Gmat_mission wrote: ↑Sun Nov 07, 2021 1:08 pm
Is \(x > y ?\)
(1) \(x + y > x - y\)
(2) \(3x > 2y\)
Answer:
E
Source: Official Guide
Target question: Is x > y ?
Statement 1: x + y > x − y
Add y to both sides of the inequality to get: x + 2y > x
Subtract x from both sides: 2y > 0
But this tells us that
y is positive
However, since we're provided no information about the value of x, statement 1 is NOT SUFFICIENT
Statement 2: 3x > 2y
There are several values of x and y that satisfy statement 2. Here are two:
Case a: y = 2 and y = 1. In this case, the answer to the target question is
YES, x is greater than y
Case b: y = 2 and y = 2. In this case, the answer to the target question is
NO, x is not greater than y
Since we can’t answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1 indirectly tells us that
y is positive
Statement 2 tells us that 3x > 2y
Strategy tip: It's hard to tell whether the combined statements are sufficient. This is a good time to see if we can
reuse the values we used earlier with statement 2.
It turns out that the counterexamples we used for statement 2 also satisfy statement 1. That is...
Case a: y = 2 and y = 1. In this case, the answer to the target question is
YES, x is greater than y
Case b: y = 2 and y = 2. In this case, the answer to the target question is
NO, x is not greater than y
Since we can’t answer the
target question with certainty, the combined statements are NOT SUFFICIENT
Answer: E
Cheers,
Brent
