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Quantitative Aptitude (QA) Test - 24

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Quantitative Aptitude (QA) Test - 24
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  • Question 1
    3 / -1

    A thief is running on a circular track of radius 5 m at 1.5 m / s . A policeman whose speed is twice that of the thief arrived at the starting point of the track 4 seconds after the thief. The policeman can either run along the circular track in the direction of the thief or go to the centre and then go to any point on the circle from the centre. Find the minimum distance covered by the thief after the policeman starts chasing him.

    Solution

    When the policeman arrives, the thief has traveled 6 meters.

    So, the time taken by the policeman to catch the thief along the circular track = 6/1.5 = 4 seconds.

    The total distance covered by the policeman = 12 meters.

    Thus, the minimum distance is when the policeman takes the route via the center i.e. he travels a length of 2 x 5 = 10 meters.

    The minimum time taken = 10/3 seconds.

    The minimum distance covered by the thief = 1.5 x (10/3) = 5 meters

    Hence, option 3.

     

  • Question 2
    3 / -1

    If x = 44 x 56 x 65 x 710 x 88, then how many factors of x are of the form 6 A2?

    Solution

     x = 44 x 56 x 65 x 710 x 88

    ⇒ x = 237 x 35 x 56 x 710 = (2 x 3) (236 x 34 x 56 x 710)

    Power of 2 can take values of 0, 2 , 4 , . . . , 36 = 19

    Power of 3 can take values of 0, 2,4 = 3

    Power of 5 can take values of 0, 2,4, 6 = 4

    Power of 7 can take values of 0, 2,4, 6, 8, 10 = 6

    Total number of factors = 19 x 3 x 4 x 6 = 1368

     

  • Question 3
    3 / -1

    x is a positive integer with value at most equal to 110. How many values of x are possible if x is not a factor of (x - 1)!?

    Solution

    If x is a prime number greater than 1, then x is not a factor of (x - 1)!

    There are 29 primes up to 110. 4 is also one such number.

    Hence, option 4.

     

  • Question 4
    3 / -1

    The speed of a boat in still water is 24 kmph. If it can travel 20 km downstream in the same time as it can travel 12 km upstream, then it is ______ times as fast as the stream. Key in the number.

    Solution

    Let the speed of the stream be v kmph.

    Speed of boat in still water is 24 kmph.

    Hence, the speed of boat upstream is (24 – v) kmph and the speed of boat down stream is (24 + v) kmph.

    Putting v = 6 kmph:

    Thus, the speed of boat in still water is 4 times as fast as the speed of the stream.

     

  • Question 5
    3 / -1

    Find the minimum value of the quadratic expression 3x2 + 11x - 23.

    Solution

    The minimum value of a quadratic expression ax2 + bx + c (when a > 0) occurs at x = -b / 2a and its minimum value is -(b2 - 4ac) / 4a

    The minimum value of the equation is = [4(3)(-23) - (11)2]/12 = -397 / 12

    Hence, option 4.

     

  • Question 6
    3 / -1

    50 square stone slabs of equal size were needed to cover, a floor area of 72 sq. m. The length of each stone slab is :

    Solution

    Area of each slab = 72 / 50 m2 = 1.44 m2

    Length of each slab =√1.44 =1.2m =120cm

     

  • Question 7
    3 / -1

    37% of the total number of people in a city read newspaper ABC and exceed the number of people who read XYZ by 8000. If 27% of the total population do not read any newspaper then find the population of the city if there are only two newspapers in the city. [Assume that no one reads more than one newspaper].

    Solution

    Let the total population of the town be x.

    The number of people who read XYZ = 0.37x - 8000

    0.37x+0.37x - 8000 + 0.27x = x

    ⇒ x = 8,00,000

    Hence, option 1.

     

  • Question 8
    3 / -1

    If x2 + x - 2 < 0; then which of the following statement is true?

    1. x - 1 > 0
    2. x - 1 < 0
    3. x + 2 > 0
    4. x - 2 < 0

    Solution

    x2 + x - 2 < 0

    ⇒ (x - 1) (x + 2) < 0

    ⇒ (x - 1) < 0 and (x + 2) > 0 or (x - 1) > 0 and (x + 2) < 0

    ⇒ x < 1, x > -2 or x > 1, x < -2 which is not possible.

    ∴ -2 < x < 1

    ⇒ (x - 1) < 0 and (x + 2) > 0 

    Hence, option 3.

     

  • Question 9
    3 / -1

    At 12:00 AM both the hour and a minute hand were overlapping each other. How many more minutes does the minute hand travel than the hour hand in the next 54 minutes?

    Solution

    When the minute hand travels 60 minutes, the hour hand travels 5 minutes.

    The minute hand travels 55 minutes more than the hour hand in an hour.

    In 54 minutes, the Minute hand travels = (54 x 55/ 60) = 49.5

    Hence, option 3.

     

  • Question 10
    3 / -1

    A and B start working together on a project and both have the same efficiency in the beginning. However the efficiency of A decreases to 0.6 times the usual after working for 2 hours. If the project can be finished in 120 man hours, then find the minimum number of days required to finish the work if both do an equal manhours of work each day and the sum of the total number of hours of work by both each day is 12. [ Initial efficiency of A = Efficiency of B = 1 man hour].

    Solution

    Let the number of hours worked by B be x.

    The hours worked by A = (12 - x)

    The manhours of work finished by A = (12 - x - 2) x 0.6 + 2

    ∵ (12 - x - 2) x 0.6 + 2 = x

    ⇒ x = 5

    The total manhours of work done by them in a day = 2 * x = 2 * 5 = 10

    Thus, the number of days required to finish the work = 120/10 =12 days

    Hence, option 2.

     

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