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CAT Quantitative Aptitude Questions - Tests of Divisibility

Nov 20, 2018 16:59 IST

    CAT Quantitative Aptitude has questions on Test of Divisibility concepts. A natural number can be checked for divisibility by other natural numbers quickly in special cases as follows:

    • By Primes:

    Tests for divisibility by the following primes use the digits of the given number. The number is divisible

    By 2: If the last digit is even (i.e. divisible by 2)

    By 3: If the sum of digits is divisible by 3

    By 5: If the last digit is either 0 or 5 (i.e. divisible by 5)

    By 11: If the difference between the sum of the digits in even places and the sum of the digits in odd places is divisible by 11

     

    • By Powers of Primes:

     

    By 4 (= 2⊃2;): If the number formed by the last two digits is divisible by 4

    By 8 (=2⊃3;): If the number formed by the last three digits is divisible by 8

    By 2 k: If the number formed by the last k digits is divisible by 2k

    By 9: If the sum of the digits is divisible by 9

    By 25 (= 5⊃2;): If the number formed by the last two digits is divisible by 25

    By 125 (= 5⊃3;): If the number formed by the last three digits is divisible by 125

    By 5k: If the number formed by the last k digits is divisible by 5k

     

    • By Other Composite Numbers:

    In this case we need to check for divisibility by each prime power that divides the given number.

    For example:

    By 6: Check for divisibility by 2 and by 3

    By 12: Check for divisibility by 4 and by 3

    By 22: Check for divisibility by 2 and by 11 etc.

    Examples: (1) 475 is divisible by 25 but not by 125.

    (2) 465 is divisible by 5 but not by a higher power of 5.
    As 4 + 6 + 5 = 15, it is divisible by 3 though.

    (3) To check for divisibility of 8976730213 by 11, we first form the two sums: 8 + 7 + 7 + 0 + 1 (= 23) and 9 + 6 + 3 + 2 + 3 (= 23)

    then find the difference between the two 23 -23 = 0.

    As 0 is divisible by 11, so is the number 8976730213.
    (8976730213 = 11 × 816066383).

    Now you can apply the concept to solve the toughest CAT Quantitative Aptitude Questions.

    Good Luck for CAT 2018!!

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