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If m and n are positive integers...

This topic has 1 expert reply and 0 member replies

If m and n are positive integers...

Post Wed Nov 08, 2017 7:10 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    If m and n are positive integers such that m>n, what is the remainder when m^2-n^2 is divided by 21?

    1) The remainder when (m+n) is divided by 21 is 1.
    2) The remainder when (m-n) is divided by 21 is 1.

    The OA is C.

    Please, can any expert explain this DS question for me? I have many difficulties to understand why that is the correct answer. Thanks.

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
    Post Wed Nov 08, 2017 11:09 pm
    swerve wrote:
    If m and n are positive integers such that m>n, what is the remainder when m^2-n^2 is divided by 21?

    1) The remainder when (m+n) is divided by 21 is 1.
    2) The remainder when (m-n) is divided by 21 is 1.

    The OA is C.

    Please, can any expert explain this DS question for me? I have many difficulties to understand why that is the correct answer. Thanks.
    We have to get the remainder when (m^2 - n^2) is divided by 21.

    1) The remainder when (m+n) is divided by 21 is 1.

    Say m + n = 21a + 1; where a is any integer (quotient)

    We cannot conclude on this basis whether (m^2 - n^2) is divisible by 21. Insufficient.

    2) The remainder when (m-n) is divided by 21 is 1.

    Say m - n = 21b + 1; where b is any integer (quotient)

    We cannot conclude on this basis whether (m^2 - n^2) is divisible by 21. Insufficient.

    (1) and (2) combined:

    From both the statements, we get that m^2 - n^2 = (21a + 1)*(21b + 1) = 21^2.ab + 21b + 21a + 1

    Since 21^2.ab + 21b + 21a is divisible by 21, the remainder when 21^2.ab + 21b + 21a + 1 divided by 21 is 1. Sufficient.

    The correct answer: C

    Hope this helps!

    -Jay
    _________________
    Manhattan Review GMAT Prep

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    Thanked by: swerve

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