Is Y < 40? (1) Y - X > 40 (2) X + Y = 40

(1) Y - X > 40
\(Y>X+40\)
If \(X\geq 0\), answer is NO. Otherwise YES.

(2) X + Y = 40
\(Y=40-X\)
If \(X> 0\), answer is YES. Otherwise NO.

Combined
Substitute X=40-Y in statement I => \(Y-(40-X)>40...........Y-40+Y>40........2Y>80....Y>40\)

C
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Target question: Is y < 40?

Statement 1: y - x > 40
This statement doesn't feel sufficient, so I'll TEST some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: y = 50 and x = 1. In this case, the answer to the target question is NO, y is NOT less than 40
Case b: y = 30 and x = -20. In this case, the answer to the target question is YES, y is less than 40
Since we can’t answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x + y = 40
There are several values of x and y that satisfy statement 2. Here are two:
Case a: y = 50 and x = -10. In this case, the answer to the target question is NO, y is NOT less than 40
Case b: y = 30 and x = 10. In this case, the answer to the target question is YES, y is less than 40
Since we can’t answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 2 tells us that x + y = 40, which means x = 40 - y

Statement 1 tells us that y - x > 40
Replace x with 40 - y to get: y - (40 - y) > 40
Simplify: 2y - 40 > 40
Add 40 to both sides of the inequality: 2y > 80
Divide both sides by 2 to get: y > 40
So, the answer to the target question is NO, y is NOT less than 40
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent
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