Common Problem Solving Practice Test 2

Question – 1

1. The first day of a leap year is a Sunday. How many Mondays does the year contain? Indicate the correct option.

• A. 50

• B. 51

• C. 52

• D. 53

• E. 54

Every seventh day of the year will be a Sunday.
A leap year has 365+1=366 days
The year contains 52*7+2 days
The second day is a Monday and hence the 365th day will be a Sunday and the 366th day will be a Monday.
There are 53 Mondays in the year.

Question – 2

(Note:[x^2=x*x] )

• A. 2

• B. 4

• C. 6

• D. 7

• E. 9

Put x = 2 in the given polynomial
6x^3-2ax^2+ax-6 = 6*(2^3) -2a*(2^2)+a*2-6=048-8a+2a-6=0
6a=42
a=7
Option D is correct.

Question – 3

3. The volume of a cylinder is 550 cc and its radius is 5cm. What is the height per unit radius of the cylinder? Indicate the correct option.

• A. 1

• B. 5

• C. 1.4

• D. 0.71

• E. 7

Volume of cylinder = pi*r^2*h, where r and h are radius and height of the cylinder.
550=pi*5^2*h
h=550*7/(22*5*5)
= 7
Height of the cylinder = 7 cm
Option C is correct.

Question – 4

(Note:[x^2=x*x] ).

• A. 1/3

• B. 1

• C. 1/9

• D. 3

• E. 27

[81*3^(n+1)-9*3^n]/[81*3^(n+3)-3*3^(n+3)]
= [3^(n+5)-3^(n+2)]/[3^(n+7)-3^(n+4)]
= [3^(n+5)-3^(n+2)]/{(3^2)*[3^(n+5)-3^(n+2)]}
=1/3^2
= 1/9
Option C is true.

Question – 5

(Note:[pi=22/7] ).

• A. 169 m

• B. 10 m

• C. 26 m

• D. 13pi m

• E. 26pi m

The shortest path will be along the diameter of the field.
Area = 169pi = pi*r^2, where r is the radius of the circle
r^2=169
r=13
The length of the shortest path is 2*13=26m.
Option C is true.

Question – 6

6. A cylinder’s diameter is reduced to one-third. The volume remains the same. How many times will the length become? Indicate the correct option.

• A. 3

• B. 6

• C. 5

• D. 12

• E. 9

Let the initial length be l and new length be l’.
Let the original diameter be 6r and radius be 6r/2=3r.
The new diameter will be 6r/3=2r and radius will be 2r/2=r
Volume=pi*(3r)^2*l = pi*r^2*l’
9r^2*l=r^2*l’
9l=l’
The length becomes 9 times itself.
Option E is true.
[x^2=x*x]
[pi=22/7]

Question – 7

(Note:[x^2=x*x] ).

• A. 16

• B. 4

• C. 18

• D. 12

• E. 14

x+1/x=4
(x+1/x)^2=x^2+1/x^2+2*x*1/x
x^2+1/x^2=(x+1/x)^2-2
=4^2-2=16-2=14
Option E is correct.

Question – 8

8. Triangle ABC is right angled at A. AL is drawn perpendicular to BC. Which of the following is true? Indicate the correct option.

• A. Angle ABC = Angle ACB

• B. Angle BAL = Angle ALC

• C. Angle ACL = Angle ABL

• D. Angle BAL = Angle ACB

• E. Angle ALB = Angle ACB

Options A and C need not be true and hence they are incorrect.
Option B is false as angle ALC is a right angle while angle BAL is an acute angle.
Similarly option E is false.
We check option D now.In triangle ABL,
angle BAL+angle ALB+angle B=180
angle BAL+90+angle B=180
angle BAL+angle B=90
angle BAL=90-angle B …(1)

In triangle ABC,
angle A + angle B + angle C = 180
90 + angle B +angle C = 180
angle B + angle C = 180-90=90
angle ACB=90-angle B …(2)
From (1) and (2), we conclude that option D is true.

Question – 9

9. Pam has a field in the shape of a polygon with 10 sides. Into how many triangular fields can she cut her field so that she can access each field from the same vertex? Indicate the correct option.

• A. 3

• B. 5

• C. 7

• D. 8

• E. 9

A polygon with n sides can be cut into (n-2) triangles with a common vertex.
The bigger field with 10 sides can be cut into (10-2)=8 triangular fields with a common vertex.
Option D is true.

Question – 10

10. What is the area enclosed by the points (1,4), (4,-2) and (9,-12)? Indicate the correct option.

• A. 0

• B. 24

• C. 38

• D. 26

• E. 36

(1,4), (4,-2), (9,-12) are the three points.
Area = 1/2[1*(-2)-4*4+4*(-12)-(-2)*9+9*4-1*(-12)]
=1/2[-2-16-48+18+36+12]
=1/2(0)=0
Option A is true..

Question – 11

11. If 20% of Adam’s share is 10% of Eve’s share then how much percent of Adam’s share is 4% of Eve’s share? Indicate the correct option.

• A. 2

• B. 4

• C. 2/25

• D. 8

• E. 0.08

Let Adam’s and Eve’s shares be x and y respectively.
20%*x=10%*y
20/100*x = 10/100*y
2x=y
4% of y = 4/100*y
= y/25 = 2x/25
= 2/25*100% of x
= 8% of x.

Question – 12

12. A company gave a bonus of \$500 dollars per employee on an average. The bonus packets of five employees worth \$300 each and two employees worth \$500 each got lost before being distributed. As a result, the company had to make new bonus packets for them. The company spent an added 10% on the bonus per employee as a result of this added expense. How many employees does the company have? Indicate the correct option.

• A. 10

• B. 28

• C. 50

• D. 55

• E. 32

Let the number of employees be x
Average = Sum of bonus/number of employees
500 = Sum/x
Sum=500xBonus lost = 5*\$300+2*\$500
= 1500+1000
= 2500

New average bonus = 500+500*10/100
= 500+50=550
New average = (500x+2500)/x = 550
500x+2500=550x
50x=2500
x=2500/50=50

The company has 50 employees.
Option C is true.

Question – 13

13. A water tank can hold 5760 litres of water. The inlet fills water at the rate of 4 litres per minute and the outlet can empty the tank in 6 hours. How many hours would it take to empty the tank if the inlet and outlet are both open? Indicate the correct option

• A. 4

• B. 5

• C. 6

• D. 7

• E. 8

Rate of water in = 4 litres/min
Rate of water out = 5760/(6*60)
= 16 litres/min
Relative rate at which water goes out when the inlet and outlet are both open = 16-4=12 litres/min
Time taken to empty the tank = 5760/12= 480 minutes
= 480/60 hours = 8 hours
Option E is true.

Question – 14

14. A and B have to cover a distance of 500m. Their speeds are in ratio 3:4 respectively. How many meters should A be before B at the time of starting so that they reach the finish line together? Indicate the correct option.

• A. 0

• B. 125

• C. 30

• D. 50

• E. 150

Let the speed of A be 3x m/s and that of B be 4x m/s
Let the distance covered by A be (500-y) meters.
Time taken by them is the same,
(500-y)/3x=500/4x
4*(500-y)=3*500
2000-4y=1500
4y=2000-1500=500
y=500/4=125
A should be ahead of B by 125 meters
Option B is correct.

Question – 15

15. Which of the following is equal to P(15,5)? Indicate the correct option.

• A. 360306

• B. 300600

• C. 306306

• D. 360360

• E. 330660