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Quiz: Number System and HCF & LCM

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Number of Questions: 43

Question: 31 -

Which natural number is nearest to 8485, which is completely divisible by 75 ?

Options:

  1. 8500

  2. 8475

  3. 8550

  4. 8525

    5. Answer:

    8475
    Solution:

    On dividing we get

    75)8485(113
         75
         ------
           98
           75
          ------
           235
           225
          ------
             10
          ------
    Required number = (8485-10)=8475.

Question: 32 -

How many terms are in the G.P. 3, 6, 12, 24, ......., 384 ?

Options:

  1. 10

  2. 11

  3. 9

  4. 8

    5. Answer:

    8
    Solution:

    Here a = 3 and r = 6/3 = 2. Let the number of terms be n.
    Then, t = 384 => a * r^(n-1) = 384
    => 3 * 2^(n-1) = 384 => 2^(n-1) = 128 = 2^(7)

    => n-1 = 7 => n = 8.

Question: 33 -

On dividing 2272 as well as 875 by 3-digit number N,we get the same remainder. The sum of the digits of N is:

Options:

  1. 13

  2. 10

  3. 11

  4. 12

    5. Answer:

    10
    Solution:

    (2272-875) = 1397, is exactly divisible by N.
    Now , 1397 = 11 x 127
    The required 3-digit number is 127
    the sum of digits is 10.

Question: 34 -

Which one of the following cannot be the square of a natural number?

Options:

  1. 81225

  2. 20164

  3. 32761

  4. 42437

    5. Answer:

    42437
    Solution:

    The square of a natural number never ends in 7.
    42437 is not the square of a natural number

Question: 35 -

If 60% of 3/5 of a number is 36, then the number is

Options:

  1. 115

  2. 94

  3. 86

  4. 100

    5. Answer:

    100
    Solution:

    Let the number be x.Then
    => 60% of 3/5of x=36.
    => (60/100*3/5*)x=36
    => 9x/25=36 => x=25*36/9=100

     Required number is 100.