# Free Arithmetic 03 Practice Test - CAT

### Question 1

In a survey of 2000 people for the top movie of 2008 among three: RNBDJ, Ghajni and Singh is King. 960 like RNBDJ, 1080 like Ghajni,1280 like Singh is King, 560 like RNBDJ and Ghajni, 640 like Ghajni and Singh is King, 600 like Singh is King and RNBDJ. Only 120 likes none of the three.

Determine the number of people who like RNBDJ and Singh is King but not Ghajni.

#### SOLUTION

Solution :D

Number of people , who likes at least one movie = 2000 - 120 = 1880

x + 40 + x - 120 + x - 200 + 640 - x + 560 - x + 600 - x + x = 1880

x = 360

The number of people who like RNBDJ and Singh is King but not Ghajni = (600 - 360) = 240. Hence option (d)

### Question 2

In a survey of 2000 people for the top movie of 2008 among three: RNBDJ, Ghajni and Singh is King. 960 like RNBDJ, 1080 like Ghajni,1280 like Singh is King, 560 like RNBDJ and Ghajni, 640 like Ghajni and Singh is King, 600 like Singh is King and RNBDJ. Only 120 likes none of the three.

Calculate the ratio of people who like only RNBDJ to the number who like only Ghajni.

#### SOLUTION

Solution :C

Number of people , who likes at least one movie = 2000 - 120 = 1880

x + 40 + x - 120 + x - 200 + 640 - x + 560 - x + 600 - x + x = 1880

x = 360

160: 240 = 2: 3. Hence option (c)

### Question 3

In a survey of 2000 people for the top movie of 2008 among three: RNBDJ, Ghajni and Singh is King. 960 like RNBDJ, 1080 like Ghajni,1280 like Singh is King, 560 like RNBDJ and Ghajni, 640 like Ghajni and Singh is King, 600 like Singh is King and RNBDJ. Only 120 likes none of the three.

Determine the percentage of those who like at least two of these three movies.

#### SOLUTION

Solution :B

240 + 200 + 280 + 360 = 1080 = 54% Hence option (b)

### Question 4

In a group of 500 people, 350 are engineers and 250 are MBAs.

How many are both Engineers and MBAs?

#### SOLUTION

Solution :A

As, we know {A ∪ B} = A + B - (A ∩ B)

A ∪ B = 500 , A = 250 and B = 350

500 = 250 + 350 - (A ∩ B)

(A ∩ B) = 100

100 are both Engineers and MBAs.

Hence option (a)

### Question 5

In a group of 500 people, 350 are engineers and 250 are MBAs

How many are either only MBA or only Engineers?

#### SOLUTION

Solution :D

People who are only Engineer = 250

People who are only MBA = 150

No. of people who are either only MBA or only Engineer = 250 + 150 = 400

Hence option (d)

### Question 6

In an examination, 38% of students failed in Science and 33% failed in Maths while 19% failed in both the subjects. If the number of students who passed in only Science is 700, then determine the total number of students who appeared in the examination.

#### SOLUTION

Solution :C

Soln:

So, the % of students failed in at least one subject = 19 + 19 + 14 = 52 %

So, the % of students who didn’t fail even in one subject = 100 – 52 = 48%

% of students failed in Science = 38%

% of students who passed in Science = 100 – 38 = 62%

% of students failed in Maths = 33%

% of students who passed in Mathematics = 100 – 33 = 67%

Now, consider the % of students who passed:

So, as we see from the Venn diagram, % of students passed in only Science = 14%.

If the total no. of students who appeared = x, then .14x = 700 x = 5000.

Hence option (c)

### Question 7

In a music school, three instruments are taught: Tabla, Violin and Guitar. Out of 278 students in the school, 20 learn Tabla and Violin, 23 learn Violin and Guitar and 21 learn Tabla and Guitar. 9 students learn all three instruments. It is known that the equal number of seats in all three instruments classes. (If a student is learning Guitar as well as Tabla, then he occupies two seats: one in Tabla class and one in Guitar class)

Determine the number of students who have occupied only one seat.

#### SOLUTION

Solution :A

No. of students who have occupied only one seat = x + y + z + 14 + 12 + 11 + 9 = 278

=> x + y + z =278-46 = 232.

Hence option (a)

### Question 8

In a music school, three instruments are taught: Tabla, Violin and Guitar. Out of 278 students in the school, 20 learn Tabla and Violin, 23 learn Violin and Guitar and 21 learn Tabla and Guitar. 9 students learn all three instruments. It is known that the equal number of seats in all three instruments classes. (If a student is learning Guitar as well as Tabla, then he occupies two seats: one in Tabla class and one in Guitar class)

Determine the number of students who have occupied seats in Violin or Guitar class, but not in Tabla Class.

#### SOLUTION

Solution :E

As per the information given in the question, we get the venn diagram as:

We get the equations as:

T + 32 = V + 34 = G + 35

and V + T + G + 46 = 278 => V + T + G = 232

So, by solving the equations we get, no. of students who have occupied seat in Violin Class or Guitar Class, but not inTabla Class = 77 + 14 + 76 = 167. Hence option (e)

### Question 9

In a music school, three instruments are taught: Tabla, Violin and Guitar. Out of 278 students in the school, 20 learn Tabla and Violin, 23 learn Violin and Guitar and 21 learn Tabla and Guitar. 9 students learn all three instruments. It is known that equal number of seats in all three instrument classes. (If a student is learning Guitar as well as Tabla, then he occupies two seats: one in Tabla Class and one in Guitar Class)

Determine the number of students who have occupied seats in Tabla and Violin Class but not in Guitar Class.

#### SOLUTION

Solution :B

Going by the information given in the question, we get the three sets venn diagram as:

Hence, no. of students who have occupied the seat in Tabla and Violin Class, but not in Guitar Class = 20 – 9 = 11. Hence option (b)

### Question 10

In an examination, it was found that every student has failed in at least one subject out of the three subjects: English, Maths and Science. 28 students failed in English, 30 students failed in Maths and 32 students failed in Science. 6 students failed in English and Maths, 8 students failed in Maths and Science and 10 students failed in English and Science. The number of students who failed in only one subject is 54. Also, 20 students failed only in Maths.

Determine the number of students who appeared in the examination.

#### SOLUTION

Solution :D

No. of students who failed only in Maths= 20 (Given)

According to condition given,

Students who failed in Maths and English only + Students who failed in Science and Maths only + Students who failed in all three papers= 30-20= 10.

Therefore, 6+8-x=10 (x being the number of students who failed in all three subjects)

Solving the above equation gives x=4

Student who failed in:-

All three subjects=4

Maths and English only=2

Maths and Science only=4

Science and English only=6

English only=16

Science only=18

Therefore total no. of students= 16+18+20+2+4+6+4=70

Hence answer option d.

### Question 11

In an examination, it was found that every student has failed in at least one subject out of the three subjects: English, Maths and Science. 28 students failed in English, 30 students failed in Maths and 32 students failed in Science. 6 students failed in English and Maths, 8 students failed in Maths and Science and 10 students failed in English and Science. The number of students who failed in only one subject is 54. Also, 20 students failed only in Maths.

The number of students who failed in English and Science but not Maths is

#### SOLUTION

Solution :No. of students who failed only in Maths= 20 (Given)

According to condition given,

Students who failed in Maths and English only + Students who failed in Science and Maths only + Students who failed in all three papers= 30-20= 10.

Therefore, 6+8-x=10 (x being the number of students who failed in all three subjects)

Solving the above equation gives x=4

Student who failed in:-

All three subjects=4

Maths and English only=2

Maths and Science only=4

Science and English only=6

English only=16

Science only=18

### Question 12

Find the maximum number of people who suffered at least one injury.

#### SOLUTION

Solution :D

Option (d)

### Question 13

Answer the questions based on the information given below:

Out of 210 accidents that occurred on the DND Flyway, 50 resulted in Head Injury, 105 in Chest Injury and 56 in Limb Injury. 32 suffered both Head and Chest Injury, 30 suffered both Head and Limb Injury and 45 suffered both Limb and Chest Injuries.

The number of people having no injuries is

#### SOLUTION

Solution :All the people were involved in atleast one accident. Hence, 123

### Question 14

Find the maximum number of people who suffered all the three injuries.

#### SOLUTION

Solution :A

Option (a)

### Question 15

Out of 210 accidents that occurred on the DND Flyway, 50 resulted in Head Injury, 105 in Chest Injury and 56 in Limb Injury. 32 suffered both Head and Chest Injury, 30 suffered both Head and Limb Injury and 45 suffered both Limb and Chest Injuries.

The minimum number of people who suffered all the three injuries is

#### SOLUTION

Solution :Number of people who suffered all the injuries is x

123= 55+72+65-23-26-28+x

⇒x=8