BTGModeratorVI wrote: ↑

Sat Aug 08, 2020 7:05 am

Is x + y > 6?

(1) x + 2y > 8
(2) 2x + y > 8

Answer: E
Source: Nova

Target question: Is x + y > 6?

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