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MAT (Stage-2) Mock Test - 30

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Weekly Quiz Competition
  • Question 1
    1 / -0

    The difference between the squares of two consecutive odd integers is always divisible by

    Solution

    Let the two consecutive odd integers be (2x + 3) and (2x + 1).
    Then,
    (2x + 3)2 - (2x + 1)2
    = 4x2 + 9 + 12x - 4x2 - 1 - 4x
    = 8 + 8x
    = 8(1 + x), which is divisible by 8

     

  • Question 2
    1 / -0

    A number, when divided by 114, leaves a remainder of 21. If the same number is divided by 19, the remainder will be

    Solution

    Any number divisible by 114 will also be divisible by 19 because 114 is a multiple of 19.
    When the number is divided by 114, it leaves a remainder of 21.
    If 21 is divided by 19, then the remainder will be 2.

     

  • Question 3
    1 / -0

    Two out of six papers for an examination are of physics. What are the number of ways in which the papers can be arranged so that two physics papers are not together?

    Solution

    Arrangement of total number of papers = 6! or 720
    Number of ways when two physics papers are set together = 5! × 2 = 240
    So, required number of ways = 720 - 240 = 480

     

  • Question 4
    1 / -0

    The average monthly rainfall for a year in Tokyo is 2.7 inches. The average for the first 7 months is 1.1 inches less than the annual average. If the total rainfall for the next 4 months is 20.8 inches, calculate the rainfall in the last month.

    Solution

    Annual rainfall = 2.7 × 12 = 32.4 inches
    Total rainfall of first 7 months = (2.7 - 1.1) × 7 = 11.2 inches
    Rainfall in last month = annual rainfall – [total rainfall of first 7 and next 4 months]
    = 32.4 – [11.2 + 20.8] = 32.4 – 32 = 0.4 inches

     

  • Question 5
    1 / -0

    The average score of 60 students in a class is 32.5. What will be the new average if the score of one student is altered from 88 to 78 and the score of another is altered from 13 to 43?

    Solution

    Total score of 60 students = 60 × 32.5 = 1950
    Decrease in the score of first student = 88 - 78 = 10
    Increase in the score of second student = 43 - 13 = 30
    ∴Newtotal score = 1950 - 10 + 30 = 1970
    New average = 1970/60
    = 32.83

     

  • Question 6
    1 / -0

    In 21 kg of an alloy, the ratio of copper to zinc by mass is 5 : 2. If 4 kg of copper is added to the alloy, then what will be the new ratio of zinc to copper?

    Solution

    Mass of copper present in 21 kg of alloy = [5/(5 + 2)] x 21 = 15 kg
    Mass of zinc = 21 - 15 = 6 kg
    New mass of copper = 15 + 4 = 19 kg
    Hence, ratio of zinc to copper by mass = 6 : 19

     

  • Question 7
    1 / -0

    Rs. 1400 is divided among three labourers: K, L and M in such a way that the ratio of L's share and K's share is 3 : 2 and the ratio of M's share and L's share is 5 : 4.

    Which of the following is K's share?

    Solution

    Let the shares of K, L and M be x, y and z, respectively.
    Given: x : y = 2 : 3 = 8 : 12
    y : z = 4 : 5 = 12 : 15
    Hence, x : y : z = 8 : 12 : 15
    Therefore, K's share = [8/(8+12+15)] x 1400 = 8/35 × 1400 = Rs. 320

     

  • Question 8
    1 / -0

    A can do a piece of work in 20 days, while B can do it in 12 days. B works for 9 days and then leaves. In how many days can A alone finish the remaining work?

    Solution

    B's 1 day's work = 1/12
    ∴ B's 9 days' work = 9/12
    Remaining work = 1 - 9/12 = 3/12
    Now, A takes 20 days to complete the whole work.
    Time taken by A to complete 3/12 of the work = 20 x 3/12 = 5 days

     

  • Question 9
    1 / -0

    The speed of a boat in still water is 10 m/s and the speed of stream is 6 m/s. If the boat goes upstream and comes back downstream, then what is the ratio of the time taken to cover a particular stretch of distance in each direction?

    Solution

    Let the distance be x m.
    Speed of boat upstream = 10 - 6 = 4 m/s
    Speed of boat downstream = 10 + 6 = 16 m/s
    Time taken by boat downstream = x/16 s
    Time taken by boat upstream = x/4 s
    Required ratio = x/4 : x/16
    = 4 : 1

     

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