of 400 cadets at MERI Kolkata, 50% students
participated in exactly one of the three activities,
Swimming, Kick Boxing and Marching, total 160
students participated in swimming, 150 in Kick
Boxing and 120 in Marching. Number of cadets
who enrolled for swimming and kick boxing only is
20 more than the number of students who enrolled
for kick boxing and marching only. If all those who didn’t participated in any
of the three said activity got an order from
authority to participate in Social Activity,
what is the ratio of maximum to minimum
number of cadets participated in social
Activity?

Out of 400 cadets at MERI Kolkata, 50% students
participated in exactly one of the three activities,
Swimming, Kick Boxing and Marching, total 160
students participated in swimming, 150 in Kick
Boxing and 120 in Marching. Number of cadets
who enrolled for swimming and kick boxing only is
20 more than the number of students who enrolled
for kick boxing and marching only. What is the maximum number of cadets who participated in exactly two activities?

Out of 400 cadets at MERI Kolkata, 50% students
participated in exactly one of the three activities,
Swimming, Kick Boxing and Marching, total 160
students participated in swimming, 150 in Kick
Boxing and 120 in Marching. Number of cadets
who enrolled for swimming and kick boxing only is
20 more than the number of students who enrolled
for kick boxing and marching only. Due to increasing popularity of Social Activity all those who earlier participated in only one activity joined Social Activity, then what is the maximum possible number of cadets who like only one activity? [Use data of previous question if require]

Out of 400 cadets at MERI Kolkata, 50% students
participated in exactly one of the three activities,
Swimming, Kick Boxing and Marching, total 160
students participated in swimming, 150 in Kick
Boxing and 120 in Marching. Number of cadets
who enrolled for swimming and kick boxing only is
20 more than the number of students who enrolled
for kick boxing and marching only. Due to increasing popularity of Social Activity Kick boxing program is dissolve and all the cadets shifted to Social Activity, then what is the Minimum possible number of cadets who like only one activity? [Use data of previous question if require]

Out of 400 cadets at MERI Kolkata, 50% students
participated in exactly one of the three activities,
Swimming, Kick Boxing and Marching, total 160
students participated in swimming, 150 in Kick
Boxing and 120 in Marching. Number of cadets
who enrolled for swimming and kick boxing only is
20 more than the number of students who enrolled
for kick boxing and marching only. Due to increasing popularity of Social Activity all the cadets at MERI participated
in Social Activity then what could be the number of cadets who like only 2 activities.

At Pioneer Career a leading IIT JEE training
institute, a survey is conducted on 80 students of a
batch and it was found that 20% students don’t like
a single subject from three subjects Phy, Che and
maths. 50% students like Phy and Maths. Numer
of students who like Phy and Che both is equal
to number of students who like Maths and Che
both, Total 10% students like exactly 1 subjects.
Number of students who like Phy is same as that of
students who like Che and in turn equal to number
of students who like Maths which is equal to 50.
After 1st mock test each of the students changed
their liking (i.e if a student who liked maths and
Phy only now like Che, the one who like all the
three now like none, if a student who like only one
subject will now like 2 subjects, if a student earlier
like 2 subjects will now like only 1 subject and so
on) How many students who like Phy now had liking for Maths before mock test?

At Pioneer Career a leading IIT JEE training
institute, a survey is conducted on 80 students of a
batch and it was found that 20% students don’t like
a single subject from three subjects Phy, Che and
maths. 50% students like Phy and Maths. Numer
of students who like Phy and Che both is equal
to number of students who like Maths and Che
both, Total 10% students like exactly 1 subjects.
Number of students who like Phy is same as that of
students who like Che and in turn equal to number
of students who like Maths which is equal to 50.
After 1st mock test each of the students changed
their liking (i.e if a student who liked maths and
Phy only now like Che, the one who like all the
three now like none, if a student who like only one
subject will now like 2 subjects, if a student earlier
like 2 subjects will now like only 1 subject and so
on) How many students don’t like Phy before and after Mock.

At Pioneer Career a leading IIT JEE training
institute, a survey is conducted on 80 students of a
batch and it was found that 20% students don’t like
a single subject from three subjects Phy, Che and
maths. 50% students like Phy and Maths. Numer
of students who like Phy and Che both is equal
to number of students who like Maths and Che
both, Total 10% students like exactly 1 subjects.
Number of students who like Phy is same as that of
students who like Che and in turn equal to number
of students who like Maths which is equal to 50.
After 1st mock test each of the students changed
their liking (i.e if a student who liked maths and
Phy only now like Che, the one who like all the
three now like none, if a student who like only one
subject will now like 2 subjects, if a student earlier
like 2 subjects will now like only 1 subject and so
on) What is the difference between total number of students who like Phy before Mock and
like Che after Mock.

At Pioneer Career a leading IIT JEE training
institute, a survey is conducted on 80 students of a
batch and it was found that 20% students don’t like
a single subject from three subjects Phy, Che and
maths. 50% students like Phy and Maths. Numer
of students who like Phy and Che both is equal
to number of students who like Maths and Che
both, Total 10% students like exactly 1 subjects.
Number of students who like Phy is same as that of
students who like Che and in turn equal to number
of students who like Maths which is equal to 50.
After 1st mock test each of the students changed
their liking (i.e if a student who liked maths and
Phy only now like Che, the one who like all the
three now like none, if a student who like only one
subject will now like 2 subjects, if a student earlier
like 2 subjects will now like only 1 subject and so
on) What is difference between total number of students who like all the three subject before
and after Mock test.

In society only three types of news paper TOI, HT or
Tel are supplied, number of families who read TOI,
HT and Tel is 43, 65, 37. Given that total number
of family in the society is 100 and each family read
at least one news paper. If number of family who read HT only is minimum possible then what is the maximum
possible number of family who read TOI and Tel but not HT.

In society only three types of news paper TOI, HT or
Tel are supplied, number of families who read TOI,
HT and Tel is 43, 65, 37. Given that total number
of family in the society is 100 and each family read
at least one news paper. If number of family who read all the three news paper is maximum possible then what
is the maximum possible number of family who read only TOI

In society only three types of news paper TOI, HT or
Tel are supplied, number of families who read TOI,
HT and Tel is 43, 65, 37. Given that total number
of family in the society is 100 and each family read
at least one news paper. If number of family who read TOI only is
more than the number of family who read
HT only then what is the maximum number
of family who read all the three news paper.

In society only three types of news paper TOI, HT or
Tel are supplied, number of families who read TOI,
HT and Tel is 43, 65, 37. Given that total number
of family in the society is 100 and each family read
at least one news paper. What is the minimum number of family who read at least two news paper.

In society only three types of news paper TOI, HT or
Tel are supplied, number of families who read TOI,
HT and Tel is 43, 65, 37. Given that total number
of family in the society is 100 and each family read
at least one news paper. What is the Sum of maximum to minimum number of students who read only Tel?

In a school when a survey is conducted on liking
of subjects out of three subjects physic, chemistry,
mathematics, then outcome is as follows :-
Total number of students who like physics,
chemistry and mathematics is 30, 40, 50
respectively.10 students shown interest in all three
subjects, Number of students who like physics and
mathematics both is equal to number of students
who like chemistry and mathematics both and
is equal to ¾ times number of students who like
physics and chemistry both15 students like only
chemistry.
When class teacher saw this survey report he told
head master that at least 20 and at max 40% of
those who told they like physics are liars about
physics liking. Same percentage for chemistry is
40% to 50%.
Further class teacher added that the liars must
belong to those who like only 1 subject and if
numbers of liars is more then it belongs to those
who like 2 subjects and probability that the who
likes all three subjects is a liar is negligible. According to survey what is the ratio of number of students who like only Phy to
those who like only Che to those who like only Maths.

In a school when a survey is conducted on liking
of subjects out of three subjects physic, chemistry,
mathematics, then outcome is as follows :-
Total number of students who like physics,
chemistry and mathematics is 30, 40, 50
respectively.10 students shown interest in all three
subjects, Number of students who like physics and
mathematics both is equal to number of students
who like chemistry and mathematics both and
is equal to ¾ times number of students who like
physics and chemistry both15 students like only
chemistry.
When class teacher saw this survey report he told
head master that at least 20 and at max 40% of
those who told they like physics are liars about
physics liking. Same percentage for chemistry is
40% to 50%.
Further class teacher added that the liars must
belong to those who like only 1 subject and if
numbers of liars is more then it belongs to those
who like 2 subjects and probability that the who
likes all three subjects is a liar is negligible. As per the observation of class teacher what could be the number of students who don’t like a single subject?

In a school when a survey is conducted on liking
of subjects out of three subjects physic, chemistry,
mathematics, then outcome is as follows :-
Total number of students who like physics,
chemistry and mathematics is 30, 40, 50
respectively.10 students shown interest in all three
subjects, Number of students who like physics and
mathematics both is equal to number of students
who like chemistry and mathematics both and
is equal to ¾ times number of students who like
physics and chemistry both15 students like only
chemistry.
When class teacher saw this survey report he told
head master that at least 20 and at max 40% of
those who told they like physics are liars about
physics liking. Same percentage for chemistry is
40% to 50%.
Further class teacher added that the liars must
belong to those who like only 1 subject and if
numbers of liars is more then it belongs to those
who like 2 subjects and probability that the who
likes all three subjects is a liar is negligible. As per the observation of class teacher what could be the number of students who like
only one subject?

In a school when a survey is conducted on liking
of subjects out of three subjects physic, chemistry,
mathematics, then outcome is as follows :-
Total number of students who like physics,
chemistry and mathematics is 30, 40, 50
respectively.10 students shown interest in all three
subjects, Number of students who like physics and
mathematics both is equal to number of students
who like chemistry and mathematics both and
is equal to ¾ times number of students who like
physics and chemistry both15 students like only
chemistry.
When class teacher saw this survey report he told
head master that at least 20 and at max 40% of
those who told they like physics are liars about
physics liking. Same percentage for chemistry is
40% to 50%.
Further class teacher added that the liars must
belong to those who like only 1 subject and if
numbers of liars is more then it belongs to those
who like 2 subjects and probability that the who
likes all three subjects is a liar is negligible. As per the observation of class teacher what is the maximum number of students who like
Phy and Che both.

In a school when a survey is conducted on liking
of subjects out of three subjects physic, chemistry,
mathematics, then outcome is as follows :-
Total number of students who like physics,
chemistry and mathematics is 30, 40, 50
respectively.10 students shown interest in all three
subjects, Number of students who like physics and
mathematics both is equal to number of students
who like chemistry and mathematics both and
is equal to ¾ times number of students who like
physics and chemistry both15 students like only
chemistry.
When class teacher saw this survey report he told
head master that at least 20 and at max 40% of
those who told they like physics are liars about
physics liking. Same percentage for chemistry is
40% to 50%.
Further class teacher added that the liars must
belong to those who like only 1 subject and if
numbers of liars is more then it belongs to those
who like 2 subjects and probability that the who
likes all three subjects is a liar is negligible. As per the observation of class teacher if number of liars from maths group is maximum then how many students like only one subject?

In MERI kolkata 400 cadets have to participate
in exactly one activity at Morning, One Activity
at day Time and one activity at evening. Morning
activities are Yoga and PT, Day time activity is
Mess Club and Cooperative society and evening
activity is sports and marching.
Following facts are known further:-
Number of students who participate in PT and
sports both is 100
Number of students who participate in yoga and
co-operative both is 90
Number of students who participate in marching
and mess actives both is 110
Number of students who participate in PT and
morning but not in mess and sports is 60 If 190 students do not participate in mess activity then what is the number of students
who neither participate in yoga in morning, nor in mess society in day time?

In MERI kolkata 400 cadets have to participate
in exactly one activity at Morning, One Activity
at day Time and one activity at evening. Morning
activities are Yoga and PT, Day time activity is
Mess Club and Cooperative society and evening
activity is sports and marching.
Following facts are known further:-
Number of students who participate in PT and
sports both is 100
Number of students who participate in yoga and
co-operative both is 90
Number of students who participate in marching
and mess actives both is 110
Number of students who participate in PT and
morning but not in mess and sports is 60 If number of students who like yoga is 190 then what is the number of students who participate in PT and also in Marching?

In MERI kolkata 400 cadets have to participate
in exactly one activity at Morning, One Activity
at day Time and one activity at evening. Morning
activities are Yoga and PT, Day time activity is
Mess Club and Cooperative society and evening
activity is sports and marching.
Following facts are known further:-
Number of students who participate in PT and
sports both is 100
Number of students who participate in yoga and
co-operative both is 90
Number of students who participate in marching
and mess actives both is 110
Number of students who participate in PT and
morning but not in mess and sports is 60 If k is the number of students who participate in yoga in morning and mess in day time and
PT in evening then which of the following is correct about K?