Is x + y > 6?
(1) x + 2y > 8
(2) 2x + y > 8
The OA is the option E.
Why are not sufficient both statements together? Could someone explain it to me? Thanks.
Is x + y > 6?
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Target question: Is x + y > 6?M7MBA wrote:Is x + y > 6?
(1) x + 2y > 8
(2) 2x + y > 8
Statement 1: x + 2y > 8
Let's TEST some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 10 and y = 10. In this case, x + y = 10 + 10 = 20, which is greater than 6. So, the answer to the target question is YES, x+y IS greater than 6
Case b: x = 1 and y = 4. In this case, x + y = 1 + 4 = 5, which is NOT greater than 6. So, the answer to the target question is NO, x+y is NOT greater than 6
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: 2x + y > 8
Let's TEST some values again.
There are several values of x and y that satisfy statement 2. Here are two:
Case a: x = 10 and y = 10. In this case, x + y = 10 + 10 = 20, which is greater than 6. So, the answer to the target question is YES, x+y IS greater than 6
Case b: x = 4 and y = 1. In this case, x + y = 4 + 1 = 5, which is NOT greater than 6. So, the answer to the target question is NO, x+y is NOT greater than 6
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1 tells us that x + 2y > 8
Statement 2 tells us that 2x + y > 8
Since the inequality symbols are facing the same direction, we can ADD the inequalities to get: 3x + 3y > 16
Divide both sides of the inequality by 3 to get: x + y > 16/3 (aka 5.3333333....)
If x+y is greater than 16/3, then x+y COULD equal 7, in which case, x+y IS greater than 6
However, x+y COULD also equal 5.5, in which case, x+y is NOT greater than 6
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT
Answer: E
Cheers,
Brent