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3x and 6/x are positive integers

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Source: — Data Sufficiency |
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by DanaJ » Sun Jan 18, 2009 9:32 am
1. insufficient, since 6/3 = 2 and 6/1 = 6. Both 2 and 6 are even, so you would have at least two options for x.
2. 8/x is greater than 10 means x is smaller than 8/10 = 4/5. Since 3x is an integer, x is smth like a/3. For x to be smaller than 4/5, a has to be either 1 or 2. Both 8/(1/3) = 24 and 8/(2/3) = 12 are greater than 10. So 2 by itself is insufficient.

Now we need to check to see if both statements taken together are sufficient. Well, since from 2 we deducted that x can be either 1/3 or 2/3. We need to see which one fits "6/x is even".
6/1/3 = 18 - is even
6/2/3 = 1 - is odd.

So both statements taken together are sufficient.
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by Brent@GMATPrepNow » Sun Jan 18, 2009 9:47 am
Noce work - C it is.

3x is an integer means that x is greater than or equal to 1/3
6/x means that x is less than or equal to 6
Possible values for x: 1/3, 2/3, 1, 2, 3, 6

(1) Means that x can equal 1/3, 1 or 3 (INSUFF)
(2) Means that x can equal 1/3 or 2/3
(1) + (2) means that x = 1/3
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