j_shreyans wrote:If x and y are positive integers, is x a factor of y?
1) x = y²
2) y > 1
Target question: Is x a factor of y?
Given: x and y are POSITIVE INTEGERS
Statement 1: x = y²
This statement seems to SUGGEST that x is greater than 1 (since x and y are POSITIVE INTEGERS).
If x is greater than y, x cannot by a factor of y. So, it would
seem, that this statement is sufficient.
HOWEVER, there is one possible value for y that we need to consider and that's y = 1
case a) If y = 1, then x = 1, in which case
x IS a factor of y.
However, if y equals any other positive integer
other than 1, then we have...
case b) If y = any other positive integer
other than 1, then x is GREATER THAN y, which means
x is NOT a factor of y.
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: y > 1
Since there's no information about x, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1 was insufficient, because there are two possible cases that reveal DIFFERENT answers to the target question:
case a) If y = 1, then x = 1, in which case
x IS a factor of y.
case b) If y = any other positive integer
other than 1, then x is GREATER THAN y, which means
x is NOT a factor of y.
Statement 2 RULES OUT case a, which means case b is the ONLY POSSIBLE case.
This means that we can conclude that
x is NOT a factor of y
Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer =
C
Cheers,
Brent
