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The positive integers m and n leave remainders of 2 and 3
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06 Feb 2016, 14:07
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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
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06 Feb 2016, 14:15
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, mn = 6p+26q3 = 6p6q1 = 6p6q+56 = (6p6q6)+5 = 6(pq1) + 5. Thus you will get a remainder of 5 when mn is divided by 6. E is thus the correct answer. Hope this helps.



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Re: The positive integers m and n leave remainders of 2 and 3
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06 Feb 2016, 15:52
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 6So, m COULD equal 8 n leaves are remainder of 3 when divided by 6So, 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
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The positive integers m and n leave remainders of 2 and 3
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Updated on: 07 Feb 2016, 07:15
m=6q+2 (even) n=6p+3 (odd)
mn=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 \(\frac{mn}{6}\) will give us \(\frac{6(qp)+5}{6}\), 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.



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Re: The positive integers m and n leave remainders of 2 and 3
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07 Feb 2016, 04:07
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. Answer: E.
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Re: The positive integers m and n leave remainders of 2 and 3
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07 Feb 2016, 04:15
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 mn means 2(3) =5 more than a multiple of 6.....
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Re: The positive integers m and n leave remainders of 2 and 3
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21 Mar 2016, 09:31
Best approach => let N=8 and M=3 hence => mn = 5 hence remainder => 5 so E
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Re: The positive integers m and n leave remainders of 2 and 3
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21 Mar 2016, 09:58
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
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16 Jun 2016, 20:44
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
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27 Oct 2016, 06:17
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= 149= 5 (Ans)
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Re: The positive integers m and n leave remainders of 2 and 3
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27 Oct 2016, 09:50
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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Re: The positive integers m and n leave remainders of 2 and 3
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04 Dec 2016, 07:12
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. Answer E.



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Re: The positive integers m and n leave remainders of 2 and 3
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04 Dec 2016, 10:25
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 83=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
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10 Feb 2019, 19:48
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>9 149 = 5/6 Remainder = 5 E
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Re: The positive integers m and n leave remainders of 2 and 3
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