The positive integers m and n leave remainders of 2 and 3

Question

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

ENGRTOMBA2018 · Accepted Answer

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.

Bunuel · Answer

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.

Answer: E.

BrentGMATPrepNow · Answer

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

Answer: E

Cheers,
Brent

FelixM · Answer

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).

chetan2u · Answer

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.....

stonecold · Answer

Best approach => let N=8
and M=3 
hence => m-n = 5
hence remainder => 5
so E

KarishmaB · Answer

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: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/04 ... unraveled/

gps5441 · Answer

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.

raihan422 · Answer

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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Abhishek009 · Answer

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

vitaliyGMAT · Answer

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.

Answer E.

gracie · Answer

least possible value for n=3
least possible value for m>3=8
8-3=5
5/6 gives remainder of 5
E

KanishkM · Answer

m>n
14>9

14-9 = 5/6

Remainder = 5

E

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The positive integers m and n leave remainders of 2 and 3

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