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Divisoin by 3

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Source: — Data Sufficiency |
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by Geva@EconomistGMAT » Mon Jun 13, 2011 4:04 am
vinayreguri wrote:If x, y & Z are digits of the three digit + ve integer N, what is the reminder when N is divided by 3
1. x+y+z=11
2. N=2 is divisible by 3

[spoiler]OA: D[/spoiler]
There's a rule of divisibility that says that a if the sum of the digits of a number is divisible by 3, then the number itself is divisible by 3.

(1) is an extension of the same: if the sum of the digits of a number is 11, then that number is 2 more than another number whose sum of digits is 9, which is divisible by 3. Therefore, N is 2 more than some multiple of 3, which means that the remainder when N is divide by 3 is 2. Sufficient.

(2) I assume that the statemnt actually says N-2 is divisible by 3, which is basically saying the same thing as stat. (1): N leaves a remainder of 2 when divided by 3.
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by Ian Stewart » Mon Jun 13, 2011 9:26 am
Geva@MasterGMAT wrote:
(1) is an extension of the same: if the sum of the digits of a number is 11, then that number is 2 more than another number whose sum of digits is 9,
Technically, that's not true. If the sum of the digits of k is 11, that does not mean the sum of the digits of k-2 will be 9. For example, if k = 7301, then k-2 = 7299. The sum of the digits of k is 11 but the sum of the digits of k-2 is 27.

It is true, however, that we can always find remainders by 3 or by 9 by using the sum of our digits, so Statement 1 is sufficient in the question above.
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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