M7MBA wrote:The remainder, when a number n is divided by 6, is p. The remainder, when the same number n is divided by 12, is q. Is p < q?
1) n is a positive number having 8 as a factor.
2) n is a positive number having 6 as a factor.
Statement 1:
Case 1: n=8
Since n/6 = 8/6 = 1 R2, p=2.
Since n/12 = 8/12 = 0 R8, q=8.
In this case, p<q, with the result that the answer to the question stem is YES.
Case 2: n=16
Since n/6 = 16/6 = 2 R4, p=4.
Since n/12 = 16/12 = 1 R4, q=4.
In this case, p=q, with the result that the answer to the question stem is NO.
INSUFFICIENT.
Statement 2:
Case 3: n=6
Since n/6 = 6/6 = 1 R0, p=0.
Since n/12 = 6/12 = 0 R6, q=6.
In this case, p<q, with the result that the answer to the question stem is YES.
Case 3: n=12
Since n/6 = 12/6 = 2 R0, p=0.
Since n/12 = 12/12 = 1 R0, q=0.
In this case, p=q, with the result that the answer to the question stem is NO.
INSUFFICIENT.
Statements combined:
Since n must be divisible by 8 and 6, n must be a multiple of 24:
24, 48, 72...
Dividing a multiple of 12 by 6 will yield a remainder of 0.
Thus, p=0.
Dividing a multiple of 24 by 12 will also yield a remainder of 0.
Thus, q=0.
Since p=q, the answer to the question stem is NO.
SUFFICIENT.
The correct answer is
C.[/quote]
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