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General strategy for Number Properties Test

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General strategy for Number Properties Test [#permalink] New post 04 Aug 2009, 14:23
If X is a positive integer, what is the remainder of \frac{X}{3} ?

1. The remainder of \frac{X}{4} is 1
2. The remainder of \frac{X}{7} is 6

(C) 2008 GMAT Club - Number properties - III#1

* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
* Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
* BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
* EACH statement ALONE is sufficient
* Statements (1) and (2) TOGETHER are NOT sufficient

Every time I see one of these questions the solution is to plug in numbers. Is that generally the quickest way of going about these?
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Re: General strategy for Number Properties Test [#permalink] New post 04 Aug 2009, 15:12
I plug numbers too....but I find it quick.....here is what I did....

(1) Remainder is 1 when divided by 4. So numbers could be

1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41.....etc (keep adding 4...)
But as you can all these numbers do not give the same remainder when divided by 3. INSUFF.

(1) Remainder is 6 when divided by 7. So numbers could be

6, 13, 20, 27, 34, 41.....etc (keep adding 7...)
But as you can all these numbers do not give the same remainder when divided by 3. INSUFF.

Combine (1) and (2). Pick any 2 common numbers out the above lists.

13 and 41 are present in boith the lists. But 13 gives a remainder of 1 and 41 gives remainder of 2 when divided by 3.
Hence INSUFF.

Answerr is E. Whats the OA???
Re: General strategy for Number Properties Test   [#permalink] 04 Aug 2009, 15:12
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