carcass wrote:
If m and n are positive integers, is m + n divisible by 4 ?
(1) m and n are each divisible by 2.
(2) Neither m nor n is divisible by 4.
Statement 1:
Case 1: m=2 and n=2, with the result that m+n=4
In this case, m+n is divisible by 4, so the answer to the question stem is YES.
Case 2: m=2 and n=4, with the result that m+n=6
In this case, m+n is not divisible by 4, so the answer to the question stem is NO.
Since the answer is YES in Case 1 but NO in Case 2, INSUFFICIENT.
Statement 2:
Case 1: m=2 and n=2, with the result that m+n=4
In this case, m+n is divisible by 4, so the answer to the question stem is YES.
Case 3: m=1 and n=2, with the result that m+n=3
In this case, m+n is not divisible by 4, so the answer to the question stem is NO.
Since the answer is YES in Case 1 but NO in Case 2, INSUFFICIENT.
Statements combined:
Since m is divisible by 2 but not by 4, m = 2a, where a is ODD.
Since n is divisible by 2 but not by 4, n = 2b, where b is ODD.
Thus:
m+n = 2a + 2b = 2(a+b) = 2(ODD + ODD) = 2(EVEN) = multiple of 4
The answer to the question stem is YES.
SUFFICIENT.
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