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If m and n are positive integers, what is the remainder when m^2 - n^2

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If m and n are positive integers, what is the remainder when m^2 - n^2  [#permalink]

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New post 27 Jan 2018, 23:03
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If m and n are positive integers, what is the remainder when m^2 - n^2 is divided by 10?

(1) The remainder when m is divided by 10 is 3.
(2) The remainder when n is divided by 10 is 3.

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Re: If m and n are positive integers, what is the remainder when m^2 - n^2  [#permalink]

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New post 27 Jan 2018, 23:34
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gmatbusters wrote:
If m and n are positive integers, what is the remainder when
m^2 - n^2 is divided by 10?
(1) The remainder when m is divided by 10 is 3.
(2) The remainder when n is divided by 10 is 3.


\(\frac{m^2-n^2}{10}=\frac{(m+n)(m-n)}{10}\). we need to know the value of \(m\) & \(n\) to get the remainder

Statement 1: implies \(m=10k+3\). but nothing mentioned about \(n\). Insufficient

Statement 2: implies \(n=10q+3\). but nothing mentioned about \(m\). Insufficient

Combining 1 & 2: we have \(m-n=10k+3-10q-3=10(k-q)\) which is divisible by \(10\). Hence remainder will be \(0\). Sufficient

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Re: If m and n are positive integers, what is the remainder when m^2 - n^2  [#permalink]

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New post 28 Jan 2018, 18:21
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Bunuel , would you please move this question to DS?
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Re: If m and n are positive integers, what is the remainder when m^2 - n^2  [#permalink]

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New post 28 Jan 2018, 19:17
gmatbusters wrote:
If m and n are positive integers, what is the remainder when m^2 - n^2 is divided by 10?

(1) The remainder when m is divided by 10 is 3.
(2) The remainder when n is divided by 10 is 3.



Note :- Remainder when div by 10 means the units digit of the number.

\(m^2-n^2...(m-n)(m+n)\)..
Let's see the statements..

1) The remainder when m is divided by 10 is 3.
This means units digit of m is 3, but nothing about n.
Insufficient

(2) The remainder when n is divided by 10 is 3.[/quote]
This means units digit of n is 3, but nothing about m.
Insufficient

Combined..
Units digit of m and n both are 3, so m^2-n^2 will lead to units digit as 9-9=0
So it will be div by 10..
C
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: If m and n are positive integers, what is the remainder when m^2 - n^2  [#permalink]

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New post 28 Jan 2018, 19:25
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Re: If m and n are positive integers, what is the remainder when m^2 - n^2 &nbs [#permalink] 28 Jan 2018, 19:25
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If m and n are positive integers, what is the remainder when m^2 - n^2

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