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Re: What is the remainder when the positive integer n is divided by 6?
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03 Dec 2017, 10:07

Bunuel wrote:

What is the remainder when the positive integer n is divided by 6?

(1) n when divided by 12 leaves a remainder of 1 (2) n when divided by 3 leaves a remainder of 1

(1) n/12 = 12q + 1/12: so n could be {1,13,25,37...} and the numbers in this set divided by 6 all give a remainder of 1. sufficient. (2) n/3 = 3q + 1/3: so n could be {1,4,7,10,13...} and the numbers in this set divided by 6 give a remainder of 1 or 4. not suf. (A) is the answer.

Re: What is the remainder when the positive integer n is divided by 6?
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03 Dec 2017, 10:20

Top Contributor

Bunuel wrote:

What is the remainder when the positive integer n is divided by 6?

(1) n when divided by 12 leaves a remainder of 1 (2) n when divided by 3 leaves a remainder of 1

Target question:What is the remainder when the positive integer n is divided by 6?

Statement 1: n when divided by 12 leaves a remainder of 1 USEFUL RULE #1: "If N divided by D equals Q with remainder R, then N = DQ + R" For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2 Likewise, since 53 divided by 10 equals 5 with remainder 3, then we can write 53 = (10)(5) + 3

No onto the question........... Statement 1 does not tell us the quotient, so let's just say that n divided by 12 equals k with remainder 1 So, we can write: n = 12k + 1, where k is some integer We can also write 12k a different way: n = (6)(2)(k) + 1 Or n = (6)(2k) + 1 As you can see, (6)(2k) is a multiple of 6, which means (6)(2k) + 1 is ONE MORE than a multiple of 6 So, when (6)(2k) + 1 (aka n) is divided by 6, the remainder must be 1 Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: n when divided by 3 leaves a remainder of 1 USEFUL RULE #2: If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc. For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.

So, for statement 2, some possible values of n are: 1, 4, 7, 10, 13, 16, 19, 22, etc. Let's TEST some values... Case a: If n = 1, then the remainder is 1, when n is divided by 6 Case b: If n = 4, then the remainder is 4, when n is divided by 6 Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Re: What is the remainder when the positive integer n is divided by 6?
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04 Dec 2017, 00:38

From 1) we know \(\frac{n}{12} = x + \frac{1}{12}\) so adjusting it to become \(n = 12x + 1\) if we let \(x = 0\) then\(n = 1\), plug in in the question stem \(\frac{1}{6}\) remainder is 1, if we let \(x = 1\), then \(n = 13\), plug in \(\frac{13}{6} = 2 \frac{1}{6}\) another remainder of 1 and so it goes. A is sufficient.

From 2) \(\frac{n}{3} = x + \frac{1}{3}\) so adjusting it to become \(n = 3x + 1\) if we let \(x = 0\) then \(n = 1\), plug in in the question stem \(\frac{1}{6}\) remainder is 1, if we let \(x = 1\), then \(n = 4\), plug in question stem \(\frac{4}{6}\) a remainder of 4. Because we get two different answers it is insufficient.

The answer is A

gmatclubot

Re: What is the remainder when the positive integer n is divided by 6? &nbs
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04 Dec 2017, 00:38