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Quiz: Number System and HCF & LCM

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Number of Questions: 43

Question: 41 -

What is the smallest number by which 2880 must be divided in order to make it into a perfect square ?

Options:

  1. 4

  2. 3

  3. 2

  4. 5

    5. Answer:

    5
    Solution:

    By trial and error method, we get
    2880/3 = 960 is not a perfect square
    2880/4 = 720 is not a perfect square
    2880/5 = 576 which is perfect square of 24
    Hence, 5 is the least number by which 2880 must be
     divided in order to make it into a perfect square.

Question: 42 -

A solid cube of side 6 is first painted pink and then cut into smaller cubes of side 2. How many of the smaller cubes have paint on exactly 2 sides?

Options:

  1. 8

  2. 30

  3. 12

  4. 24

    5. Answer:

    12
    Solution:

    When the larger cube is cut into smaller cubes,  the corner cubes will have paint on three sides. The cubes in the middle of the faces will have paint on only one side, but the cubes cut from the edges will have paint on two sides. In this case, there will be only one cube one each edge (excluding the corners), and since there are 12 edges, there will be 12 cubes with paint on two sides.

Question: 43 -

Courier charges for packages to a certain destination are 65 cents for the first 250 grams  and 10 cents for each additional 100 grams or part thereof. What could be the weight in grams of a package for which the charge is $1.55 ?

Options:

  1. 1155

  2. 1145

  3. None of these

  4. 1040

    5. Answer:

    1145
    Solution:

    The weight will be 250g plus (1.55 - 0.65)/0.10 units 
    of 100g
    => 250 + 900 = 1150
    This is the maximum weight that can be sent at that price. But, weights exceeding, 250 + 800 will also get charged this amount (that is what the ‘part thereof’ implies).
    Hence a package weighing 1145 will be charged
     => $1145