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Pls help me to sovle this problem, thank you....

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tracyyahoo
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Pls help me to sovle this problem, thank you.... [#permalink] New post   22 Jul 2011, 20:24
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If M and N are postivie integers that have remainders of 1 and 3, respectively, when divided by 6, which of following could Not be a possible value of M + N?

a) 86 b) 52 c)34 d)28 e)10

why is 10 not the answer, since I use plug in: M = 1*6+1 =7 and N = 1*6+3 =9, they are already the smallest integer, thus 10 should off the limit, why is 10 is the answer, pls tell me. Thank you



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Re: Pls help me to sovle this problem, thank you.... [#permalink] New post   22 Jul 2011, 22:21
M = 6m + 1
N = 6n + 3
1 and 1 that you plug in is m and n, it is not the smallest number
condition given is "M, N is positive number" ; not the m,n
so m,n could be 0,1 ; which gives M=1 and N=9
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Re: Pls help me to sovle this problem, thank you.... [#permalink] New post   22 Jul 2011, 23:09
I think following can be reason why 10 can not be answer

first M & N are positive integers, so we only know reminder for M is 1 & N is 3.

so M= 6x+1 where x is can digit
N = 6y+3
M+N = 6*(x+y)+4
We clearly get reminder for M+N will be 4. Now first put x=0, & y=0, we get M+N=4, then x=1 & y =0, we get M+N=10

Only A is having reminder of 2. So A is right answer not E i.e. 10
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Re: Pls help me to sovle this problem, thank you.... [#permalink] New post   23 Jul 2011, 00:35
Though the previous posts have provided decent solutions, I wanted to chime in to provide a tad different perspective.
Since (M/6) = Quotient + Remainder
M = 6q1 + 1
In like vein, N= 6q2 + 3
Therefore, M + N = 6q1+1 + 6q2 + 3
= 6(q1+q2) + 4
What does that mean? look closer...
It means that when M+N is divided by 6, it leaves a remainder 4
So divided each choice by 6 and see what its remainder is. See that? Only in choice A is the remainder different from 4.[ in the remaining choices the remainder is 4.] Hence, 86 is not a possible value.

Hope it helps.
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Re: Pls help me to sovle this problem, thank you.... [#permalink] New post   23 Jul 2011, 01:14
M=6m+1
N=6n+3
M+N=6(m+n)+4 = INTEGER.
Now check each option
1) M+N=6(m+n)+4 =86 => 6(m+n)=86 - 4 =>m+n = 84/6 = NOT AN INTEGER.
2) M+N=6(m+n)+4 =52 =>m+n=8 INTEGER.
3) M+N=6(m+n)+4 =34 =>m+n=5.INTEGER.
4) M+N=6(m+n)+4 =28 =>m+n=4.INTEGER.
5) M+N=6(m+n)+4 =10 =>m+n=1.INTEGER.

OA A.
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Re: Pls help me to sovle this problem, thank you.... [#permalink] New post   23 Jul 2011, 05:19
I just want to know why 10 is right, suppose M is 1 and N is 9.

1 to be divided by 6, the remainder is not 1. it is wrong.

9 to be divided by 6, the remainder is 3, it is right.


However when we use the formular 6m+1 and 6n+3, is right. why is that ~~~

jagdeepsingh1983 wrote:
I think following can be reason why 10 can not be answer

first M & N are positive integers, so we only know reminder for M is 1 & N is 3.

so M= 6x+1 where x is can digit
N = 6y+3
M+N = 6*(x+y)+4
We clearly get reminder for M+N will be 4. Now first put x=0, & y=0, we get M+N=4, then x=1 & y =0, we get M+N=10

Only A is having reminder of 2. So A is right answer not E i.e. 10




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Re: Pls help me to sovle this problem, thank you.... [#permalink]
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