N is a positive integer and N<15

[dlginsberg89]

This question is from Advantage Testing's Gmat Math test 5 #21

N is a positive integer and N(is less than or equal to) 15. M=3767+N. What is the value of N?

1) M is a multiple of 7
2) M is a multiple of 11

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My strategy was to find out how many times 7 and 11 went into 3767 and what the remainder was. N must be equal to the remainder or in the case of clue 1, 7 + (the remainder).
1)
3767/7 = 538 R1

so N could equal 1, 8, or 15

2)
3767/11= 342 R5

so N could equal 5

The answer would be B but both hints have to be correct and if N is equal to 5, 3767+N is not divisible by 7. I must be doing something wrong but I can't figure out what it is!

[RonPurewal]

your error occurs where you start listing possible values for "n".

remember what a remainder is"”it's the amount over and above a multiple of whatever number.

you are correct that the remainder of 3767/7 is 1. but remember what this means: it means that 3767 is 1 MORE than a multiple of 7.
this means that n must be 1 LESS than a multiple of 7, so that, when you add 3767 + n, they cancel and you're left with a multiple of 7.

so, in statement 1, you've got the wrong values of n; it should be 6 or 13 (= 7 - 1 and 14 - 1). the subsequent values (21 - 1, 28 - 1, etc.) are too big.

similarly, in statement 2, you should just have 6 (= 11 - 5). all of the subsequent values (22 - 5, 33 - 5, etc) are too big.

so, n = 6 belongs to both statements.
(you don't ever have to combine the statements, but you are correct that they should be consistent with each other.)