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

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Senior DS Moderator
Joined: 27 Oct 2017
Posts: 1195
Location: India
GPA: 3.64
WE: Business Development (Energy and Utilities)
If m and n are positive integers, what is the remainder when m^2 - n^2  [#permalink]

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27 Jan 2018, 22:03
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Question Stats:

91% (01:19) correct 9% (01:49) wrong based on 65 sessions

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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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27 Jan 2018, 22:34
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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

Option C
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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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28 Jan 2018, 17:21
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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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28 Jan 2018, 18:17
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
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
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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28 Jan 2018, 18:25
I apologize for my mistake in posting DS in PS forum

generis wrote:
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 &nbs [#permalink] 28 Jan 2018, 18:25
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