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What is the remainder when the positive integer n is divided

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What is the remainder when the positive integer n is divided

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What is the remainder when the positive integer n is divided by 5 ?

(1) When n is divided by 3, the quotient is 4 and the remainder is 1.
(2) When n is divided by 4, the remainder is 1.

A

Source: Official Guide 2020

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Statement 1 tells us that n is equal to 13, so of course we can answer any question about n, and Statement 1 is sufficient.

The remainder you get when you divide by 4 has no relationship to the remainder you get when you divide by 5, so Statement 2 is useless. For example, n could be 5, and then the remainder is 0 when we divide by 5, or n could be 9, and the remainder is 4 when we divide by 5.

So the answer is A.

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AbeNeedsAnswers wrote:
What is the remainder when the positive integer n is divided by 5 ?

(1) When n is divided by 3, the quotient is 4 and the remainder is 1.
(2) When n is divided by 4, the remainder is 1.
Target question: What is the remainder when the positive integer n is divided by 5 ?

Statement 1: When n is divided by 3, the quotient is 4 and the remainder is 1.
There's a nice rule that says, "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

So, from statement 1, we can write: n = (3)(4) + 1 = 13
If n = 13, then we get a remainder of 3 when we divide 13 by 5
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: When n is divided by 4, the remainder is 1.
We have a nice rule that says: 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.

Some possible values of n are: 1, 5, 9, 13, 17, . . . etc.
Case a: If n = 1, then we get a remainder of 1 when we divide 1 by 5.
Case b: If n = 5, then we get a remainder of 0 when we divide 5 by 5.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers.
Brent

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Hi All,

We're told that N is a positive integers. We're asked for the remainder when N is divided by 5. This question can be solved with a mix of Arithmetic and TESTing VALUES.

(1) When N is divided by 3, the quotient is 4 and the remainder is 1.

Fact 1 gives us remarkably specific information....
N/3 = 4r1
This outcome can only occur when N = 13, since 13/3 = 4r1. No other value of N fits this information, so we have 13/5 = 2r3 and the answer to the question must be 3.
Fact 1 is SUFFICIENT

(2) When N is divided by 4, the remainder is 1.

Fact 2 isn't quite as 'restrictive' as Fact 1 is. There are lots of different values of N that will fit here:
IF...
N = 1, then 1/4 = 0r1 and the answer to the question is 1/5 = 0r1.... 1
N = 5, then 5/4 = 1r1 and the answer to the question is 5/5 = 1r0.... 0
Fact 2 is INSUFFICIENT

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

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Contact Rich at Rich.C@empowergmat.com

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