Arithmetic(Exams > Cat > Quantitaitve Aptitude ) Questions and answers for exam Preparation

Exams > Cat > Quantitaitve Aptitude

ARITHMETIC MCQs

Total Questions : 147 | Page 13 of 15 pages

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.

Discuss Question

Answer: Option B. -> 50
:
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 122.

Discuss Question

Answer: Option B. -> 0
:
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 123.

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

100
60
50
Cannot be determined

Discuss Question

Answer: Option B. -> 60
:
B

Question 124.

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?

70
82.3
73.33
50.54

Discuss Question

Answer: Option C. -> 73.33
:
C
If we assume the total number of students=100, then
the number of students who both draw and paint= 40
Also, let the number of students who draw=x; then

the 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 125.

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.

Discuss Question

Answer: Option B. -> 50
:
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 126.

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.

Discuss Question

Answer: Option C. -> 75
:
C

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

Question 127.

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

15
30
45
Cannot be determined

Discuss Question

Answer: Option D. -> Cannot be determined
:
D

Question 128.

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.

Discuss Question

Answer: Option C. -> 7
:
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 129.

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?

Discuss Question

Answer: Option D. -> 80%
:
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 = $\frac{16}{20} \times 100 = 80$

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 130.

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 $\cap$ B) $\cup$ (C $\cap$ D)?

squares
rectangles
parallelograms
rhombi

Discuss Question

Answer: Option D. -> rhombi
:
D

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