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factors

by jayanti » Mon Aug 08, 2011 1:01 am
If Z is an integer, is 22 a factor of Z?

(1) 22 is a factor of 15Z.

(2) 22 is a factor of 16Z.
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Source: — Data Sufficiency |
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by gmatboost » Mon Aug 08, 2011 8:00 am
Since 22 = 2 * 11, 22 is a factor of Z if both
A) 2 is a factor of Z
B) 11 is a factor of Z

St 1:
If 22 is a factor of 15Z, 2 and 11 are both factors of 15Z.
Since 15=3*5, neither the 2 nor the 11 is coming from the 15, so they must both come from Z.
That means 22 is a factor of Z. Sufficient.

St 2:
If 22 is a factor of 16Z, 2 and 11 are both factors of 16Z.
Since 16=2^4, the 2 could have come from the 16, rather than from the Z.
That means 11 is a factor of Z, but 22 is not necessarily a factor of Z, though it might be. Insufficient.
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