Bunuel 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
Answer is CStatement 1(p>q)Case-1 - Let p=5 and q=-4, then (q-1=-5 is (-1) times p or 5)
Case-2 - Let p=7 and q =5, then (q-1=4 cannot be expressed as a multiple of p or 7)
Hence, Statement 1 is not sufficient.
Statement 2 Case-1 - Let p=7 and q=8, then (q-1=7 is (1) times p or 7)
Case-2 - Let p=7 and q =9, then (q-1=8 cannot be expressed as a multiple of p or 7)
Hence, Statement 2 is not sufficient.
Both Statements togetherHere q is positive and >1 & p is also positive and greater than 2 (since both p & q are intergers)
Thus, p is always greater than q-1, since p & q are positive and p>q.
A small number can never be expressed as an integer multiple of a large number.
Hence, both statements together are sufficient.