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Difficulty—
Is x/y an even integer?
(1) x is even.
(2) y is a factor of x.
(1) x is even.
(2) y is a factor of x.
Target question: Is x/y an even integer?
Statement 1: x is even
Since there's no information about y, this statement is NOT SUFFICIENT
However, to be 100% certain, some students may choose to TEST some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 6 and y = 1, in which case x/y = 6/1 = 6. So, x/y is EVEN
Case b: x = 6 and y = 2, in which case x/y = 6/2 = 3. So, x/y is NOT even
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: y is a factor of x
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 6 and y = 1, in which case x/y = 6/1 = 6. So, x/y is EVEN
Case b: x = 6 and y = 2, in which case x/y = 6/2 = 3. So, x/y is NOT even
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
NOTICE that, for statement 1 and 2 above, I was able to use the same values for x and y to show why each statement on its own is NOT SUFFICIENT.
So, when we examine the statements COMBINED, the same values for x and y will apply.
That is....
Case a: x = 6 and y = 1, in which case x/y = 6/1 = 6. So, x/y is EVEN
Case b: x = 6 and y = 2, in which case x/y = 6/2 = 3. So, x/y is NOT even
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT
Answer: E
Cheers,
Brent
