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AFCAT - HCF & LCM Test 988
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AFCAT - HCF & LCM Test 988

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  • Question 1/5
    1 / -0.33
    Sum of two numbers is 304; H.C.F of the numbers is 38. The difference of the numbers is –
    Solutions

    Let the numbers be  where are co-primes.

    Possible and acceptable pairs of x and y satisfying the condition are: (1, 7) and (3, 5)

    Numbers are: 38 × 1 = 38 and 38 × 7 = 266

    & 38 × 3 = 114 and 38 × 5 = 190

    Required difference = 266 – 38 = 228

    Option C is correct.

  • Question 2/5
    1 / -0.33
    The least number which when divided by 21, 25 and 36 leaves 6 as the remainder in each case but when divided by 11 leaves no remainder is
    Solutions

    LCM of 21, 25 and 36 = 6300

    Required number = 6300K + 6 which is exactly divisible by 11 for certain value of K.

    When K = 2

    Number = 6300 × 2 + 6 = 12606 which is exactly divisible by 11.

    So, option D is correct.

  • Question 3/5
    1 / -0.33
    Let a, b be positive integers. What is HCF   equal to?
    Solutions

    Let us consider any value of a, b such that a and b are positive integer.

    For a=21 and b = 12
    H.C.F (a, b)= H.C.F(21, 12) = 3.

    Now H.C.F (a/H.C.F.(a,b),b/H.C.F.(a,b)
    =H.C.F.(21/3,12/3)
    = H.C.F. (7, 4) = 1
    For any value of positive integer a and b H.C.F.
    (a/H.C.F.(a,b),b/H.C.F.(a,b)) will always give '1' as answer.

  • Question 4/5
    1 / -0.33
    For any integer n, what is HCF (22n + 7, 33n + 10) equal to ?
    Solutions

    For any integer n.

    H.C.F. (22n + 7, 33n + 10)

    Now for n = 0, H.C.F. (7, 10) = 1

    for n = 1, H.C.F.(29, 43) = 1

    Hence for any integer n,

    H.C.F. (22n + 7, 33n + 10) equal to 1

  • Question 5/5
    1 / -0.33
    If the HCF of two numbers is 21 & their LCM is 4641. If one of the number is in is between 200 & 300 then what are the numbers.
    Solutions

     If HCF=21

    then let first number= 21a

    second number=21b

    Now LCM= 21ab= 4641

    ⇒ ab =221

    If ab= 221

    Then possible pairs of a & b is (221,1) & (13,17)

    But as one number is in between 200 and 300 then

    First number = 21 × 13=273

    Second number= 21 × 17 = 357

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