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What is the remainder when the positive integer n is divided

tagged by: Brent@GMATPrepNow

This topic has 3 expert replies and 0 member replies
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What is the remainder when the positive integer n is divided

Sun Dec 03, 2017 5:03 am
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

What's the best way to determine which statement is sufficient?

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DavidG@VeritasPrep Legendary Member
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Sun Dec 03, 2017 6:54 am
ardz24 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

What's the best way to determine which statement is sufficient?
Statement 1
Case 1: n = 1. When 1 is divided by 6, the remainder is 1
Case 2: n = 13, When 13 is divided by 6, the remainder is 1.
Case 3: n = 25. When 25 is divided by 6, the remainder is 1.
Not matter what we pick, the remainder will always be 1. This statement alone is sufficient.

Statement 2
Case 1: n = 1. When 1 is divided by 6, the remainder is 1/
Case 2: n = 4, When 4 is divided by 6, the remainder is 4. Because we can generate different results, this statement alone is not sufficient.

The answer is A

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Brent@GMATPrepNow GMAT Instructor
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Sun Dec 03, 2017 9:16 am
ardz24 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

Answer: A

RELATED VIDEO: https://www.gmatprepnow.com/module/gmat-integer-properties/video/842

Cheers,
Brent

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