sjuniv32 wrote:
Is x > 2y?
(1) 2x + y < 6
(2) 3x - y > 6
Target question: Is x > 2y? Statement 1: 2x + y < 6 Since there's no extra information about x and y, it's unlikely that statement 1 is sufficient, so let's test some values
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 0 and y = -1. In this case, the answer to the target question is
YES, x is greater than 2y Case b: x = -1 and y = 0. In this case, the answer to the target question is
NO, x is not greater than 2y Since we can’t answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: 3x - y > 6Once again, since there's no additional information how about the values of x and y, there's a good chance that statement 2 is not sufficient. So let's test more values.
There are several values of x and y that satisfy statement 2. Here are two:
Case a: x = 0 and y = -10. In this case, the answer to the target question is
YES, x is greater than 2y Case b: x = 5 and y = 5. In this case, the answer to the target question is
NO, x is not greater than 2y Since we can’t answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined Statement 1 tells us that
2x + y < 6Statement 2 tells us that
3x - y > 6Useful property: If the inequality symbols of two inequalities are facing the same direction, you can ADD those inequalities. To get the inequality symbols facing the same way, we can rewrite the bottom inequality to get:
2x + y < 6 6 < 3x - yADD the inequalities to get: 2x + y + 6 < 3x - y + 6
Subtract 6 from both sides to get: 2x + y < 3x - y
Subtract 2x from both sides: y < x - y
Add y to both sides: 2y < x
So, the answer to the target question is
YES, x is greater than 2y Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent
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