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Quiz: Number System and HCF & LCM

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Number of Questions: 43

Question: 11 -

Three numbers which are co-prime to each other are such that the product of the first two is 119 and that of the last two is 391. What is the sum of the three numbers?

Options:

  1. 53

     

  2. 41

  3. 47

  4. 51

    5. Answer:

    47
    Solution:

    Since the numbers are co-prime, their HCF = 1
    Product of first two numbers = 119
    Product of last two numbers = 391
    The middle number is common in both of these products. Hence, if we take HCF of 119 and 391, we get the common middle number.
    HCF of 119 and 391 = 17
    => Middle Number = 17
    First Number =119/17=7
    Last Number =391/17=23
    Sum of the three numbers = 7 + 17 + 23 = 47

Question: 12 -

What is the HCF of 2.04, 0.24 and 0.8 ?

Options:

  1. 0.02

  2. 0.04

  3. 1

  4. 2

    5. Answer:

    0.02
    Solution:

    Step 1: Make the same number of decimal places in all the given numbers by suffixing zero(s) in required numbers as needed.
    => 2.04, 0.24 and 0.80

    Step 2: Now find the HCF of these numbers without decimal.
    => HCF of 204, 24 and 80 = 4

    Step 3: Put the decimal point in the result obtained in step 2 leaving as many digits on its right as there are in each of the numbers.
    i.e., here we need to put decimal point in the result obtained in step 2 leaving two digits on its right.
    => HCF of 2.04, 0.24 and 0.8 = 0.04

Question: 13 -

Which of the following is a prime number ?

Options:

  1. 8

  2. 4

  3. 2

  4. 9

    5. Answer:

    2
    Solution:

    2 is a prime number. A prime number is a natural number greater than 1 which has no positive divisors other than 1 and itself. Hence the primer numbers are 2,3,5,7,11,13,17,…

Question: 14 -

What is the greatest number which on dividing 1223 and 2351 leaves remainders 90 and 85 respectively?

Options:

  1. 1133

  2. 1100

  3. 127

  4. 42

    5. Answer:

    1133
    Solution:

    Required number 
    = HCF of (1223 - 90) and (2351 - 85)
    = HCF of 1133 and 2266
    = 1133

Question: 15 -

Six bells start ringing together and ring at intervals of 4, 8, 10, 12, 15 and 20 seconds respectively. How many times will they ring together in 60 minutes ?

Options:

  1. 30

  2. 16

  3. 31

  4. 15

    5. Answer:

    31
    Solution:

    LCM of 4, 8, 10, 12, 15 and 20 = 120
    120 seconds = 2 minutes
    Hence all the six bells will ring together in every 2 minutes
    Hence, number of times they will ring together in 60 minutes 
    = 1 + 60/2 = 31