vipulgoyal wrote:If P*Q is the factor of m*P+n*Q, which of the following must be true?
I. P is factor of m*n.
II. P is factor of m.
III. P*Q is factor of m*P
(A) I only
(B) II only
(C) III only
(D) I and II
(E) None
E
Try to DISPROVE the statements, each of which describes p as a factor of another value.
If p=q, then neither p nor q must divide into m or n.
Let p=q=3, m=5 and n=7, so that pq=9 and mp + nq = 5*3 + 7*3 = 36.
I: p=3 is not a factor of mn=35.
II: p=3 is not a factor of m=5.
III: pq = 9 is not a factor of mp=15.
Thus, none of the statements must be true.
The correct answer is
E.
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