If m and n are positive integers where mn, and if z is and odd prime

Question

If m and n are positive integers where m>n, and if z is and odd prime number, is m divisible by z?

(1) (m + n)^2 is divisible by z
(2) (m - n)^2 is divisible by z

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Laila12618 · Answer

Hi Bunuel,

could you elaborate the reason why answer C is correct? I arrived at the point where neither statement A nor statement B alone is sufficient to answer the question and went for answer E…

Posted from my mobile device

Bunuel · Answer

If m and n are positive integers where m>n, and if z is and odd prime number, is m divisible by z?

(1) (m + n)^2 is divisible by z

Since m and n are integers, then if (m + n)^2 is divisible by z, it implies that m + n is divisible by z. How else would z appear in (m + n)^2 if it's not present as a factor in m + n? However, m + n being divisible by z does not necessarily mean that m is divisible by z. Not sufficient.

(2) (m - n)^2 is divisible by z

Similarly, we can deduce that m - n is divisible by z. However, this again is insufficient to determine whether m is divisible by z.

(1)+(2) From the above, we know that m + n = (a multiple of z) and m - n = (a multiple of z). If we sum these two equations, we get 2m = (a multiple of z). Given that z is an odd prime, then for 2m to be a multiple of z, z itself must be a multiple of z. Sufficient.

Answer: C.

Hope it helps.

Laila12618 · Answer

That clarifies, many thanks!!

bumpbot · Answer

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If m and n are positive integers where m>n, and if z is and odd prime

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