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If m is a positive integer and m^2 is divisible by 48, then

This topic has 1 expert reply and 0 member replies

If m is a positive integer and m^2 is divisible by 48, then

Post Thu Nov 02, 2017 9:40 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    If m is a positive integer and m^2 is divisible by 48, then the largest positive integer that must divide m is?

    (A) 3
    (B) 6
    (C) 8
    (D) 12
    (E) 16

    Is there a strategic approach to this question? Can any experts help?

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
    Post Thu Nov 02, 2017 4:05 pm
    Quote:
    If m is a positive integer and m^2 is divisible by 48, then the largest positive integer that must divide m is?

    (A) 3
    (B) 6
    (C) 8
    (D) 12
    (E) 16

    Is there a strategic approach to this question? Can any experts help?
    Hi ardz24,
    Let's take a look at your question.

    The question states:
    "If m is a positive integer and m^2 is divisible by 48, then the largest positive integer that must divide m is? "

    The largest positive integer that must divide m will be m itself.
    One way to solve this question is to check each of the option if it is true or not.
    For that purpose, square each of the given options and find out if it is divisible by 48 or not.

    Let's start from option A.
    Let m = 3 then m^2 = 9
    9 is not divisible by 48 because it is less than 48.

    Option B
    Let m = 6 then m^2 = 36
    36 is not divisible by 48 because it is less than 48.

    Option C
    Let m = 8 then m^2 = 64
    64 is not divisible by 48 because it gives a decimal quotient when we try to divide 64 by 48.

    Option D
    Let m = 12 then m^2 = 144
    144 is divisible by 48 because 144/48 = 3

    Hence, the largest positive integer that must divide m is 12.
    Therefore, Option D is correct.

    Hope it helps.
    I am available if you'd like any follow up.

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