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The digital sum of a number is the sum of its digits.

This topic has 2 expert replies and 0 member replies

The digital sum of a number is the sum of its digits.

Post Thu Nov 02, 2017 8:36 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    The digital sum of a number is the sum of its digits. For how many of the positive integers 24-125 inclusive is the digital sum a multiple of 7?

    A 7
    B 8
    C 14
    D 16
    E 20

    The OA is C.

    Do I have to make the entire list? Is there another way to solve this PS question? Experts, I want to see you explanation for this exercise. Thanks.

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    Post Thu Nov 02, 2017 9:16 am
    Vincen wrote:
    The digital sum of a number is the sum of its digits. For how many of the positive integers 24-125 inclusive is the digital sum a multiple of 7?

    A 7
    B 8
    C 14
    D 16
    E 20
    Listing and counting is a fast approach.
    25
    34
    43
    52
    61
    70
    106
    115

    Answer: B

    Cheers,
    Brent

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    Post Fri Nov 03, 2017 1:55 pm
    Hi Vincen,

    Based on the answer choices, you know that there are at least 7 numbers that fit the given description, but no more than 20. Thus, listing them all out shouldn't be too difficult. You might also find it useful to organize your numbers by 'group'

    We're restricted to the numbers 24 to 125, inclusive. We're asked to find the numbers whose digits add up to a MULTIPLE of 7:

    Numbers with digits that add up to 7:
    25 and 52
    34 and 43
    61
    70
    106
    115
    124

    Numbers with digits that add up to 14:
    59 and 95
    68 and 86
    77

    Total numbers = 9+5 = 14

    Final Answer: C

    GMAT assassins aren't born, they're made,
    Rich

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