If x and y are integers greater than 1, is x a multiple of y?
(1) 3y² + 7y = x
(2) x² - x is a multiple of y
Target question: Is x a multiple of y?
Asking whether x is a multiple of y is the same as asking whether x = (y)
(some integer)
For example, 12 is a multiple of 3 because 12 = (3)
(4)
So, let's rephrase the question as...
REPHRASED target question: Does x = (y)(some integer)?
Statement 1: 3y² + 7y = x
Factor to get x = y(
3y + 7)
If y is an integer, then (3y + 7) must be an integer
In other words:
x = y(some integer)
Since we can answer the
REPHRASED target question with certainty, statement 1 is SUFFICIENT
Statement 2: x² - x is a multiple of y
There are several values of x and y that satisfy this condition. Here are two:
Case a: x = 4 and y = 2 (this satisfies statement 2 because x² - x = 12, and 12 is a multiple of 2). In this case,
x IS a multiple of y
Case b: x = 5 and y = 2 (this satisfies statement 2 because x² - x = 20, and 20 is a multiple of 2). In this case,
x is NOT a multiple of y
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Answer =
A
Cheers,
Brent
