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Source: — Data Sufficiency |

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by Ian Stewart » Sun Sep 16, 2012 6:16 pm
grandh01 wrote:What is the remainder of dividing m by 9?

1) If m is divided by 27, the remainder is 4.
2) If m is divided by 3, the remainder is 1.

OA IS A
If Statement 1 is true, then m is 4 greater than some multiple of 27, and thus is 4 greater than some multiple of 9, which is just another way of saying that the remainder will be 4 when m is divided by 9. So Statement 1 is sufficient.

If Statement 2 is true, then m could be, for example, equal to 1, 4 or 7, which each give different remainders when you divide by 9 (they give remainders of 1, 4 and 7 respectively). So Statement 2 is not sufficient, and the answer is A.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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by everything's eventual » Sun Sep 16, 2012 6:44 pm
Taking statement A into account : list down the first few numbers which will give a remainder 4 when divided by 27 : 4,31,58, 85, 112 etc etc....divide the same numbers by 9 and you will get remainder as 4. Therefore statement A is sufficient.

Taking statement B into account : list down the first few number which will give a remainder 1 when divided by 3 : 1,4,7,10,13,16 etc etc.....divide the same numbers by 9 and you get different remainders. There statement B is not sufficient.

Answer : A
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by Brent@GMATPrepNow » Mon Sep 17, 2012 7:14 am
grandh01 wrote:What is the remainder of dividing m by 9?

1) If m is divided by 27, the remainder is 4.
2) If m is divided by 3, the remainder is 1.

OA IS A
Target question: What is the remainder when m is divided by 9?

Statement 1: If m is divided by 27, the remainder is 4.
This tells us that m = 27k + 4 for some integer k
Since 27 = (9)(3), we can also say that m = (9)(3)k + 4 for some integer k
Given this, when m is divided by 9, the remainder must be 4
Statement 1 is SUFFICIENT

Statement 2: If m is divided by 3, the remainder is 1.
This yields several possible values of m. Let's examine two conflicting cases.
case a: m=1, in which case the remainder is 1 when m is divided by 9.
case b: m=4, in which case the remainder is 4 when m is divided by 9.
Since statement 2 yields two conflicting answers to the target question, it is NOT SUFFICIENT

Answer = A

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Brent
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