Question Bank - Arithmetic - Shashank Prabhu, CAT 100 Percentiler

  • Q11) The average of temperatures at noontime from Monday to Friday is 50; the lowest one is 45, what is the maximum possible range of the temperatures?

    [OA: 25]

  • Q14) A and B ran, at their respective constant rates, a race of 480 m. In the first heat, A gives B a head start of 48 m and beats him by 1/10th of a minute. In the second heat, A gives B a head start of 144 m and is beaten by 1/30th of a minute. What is B’s speed in m/s?

    [OA: 12 m/s]

  • Q16) A container has 3L of pure wine. 1L from the container is taken out and 2L water is added.The process is repeated several times. After 19 such operations, quantity of wine in mixture is

    A. 2/7 L
    B. 3/7 L
    C. 6/19 L
    D. None of these

    [OA: Option A]

  • Q19) A combo pack having a bulb and a tubelight costs Rs. 52. If the cost of the bulb drops by 20% and the cost of the tubelight escalates by 50%, the pack would cost Rs. 50. Find the cost of a tubelight (in Rs.)

    [OA : 12 Rs]

  • Q20) M is a set of distinct positive integers whose average is 55. If a number 68 is added to this set, the average increases by 1. What is the largest number that can occur in this set?

    [OA: 594]

  • Q23) Vessel 1 contains 5 liters of alcohol and vessel 2 contains 5 liters of water. A glass of alcohol is taken from the first vessel and poured into the second vessel. The same glass is used to transfer back the new mixture from vessel 2 to vessel 1. What can be said about the percentage of alcohol in vessel 2 and the percentage of water in vessel 1?

    a. The former is greater than the latter
    b. The two are equal
    c. The latter is greater than the former
    d. Will not be consistent and will vary depending on the capacity of the glass

    [OA: Option b]

  • Q26) A combo pack having a bulb and a tubelight costs Rs. 52. If the cost of the bulb drops by 20% and the cost of the tubelight escalates by 50%, the pack would cost Rs. 50. Find the cost of a tubelight (in Rs.)

    [OA: 12 Rs]

  • Q28) Ram and Shyam run a race between points A and B, 5 km apart, Ram starts at 9 a.m from A at a speed of 5 km/hr, reaches B, and returns to A at the same speed, Shyam starts at 9:45 a.m. from A at a speed of 10 km/hr, reaches B and comes back to A at the same speed.

    1. At what time do Ram and Shyam first meet each other?
      (1) 10 a.m
      (2) 10:10 a.m
      (3) 10:20 a.m
      (4) 10:30 a.m.

    2. At what time does Shyam over take Ram?
      (1) 10:20 a.m
      (2) 10:30 a.m
      (3) 10:40 a.m
      (4) 10:50 a.m

    [OA: Option 2, Option 2]

  • Q30) A jogging park has two identical circular tracks touching each other, and a rectangular track enclosing the two circles. The edges of the rectangles are tangential to the circles. Two friends, A and B, start jogging simultaneously form the point where one of the circular tracks touches the smaller side of the rectangular track. A jogs along the rectangular track, while B jogs along the two circular tracks in a figure of eight. Approximately, how much faster than A does B have to run, so that they take the same time to return to their starting point?
    (1) 3.88%
    (2) 4.22%
    (3) 4.44%
    (4) 4.72%

    [OA: Option 4]

  • Q31) Dhurandhar deposits some money in Lena Bank at the rate of 20% p.a. simple interest. He withdraws the money after one year, deposits it in Parajaya Bank at the rate of R% p.a. compound interest (with annual compunding) for two years and gets Rs 2880 as the total interest from Parajaya Bank. If the first year’s interest at Parajaya Bank was Rs 1200, then what amount (in Rs) had Dhurandhar deposited in Lena Bank?

    [OA: 2500]

  • Q33) An outgoing batch of students wants to gift PA system worth Rs.4200 to their school. If the teachers offer to pay 50% more than the students, and an external benefactor gives three times teachers’ contribution, how much should the teachers donate?

    [OA: 900]

  • Q42) The road from village P to village Q is divided into three parts. If the first section were 1.5 times as long as it is now and the second one were 2/3 as long as it is now, then the three parts would be all equal in length. What fraction of the total length of the road is the third section?

    [OA: 5/18]

  • Q45) Ramesh and Shyam are competing in 2000 m race. Ramesh gives Shyam a lead of 200 m . Initially Ramesh runs at 4 times Shyam’s speed, but after crossing the 1200 m mark, he slows down to 1/8th of this initial speed, while Shyam continues to run at his original speed. If Ramesh and Shyam meet for the second time at distance ‘a’ m from the finishing line then find ‘a’.

    [OA: 100]

  • Q55) A particular month has 5 Tuesdays. The first and the last day of the month are not Tuesday. What day is the last day of the month?

    [OA: Wednesday]

  • Q59) Every blip is a blop. Half of all blops are blips, and half of all bleeps are blops. There are 30 bleeps and 20 blips. No bleep is a blip. How many blops are neither blips nor bleeps?

    [OA : 5]

  • Q64) Mr. X sold two books, one at a loss of 11.11% and the other at a gain of 25%. If the two books had cost him the same, what was his approximate overall gain/loss?

    [OA: 6.9 % Profit]

  • Q70) The speed of a railway engine is 45 kmph when no bogie is attached to it. It is observed that the reduction in the speed of the engine is directly proportional to the square root of the number of bogies attached to it. If the speed of the train is 9 kmph when 16 bogies are attached, find the maximum number of bogies that can be carried by the engine.

    [OA: 24]

  • Q83) A total number of 140 criminals in a jail are divided into three groups A, B and C. The average number of crimes committed by criminals of groups A, B and C are 10, 12.25 and 13 respectively. If there are a total of 45 criminals in group C, which of the following is true regarding K, where K is the average number of crimes committed by all the 140 criminals put together?
    a) K could be less than 11
    b) K must be greater than 11
    c) K must be greater than 12
    d) K cannot be greater than 12

    [OA: Option b]

  • Q85) A plane travelled a certain distance at a uniform speed. Had the speed been 216 kmph more, the journey would have taken one hour less and had the speed been 108 kmph less, the journey would have taken one hour more. Find the distance (in km) travelled by the plane.

    [OA: 1296]

  • Q92) Himanshu, Saral and Vikas start running from the same point in the same direction along a straight line at 07 : 00 a.m., 08 : 00 a.m. and 10 : 00 a.m. with speeds of 2 kmph, 3 kmph and 4 kmph respectively. When Saral catches Himanshu he sends Himanshu back (along the straight line) immediately to deliver a message to Vikas. At what time would Himanshu meet Vikas?

    [OA: 11 AM]

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