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Senior Manager  B
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The positive integers m and n leave remainders of 2 and 3  [#permalink]

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Question Stats: 70% (01:33) correct 30% (01:31) wrong based on 257 sessions

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The positive integers m and n leave remainders of 2 and 3, respectively, when divided by 6. m > n.
What is the remainder when m – n is divided by 6?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Source: Gmat Math Bible

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Re: The positive integers m and n leave remainders of 2 and 3  [#permalink]

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BrainLab wrote:
The positive integers m and n leave remainders of 2 and 3, respectively, when divided by 6. m > n.
What is the remainder when m – n is divided by 6?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Source: Gmat Math Bible

m = 6p+2
n = 6q+3

Thus, m-n = 6p+2-6q-3 = 6p-6q-1 = 6p-6q+5-6 = (6p-6q-6)+5 = 6(p-q-1) + 5. Thus you will get a remainder of 5 when m-n is divided by 6.

E is thus the correct answer.

Hope this helps.
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Joined: 12 Sep 2015
Posts: 4006
Re: The positive integers m and n leave remainders of 2 and 3  [#permalink]

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BrainLab wrote:
The positive integers m and n leave remainders of 2 and 3, respectively, when divided by 6. m > n.
What is the remainder when m – n is divided by 6?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Let's test out some values of m and n that satisfy the given information.

m leaves are remainder of 2 when divided by 6
So, m COULD equal 8

n leaves are remainder of 3 when divided by 6
So, n COULD equal 3

What is the remainder when m – n is divided by 6?
So, m - n = 8 - 3 = 5, and when we divide 5 by 6, we get 0 with remainder 5

Cheers,
Brent
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The positive integers m and n leave remainders of 2 and 3  [#permalink]

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m=6q+2 (even)
n=6p+3 (odd)

m-n=odd => the remainder can only be an odd number (even*even+ an Odd remainder can only give us an odd number). So options D) and B) are eliminated.

Also put together $$\frac{m-n}{6}$$ will give us $$\frac{6(q-p)+5}{6}$$, thus having a +5, so answer choice E).

Originally posted by FelixM on 06 Feb 2016, 17:28.
Last edited by FelixM on 07 Feb 2016, 07:15, edited 2 times in total.
Math Expert V
Joined: 02 Sep 2009
Posts: 58401
Re: The positive integers m and n leave remainders of 2 and 3  [#permalink]

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BrainLab wrote:
The positive integers m and n leave remainders of 2 and 3, respectively, when divided by 6. m > n.
What is the remainder when m – n is divided by 6?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Source: Gmat Math Bible

m is 2 more than a multiple of 6;
n is 3 more than a multiple of 6.

m - n will be 1 less than a multiple of 6 (5, 11, 17, ...), therefore m - n will yield a remainder of 5 when divided by 6.

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Posts: 7969
Re: The positive integers m and n leave remainders of 2 and 3  [#permalink]

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BrainLab wrote:
The positive integers m and n leave remainders of 2 and 3, respectively, when divided by 6. m > n.
What is the remainder when m – n is divided by 6?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Source: Gmat Math Bible

Hi,
since m>n..
i can say that m is 2 more than multiple of 6..
and n is 3 less than a multiple of 6..
so m-n means 2-(-3) =5 more than a multiple of 6.....
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GRE 1: Q169 V154 Re: The positive integers m and n leave remainders of 2 and 3  [#permalink]

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Best approach => let N=8
and M=3
hence => m-n = 5
hence remainder => 5
so E
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Re: The positive integers m and n leave remainders of 2 and 3  [#permalink]

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BrainLab wrote:
The positive integers m and n leave remainders of 2 and 3, respectively, when divided by 6. m > n.
What is the remainder when m – n is divided by 6?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Source: Gmat Math Bible

Use the basic concepts of divisibility.
m when divided by 6, will have groups of 6 and 2 leftover.
n when divided by 6 will have groups of 6 and 3 leftover.
When you subtract n from m, some groups of 6 will get subtracted out, 2 will get subtracted out and 1 more from a group of 6 will get subtracted out. From that groups of 6, only 5 will be leftover. So m - n will have groups of 6 and 5 leftover.
Remainder will be 5.

For more, check: http://www.veritasprep.com/blog/2011/04 ... unraveled/
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Re: The positive integers m and n leave remainders of 2 and 3  [#permalink]

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m=6q+2 possible values of m=8,14,20,26,32,38....
n=6q+3 possible values of n=9,15,21,27,33,39...

Now m is greater than n
subtract any value of n from m eg 38(m)-9(n)=29
Divide by 6 reminder is 5.
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Re: The positive integers m and n leave remainders of 2 and 3  [#permalink]

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We know, 6*1=6
6*2=12
Lets M= 12 & N= 6
According to question there will be remainder 2 & 3 dividing by 6, So adding remainder with 12 & 6
We get M= 14 & N = 9 which is M>N
So, M- N= 14-9= 5 (Ans)

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Re: The positive integers m and n leave remainders of 2 and 3  [#permalink]

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BrainLab wrote:
The positive integers m and n leave remainders of 2 and 3, respectively, when divided by 6. m > n.
What is the remainder when m – n is divided by 6?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Source: Gmat Math Bible

The least value of m = 14 & the least value of n = 9 ; m > n

So, m - n = 5

Or, m – n is divided by 6 is 5

Hence correct answer must be (E) 5
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Senior Manager  B
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Re: The positive integers m and n leave remainders of 2 and 3  [#permalink]

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BrainLab wrote:
The positive integers m and n leave remainders of 2 and 3, respectively, when divided by 6. m > n.
What is the remainder when m – n is divided by 6?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Source: Gmat Math Bible

In order to find the remainder of the difference we need only to take the difference of the remainders:

$$\frac{m - n}{6} = \frac{2 - 3}{6} = \frac{-1}{6} = \frac{5}{6}$$

Remainder is 5.

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Joined: 07 Dec 2014
Posts: 1222
Re: The positive integers m and n leave remainders of 2 and 3  [#permalink]

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BrainLab wrote:
The positive integers m and n leave remainders of 2 and 3, respectively, when divided by 6. m > n.
What is the remainder when m – n is divided by 6?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Source: Gmat Math Bible

least possible value for n=3
least possible value for m>3=8
8-3=5
5/6 gives remainder of 5
E
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Re: The positive integers m and n leave remainders of 2 and 3  [#permalink]

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BrainLab wrote:
The positive integers m and n leave remainders of 2 and 3, respectively, when divided by 6. m > n.
What is the remainder when m – n is divided by 6?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Source: Gmat Math Bible

m>n
14>9

14-9 = 5/6

Remainder = 5

E
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Many of life's failures happen with people who do not realize how close they were to success when they gave up. Re: The positive integers m and n leave remainders of 2 and 3   [#permalink] 10 Feb 2019, 19:48
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