Common Quantitative Comparison Practice Test 5

By ramefCommon Practice Tests

Question – 1

1. On day one, Smith ran to a shop and came back walking. He took 8 minutes to cover this trip. On the next day, he takes 6 minutes as he runs both ways.?

Column-A Column-B
Time taken to complete his trip if he walks both ways Time taken to complete his trip two times around if he runs both ways.



  • A. If the quantity on the left is greater


  • B. If the quantity on the right is greater


  • C. If both are equal


  • D. If the relationship cannot be determined without further information


  • Answer:B

  • Answer Explanation:
    Let his distance one way be k meters.
    Speed = distance/time
    Let his speed while walking be x m/min and while running be y m/min.
    On day two, he runs both ways
    y = 2k/6=k/3
    k = 3y
    On day one, he walks one way and runs the other way
    k/x+k/y=8
    k(x+y)=8xy
    Putting k = 3y in this equation, we get
    3y(x+y)=8xy
    3x+3y=8x
    3y=8x-3x=5x
    y/x=5/3When he walks both ways
    Time taken = k/x+k/x
    = 3y/x+3y/x = 6y/x
    = 6(5/3) = 2*5=10 mins

    When he runs both ways
    Time taken for going two times around = 2*6mins =12 mins

    Option B is true.




Question – 2

2. A semi-circle is rolled and a cone is formed. The radius of the circle is 21cm.?

Column-A Column-B
Lateral surface area of the cone Total surface area of the semi-circle



  • A. If the quantity on the left is greater


  • B. If the quantity on the right is greater


  • C. If both are equal


  • D. If the relationship cannot be determined without further information


  • Answer:C

  • Answer Explanation:
    Since the semi-circle is turned into a cone, the surface area of the semi-circle becomes the lateral surface area of the cone. The two quantities are equal.
    Option C is correct.




Question – 3

3. A, B and C invest $80000 in a business. A invests the most and B and C invest equal amounts. The profit earned by each is proportional to his share of investment. A gets $4000 from the total profit.?

Column-A Column-B
Investment of A Total investment of B and C



  • A. If the quantity on the left is greater


  • B. If the quantity on the right is greater


  • C. If both are equal


  • D. If the relationship cannot be determined without further information


  • Answer:D

  • Answer Explanation:
    We know the total investment, but we do not know the ratio in which A, B and C invested. Hence, we cannot calculate the total investment of A, B and C.
    Option D is correct.




Question – 4

4. From a rectangular cardboard of length 25 cm and breadth 10 cm, Adam cuts a square whose diagonal is of length 4*sqrt(2) cm.?

Column-A Column-B
Number of such squares 30



  • A. If the quantity on the left is greater


  • B. If the quantity on the right is greater


  • C. If both are equal


  • D. If the relationship cannot be determined without further information


  • Answer:B

  • Answer Explanation:
    Area of the cardboard = length*breath
    = 25*10 = 250 sq.cm.
    Diagonal of a square of side x cm is equal to x*sqrt(2) cm.
    Hence, side of square = 4 cm
    Area of square = side*side
    = 4*4 = 16 sq.cm.Number of squares that he can possibly cut = 250/16
    = 15.625
    Option B is correct.




Question – 5

5. A dishonest shopkeeper uses an 800 gm weight instead of a 1 kg weight. He claims to sell the items at their cost price.?

Column-A Column-B
Profit $50



  • A. If the quantity on the left is greater


  • B. If the quantity on the right is greater


  • C. If both are equal


  • D. If the relationship cannot be determined without further information


  • Answer:D

  • Answer Explanation:
    We can only calculate the profit percent and we cannot calculate the profit earned by the shopkeeper since we do not have sufficient data.
    Option D is correct.




Question – 6

6. 585 has to be converted to a perfect square.?

Column-A Column-B
The smallest number by which it should be multiplied The smallest number by which it should be divided



  • A. If the quantity on the left is greater


  • B. If the quantity on the right is greater


  • C. If both are equal


  • D. If the relationship cannot be determined without further information


  • Answer:C

  • Answer Explanation:
    585=3*3*5*13
    The smallest number by which it should be multiplied is 5*13=65
    The smallest number by which it should be divided is 5*13=65
    Option C is correct.




Question – 7

7. Consider three numbers a<=b<=c.?

Column-A Column-B
LCM of the three numbers HCF of the three numbers



  • A. If the quantity on the left is greater


  • B. If the quantity on the right is greater


  • C. If both are equal


  • D. If the relationship cannot be determined without further information


  • Answer:D

  • Answer Explanation:
    The LCM of three numbers is always greater than the HCF
    When a=b=c
    LCM=a and HCF=a
    Hence, the relationship cannot be established.
    Option D is correct.




Question – 8

8. log[(x+y)/3]=1/2(logx+logy).?

Column-A Column-B
(x/y+y/x) [(x+y)^2-2xy]/xy



  • A. If the quantity on the left is greater


  • B. If the quantity on the right is greater


  • C. If both are equal


  • D. If the relationship cannot be determined without further information


  • Answer:C

  • Answer Explanation:
    log[(x+y)/3]=1/2(logx+logy)
    log[(x+y)/3] = log[sqrt (xy)]
    (x+y)/3 = sqrt(xy)
    Squaring both sides, we get
    (x^2+y^2+2xy)/9=xy
    x^2+y^2= 9xy-2xy
    x^2+y^2=7xy
    Dividing by xy, we get
    x/y+y/x=7Also, (x^2+y^2)=7xy
    (x+y)^2-2xy=7xy
    [(x+y)^2-2xy]/xy=7

    Option C is true.
    [x^2=x*x]




Question – 9

9. x+1/x=3,?

Column-A Column-B
x^2+1/x^2 x^2+6/x-1/x^2

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

  • A. If the quantity on the left is greater


  • B. If the quantity on the right is greater


  • C. If both are equal


  • D. If the relationship cannot be determined without further information


  • Answer:B

  • Answer Explanation:
    x+1/x=3
    Squaring both sides, we get
    x^2+1/x^2+2*x*1/x=3^2
    x^2+1/x^2=9-2=7
    x^2+1/x^2=7x+1/x=3
    x=3-1/x
    Squaring both sides, we get
    x^2=9+1/x^2-6/x
    x^2-1/x^2+6/x=9
    Option B is correct.




Question – 10

10. 2x+y=35 and 3x+4y=65.?

Column-A Column-B
x/y. y/x



  • A. If the quantity on the left is greater


  • B. If the quantity on the right is greater


  • C. If both are equal


  • D. If the relationship cannot be determined without further information


  • Answer:A

  • Answer Explanation:
    2x+y=35     ….(1)
    3x+4y=65..(2)
    Multiply (1) by 4 and subtracting (2) from it
    8x+4y-3x-4y = 140-65
    5x=75
    x = 75/5=15Put x = 15 in (1)
    2*15+y=35
    30+y=35
    y= 35-30=5
    x/y=15/5=3
    y/x=5/15=1/3
    Option A is correct.




Question – 11

11.

Column-A Column-B
The sum of the first 100 even natural numbers divisible by 5. The sum of numbers between 35 and 95 divisible by 3



  • A. If the quantity on the left is greater


  • B. If the quantity on the right is greater


  • C. If both are equal


  • D. If the relationship cannot be determined without further information


  • Answer:A

  • Answer Explanation:
    The even natural numbers divisible by 5 are 10, 20, 30,….
    These form an AP with the first term a = 10 and the common difference d = 20-10=10
    Sum of n terms of an AP is given by
    Sn=n/2[2a+(n-1)d]
    =100/2[2*10+(100-1)*10]
    =50(20+990)
    =50*1010
    = 50500The numbers divisible by 3 and lying between 35 and 95 are 36, 39, 42,….
    These form an AP with the first term a = 36 and the common difference d = 3
    The last term is 93 and it is given by 93 = 36+(n-1)*3
    (93-36)/3=n-1
    19=n-1
    n=19+1=20
    Sum of n terms of an AP is given by
    Sn=n/2[2a+(n-1)d]
    =20/2[2*36+(20-1)*3]
    =10(72+57)
    =10*129
    = 1290
    Option A is correct.




Question – 12

12. Seven-letter words are formed by the letters of the word EQUATION.?

Column-A Column-B
Number of words that end in a vowel Number of words having a vowel in the third place



  • A. If the quantity on the left is greater


  • B. If the quantity on the right is greater


  • C. If both are equal


  • D. If the relationship cannot be determined without further information


  • Answer:C

  • Answer Explanation:
    There are 5 vowels and 3 consonants in the word EQUATION.
    The last letter of the 7 letter words can be filled in 5 ways
    The remaining 6 places can be filled by remaining 7 letters in P(7,6) ways
    P(7,6) = 7!/(7-6)!
    = 7!/1!=7*6*5*4*3*2= 5040 ways
    Total words = 5*5040 = 25200Similarly, the third place can be filled in 5 ways and the remaining places can be filled in P(7,6) ways.
    Option C is correct.




Question – 13

13. The parallel sides of a trapezium are 28m and 12m. The area of the trapezium is 180 sq.m.?

Column-A Column-B
Distance between the parallel sides 18 cm



  • A. If the quantity on the left is greater


  • B. If the quantity on the right is greater


  • C. If both are equal


  • D. If the relationship cannot be determined without further information


  • Answer:A

  • Answer Explanation:
    Area of trapezium= 1/2(sum of parallel sides)*distance between parallel sides
    180= 1/2*(28+12)*Distance
    180*2/40= Distance
    Distance = 9 m
    9m>18cm
    Option A is correct.




Question – 14

14. The volume of a solid sphere A is 87.5% less than the volume of solid sphere B.?

Column-A Column-B
Percent of surface area of A that the surface area of B is Percent of radius of A that the radius of B is



  • A. If the quantity on the left is greater


  • B. If the quantity on the right is greater


  • C. If both are equal


  • D. If the relationship cannot be determined without further information


  • Answer:A

  • Answer Explanation:
    Let r and R be the radii of sphere A and sphere B respectively.
    Volume of sphere A = 4/3*pi*r^3
    Volume of sphere B = 4/3*pi*R^3
    According to the conditions, we have
    Volume of A = volume of B – 87.5% volume of B
    4/3*pi*r^3 = 4/3*pi*R^3 – 87.5/100*4/3*pi*R^3
    r^3=R^3-875/1000*R^3
    r^3=(1000-875)/1000*R^3
    r^3= 125/1000*R^3
    Taking cube root on both sides, we get
    r = 5/10*R
    R=2rPercentage of radius = R/r*100
    = 2r/r*100
    = 200%

    Percentage of surface area = Surface area of B/surface area of A *100
    = 4pi*R^2/(4pi*r^2)*100
    = R^2/r^2*100
    = (2r)^2/r^2*100
    = 4r^2/r^2*100
    = 400%

    Option A is correct.
    [r^3=r*r*r]




Question – 15

15.

Column-A Column-B
The maximum possible value of x when 10^x divides 10*11*…*20 The maximum possible value of x when 2^x divides 20*21*…*30

(Note: [10^x=10*10*10…x times])

  • A. If the quantity on the left is greater


  • B. If the quantity on the right is greater


  • C. If both are equal


  • D. If the relationship cannot be determined without further information


  • Answer:B

  • Answer Explanation:
    Consider the product 10*11*…*20
    The number of zeros can be calculated by multiplying the digits in the unit’s place in the product
    10*12*15*20 = 10*180*20
    = 36000
    No other combination of numbers shall give a product ending in 0.
    The product is divisible by 10^3
    The maximum value of x is 3.20*21*22*…*30 = (2*2*5)*21*(2*11)*23*(2*2*2*3)*25*(2*13)*27*(2*2*7)*29*(2*15)
    2^10 can divide the product.

    Option B is correct.




Score: 0/10



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