aaron1981 wrote:If p and q are integers, can (q-1) always be expressed as an integer multiple of p?
(1) p > q
(2) q > 1
Does (q-1)/p = integer?
Statement 1: p>q
If p=2 and q=1, then (q-1)/p = 0/2 = 0, so the answer to the question stem is YES.
If p=3 and q=2, then (q-1)/p = (2-1)/3 = 1/3, so the answer to the question stem is NO.
INSUFFICIENT.
Statement 2: q>1
No information about p.
INSUFFICIENT.
Statements combined: p>q>1.
Since q>1, q-1 > 0, implying that q-1 is a POSITIVE INTEGER.
Since p>q, p is a POSITIVE INTEGER greater than q and thus greater than q-1.
Implication:
(q-1)/p = (smaller positive integer)/(greater positive integer) = fraction.
Thus, the answer to the question stem is NO.
SUFFICIENT.
The correct answer is
C.
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