# Free Arithmetic 02 Practice Test - CAT

### Question 1

In a class of 200 students who play cricket and hockey, the number of students who play neither of the games is 16 less than those who play both. The number of students who do not play cricket is 24 more than those who do not play hockey.

The number of students who play hockey is

#### SOLUTION

Solution :

Consider 2 complement sets. So if the no of students not playing hockey =x. number of students not playing cricket = x+24

Students playing both =y. Students playing neither = y-16

x+ (x+24) -(y-16)+y=200

2x+40=200

x=80

x+24=104

Those who play hockey 200-80=120

### Question 2

A group of 80 **P**eople play atleast one of the games- carrom, snooker and TT. 40 play carrom, 50 play snooker and 35 play TT. If 14 people play both Carrom and Snooker, 20 people play both Snooker and TT and 12 people play both TT and carrom, find the ratio of the number of people who play carrom only to the number who play only TT?

#### SOLUTION

Solution :C

Answer Option - C

x- number who play all 3 games

80= 125 –(14+12+20) +x

x= 1, the venn diagram can be represented as

Thus ratio=15:4

### Question 3

What is the total number of students who opted for only football?

#### SOLUTION

Solution :D

D

### Question 4

What is the total number of students who opted for hockey?

#### SOLUTION

Solution :B

B

### Question 5

What is the number of people who opt for both Football and cricket?

#### SOLUTION

Solution :D

D

### Question 6

In a survey, 100 people were asked about their favourite Holiday spot in India among three places: Goa, Shimla or Kashmir. All the people had at least one of these three spots as their favourite one. 90 people named Goa as their favourite, 80 people named Shimla as their favourite and 80 people named Kashmir as their favourite.

Determine the maximum number of people who could have named all three places as their favourite.

#### SOLUTION

Solution :C

C

For III to be the maximum, II = 0 III = 75

### Question 7

In a survey, 100 people were asked about their favourite Holiday spot in India among three places: Goa, Shimla or Kashmir. All the people had at least one of these three spots as their favourite one. 90 people named Goa as their favourite, 80 people named Shimla as their favourite and 80 people named Kashmir as their favourite.

Determine the minimum number of people who could have named all three places as their favourite.

#### SOLUTION

Solution :B

For III to be the minimum, II has to be the maximum.

also, all the equations will have to be satisfied.

We have II +2III = 150

Also I + II + III = 100.

II can take a maximum value of 50. So, III = 50, at this point all the equations are consistent, hence 50 is the minimum number of people.

### Question 8

In a survey, 100 people were asked about their favourite Holiday spot in India among three places: Goa, Shimla or Kashmir. All the people had at least one of these three spots as their favourite one. 90 people named Goa as their favourite, 80 people named Shimla as their favourite and 80 people named Kashmir as their favourite.

Determine the minimum number of people who could have name exactly two places as their favourite.

#### SOLUTION

Solution :B

B

For II to be the minimum, III has to be the maximum. The maximum value of III can be 75. So, minimum value of II = 0

### Question 9

In a survey, 100 people were asked about their favourite Holiday spot in India among three places: Goa, Shimla or Kashmir. All the people had at least one of these three spots as their favourite one. 90 people named Goa as their favourite, 80 people named Shimla as their favourite and 80 people named Kashmir as their favourite.

Determine the maximum number of people who could have name exactly two places as their favourite.

#### SOLUTION

Solution :B

For II to be maximum, III has to minimum i.e. 0. In this case, II = 150. But, II can’t be 150 as the maximum possible value in only 100.

Also,

We have II +2III = 150

Also I + II + III = 100.

So when III=50 and II =50 then all the equations are getting satisfied, hence II=50 is the minimum and maximum value for II

So, maximum value of II = 50

### Question 10

In a school, 40% of the students draw and paint. 40% of those who draw do not paint. If the students do one of the two, then what % of students paint?

#### SOLUTION

Solution :C

If we assume the total number of students=100, thenthe number of students who both draw and paint= 40Also, let the number of students who draw=x; thenthe number of students who only draw= 0.4x

Thus, 0.4x+40=x => x= 66.66

Therefore, number of students who paint= 40+(100-66.66)= 73.33. Answer is option (c)

### Question 11

In a class there are 200 students, at least 140 of students like Maths, at least 150 like Science and at least 160 like English. What is the minimum number of students who like all three subjects?

#### SOLUTION

Solution :A

A

X = I + II + III = 200

S = I + 2II + 3III = 140 + 150 + 160 = 450

S – X = II + 2III = 450 – 200 = 250

For III to be the minimum, II has to be the maximum. Now, II can take the maximum value of 200.

So, minimum value of III = 250 – 200= 50.

### Question 12

30% of the crowd at a mall is > 25 years and 80% of the crowd at the mall is <50 years. 20% of the crowd visits bantaloons. If 20% of the crowd above the age of 50 visit bantaloons, then what percentage of bantaloon visitors are < 50 years?

#### SOLUTION

Solution :D

20% of the crowd is above 50 years. 20% of this crowd visits bantaloons. Therefore 20% of 20% is 4% of the total crowd above 50 years visit bantaloons and therefore 16% of the crowd below the age of 50 years visit bantaloons.

20% of entire crowd visits bantloons

Therefore the % of crowd which visits bantaloons and below age of 50 = 1620×100=80

Shortcut:The given information can be carefully observed.

The crowd is divided into 2 groups: lesser than 50 and greater than 50. So the entire set can be made by adding both the groups.

Now the group that is greater than 50 forms 20% of the population that visit bantaloons, hence 80% of the crowd should be below the age of 50 and this is what has been asked.

### Question 13

In an examination, 53 passed in Maths, 61 passed in Physics, 60 in Chemistry, 24 in Maths & Physics, 35 in Physics & Chemistry, 27 in Maths & Chemistry and 5 in none. Find the number of students who passed in all subjects if the total number of students who had appeared in the examination was 100.

#### SOLUTION

Solution :C

X = I + II + III = 100 – 5 = 95 As 5 students have passed in none.

S = I + 2II + 3III = 53 + 61 + 60 = 174

S – X = II + 2III = 174 – 95 = 79 ... (i)

Number of people who have passed in two subject = 24 + 35 + 27 = 86 = II + 3III... (ii)

From (i) and (ii), III = 86 – 79 = 7

So, people who have passed in all three subjects = 7

### Question 14

Sets A, B, C and D are all subsets of quadrilaterals. A is the set of rhombi, B is the set of rectangles, C is the set of parallelograms, and D is the set of kites. What is the set (A ∩ B) ∪ (C ∩ D)?

#### SOLUTION

Solution :D

A ∩ B is a set of quadrilaterals that are both rhombi and rectangles - which are squares. C ∩ D is a set of quadrilaterals that are both parallelograms and kites - which are rhombi. Finally, the union of squares and rhombi are... rhombi.

### Question 15

In a survey among 70 people, 50 like Vanila and 40 like Chocolate. What is the minimum and maximum number of people who like exactly 2 flavours respectively?

#### SOLUTION

Solution :C

X = I + II = 70

S = I + 2II = 50 + 40 = 90

S – X = II = 90 – 70 = 20 = x

So, minimum and maximum value of x = 20.