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If m and n are positive integers such that m > n, what is the Re.

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If m and n are positive integers such that m > n, what is the Re.  [#permalink]

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New post 17 Oct 2016, 13:14
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If m and n are positive integers such that m > n, what is the remainder when m^2 – n^2 is divided by 21?

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

Statement 2: The remainder when (m – n) is divided by 21 is 1.

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Re: If m and n are positive integers such that m > n, what is the Re.  [#permalink]

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New post 17 Oct 2016, 13:30
stonecold 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?

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

Statement 2: The remainder when (m – n) is divided by 21 is 1.


FROM STATEMENT - I ( INSUFFICIENT)

We do not have any relationship between the value of m & n as such it won't be possible for us to find the remainder of \(\frac{(m^2 – n^2)}{21}\), since m & n can take any values...

FROM STATEMENT - I ( INSUFFICIENT)

We do not have any relationship between the value of m & n as such it won't be possible for us to find the remainder of \(\frac{(m^2 – n^2)}{21}\), since m & n can take any values...

COMBINE STATEMENT I & II (SUFFICIENT)

\(\frac{(m^2 – n^2)}{21} = \frac{( m+n )( m-n )}{21}\) = \(Remainder \ 1\)

Hence BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked, answer will be (C)


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Re: If m and n are positive integers such that m > n, what is the Re.  [#permalink]

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New post 29 Mar 2018, 02:34
stonecold 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?

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

Statement 2: The remainder when (m – n) is divided by 21 is 1.


Bunuel, pushpitkc : Please bring some light on this question using number plugging technique.

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Re: If m and n are positive integers such that m > n, what is the Re. &nbs [#permalink] 29 Mar 2018, 02:34
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If m and n are positive integers such that m > n, what is the Re.

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