Max@Math Revolution wrote:[GMAT math practice question]
If m and n are positive integers, is m+n divisible by 15?
1) m is divisible by 9 and n is divisible by 15.
2) mn is divisible by 225.
Rule:
MULTIPLE OF X + MULTIPLE OF X = MULTIPLE OF X
MULTIPLE OF X + NON-MULTIPLE OF X = NON-MULTIPLE OF X
225 = 9*25
Statements combined:
Case 1: m=9 and n=25*15, with the result that m is a multiple of 9, n is a multiple of 15, and mn = 9*25*15 = 225*15 = multiple of 225
In this case, m+n = NON-MULTIPLE OF 15 + MULTIPLE OF 15 = NON-MULTIPLE OF 15, so the answer to the question stem is NO.
Case 2: m=15*9 and n=25*15, with the result that m is a multiple of 9, n is a multiple of 15, and mn = 15*9*25*15 = 15*225*15 = multiple of 225
In this case, m+n = MULTIPLE OF 15 + MULTIPLE OF 15 = MULTIPLE OF 15, so the answer to the question stem is YES.
Since the answer is NO in Case 1 but YES in Case 2, the two statements combined are INSUFFICIENT.
The correct answer is
E.
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