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

Exams > Cat > Quantitaitve Aptitude

ARITHMETIC MCQs

Total Questions : 147 | Page 9 of 15 pages

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 ___.

Discuss Question

Answer: Option A. ->
:

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 82.

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 ___.

Discuss Question

Answer: Option A. ->
:

Number of people who suffered all the injuries is x
123= 55+72+65-23-26-28+x
$\Rightarrow x = 8$

Question 83.

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

Discuss Question

Answer: Option D. -> 134
:
D

Option (d)

Question 84.

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

Discuss Question

Answer: Option A. -> 30
:
A

Option (a)

Question 85.

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 ___.

Discuss Question

Answer: Option A. -> 30
:

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

Question 86.

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.

Discuss Question

Answer: Option B. -> 11
:
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 87.

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.

Discuss Question

Answer: Option D. -> 70
:
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 88.

A ship leaves on a long voyage. When it is 18 miles from the shore, a sea plane, whose speed is ten times that of ship, is sent to deliver mail. How far from the shore does the sea plane catch up with the ship? (1994)

24 miles
25 miles
22 miles
20 miles

Discuss Question

Answer: Option D. -> 20 miles
:
D

The ship is 18 miles from the shore, as the speed is in the ratio of 1:10 the distance will also be in the ratio of 1:10.

When the ship travels 1 mile the plane will travel 10 miles

At this point the ship is 19 miles from the shore and the plane is 10 miles away from the shore.

Next when the ship moves by 1 mile covering 20 miles totally the plane will also cover the same distance of 20 miles hence will meet the ship

Question 89.

The winning relay team in a high school sports competition clocked 48 min for a distance of 13.2 km. Its runners A, B, C and D maintained speeds of 15 km/hr, 16 km/hr, 17 km/hr and 18 km/hr respectively. What is the ratio of the time taken by B to the time taken by D?

5 : 16
5 : 17
9 : 8
8 : 9

Discuss Question

Answer: Option C. -> 9 : 8
:
C
(c) Time is inversely proportional to the speed.
Hence ratio of time taken by B and D = 18 : 16 = 9 : 8

Question 90.

A and B walk from X to Y, a distance of 27 km at 5 km/hr and 7 km/hr respectively. B reaches Y and immediately turns back meeting A at Z. What is the distance from X to Z? (1994)

25km
22.5km
24km
20km

Discuss Question

Answer: Option B. -> 22.5km
:
B

Approach 1: Convetional :
(b) Time taken by A in covering (27-x) km is same as time taken by Bin covering (27+x) km.
$\frac{27 - x}{5} = \frac{27 + x}{7}$
$x = \frac{27}{6}$
$∴ X Z = 27 - \frac{27}{6} = 27 \times \frac{5}{6} = 22.5 k m .$
Approach 2 : Alternate Approach (Using Ratios):
The total distance they will have to travel will be 2d or 54 kms. As their speeds are in the ratio of 5:7 the distances will also be in the same ratio. Hence,54 kms will have to be split in the ratio of 5:7. (i.e.,)22.5 and 41.5,hence they will meet at 22.5km.
Approach 3 : Going from answer options :
The total distance they will have to travel will be 2d or 54kms.
Now,going by the answer options :
Let us assume 25 to be the right option. Hence,A will take 5 hrs in the same time B would have covered a distance of 35 kms.hence the total distance covered will be 60, which is not what is given in the question (we need to get 54.)
Now assume 22.5 to be the right answer,hence A will take 4.5 hrs in the same time B would have covered a distance of 31.5kms,the tally of which is 54 hence that is the right option.