Common Problem Solving Practice Test 2

By ramefCommon Practice Tests

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

  • Answer:D

  • Answer Explanation:
    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

  • Answer:D

  • Answer Explanation:
    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

  • Answer:C

  • Answer Explanation:
    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
    Height/radius = 7/5 = 1.4
    Option C is correct.




Question – 4

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

  • A. 1/3


  • B. 1


  • C. 1/9


  • D. 3


  • E. 27

  • Answer:C

  • Answer Explanation:
    [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

  • Answer:C

  • Answer Explanation:
    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

  • Answer:E

  • Answer Explanation:
    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

  • Answer:E

  • Answer Explanation:
    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

  • Answer:D

  • Answer Explanation:
    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

  • Answer:D

  • Answer Explanation:
    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

  • Answer:A

  • Answer Explanation:
    (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

  • Answer:D

  • Answer Explanation:
    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

  • Answer:C

  • Answer Explanation:
    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

  • Answer:E

  • Answer Explanation:
    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

  • Answer:B

  • Answer Explanation:
    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

  • Answer:D

  • Answer Explanation:
    P(15,5) = 15!/(15-5)!
    = 15!/10!
    = 15*14*13*12*11
    = 360360
    Option D is true.




Score: 0/10



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