Data Sufficiency

BTGModeratorVI wrote: ↑

Sun Aug 02, 2020 6:59 am

What is the value of 2x + 2y ?

(1) 3x + 5y = 60
(2) 5x + 3y = 68

Answer: C
Source: GMAT prep

Target question: What is the value of 2x + 2y ?

Statement 1: 3x + 5y = 60
Since there are infinitely many solutions to the equation 3x + 5y = 60, it seems likely that statement 1 it's not sufficient.
To verify this, let's TEST some values.
There are several values of x and y that satisfy statement 1. Here are two cases:
Case a: x = 20 and y = 0. In this case, the answer to the target question is 2x + 2y = 2(20) + 2(0) = 40
Case b: x = 0 and y = 12. In this case, the answer to the target question is 2x + 2y = 2(0) + 2(12) = 24
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 5x + 3y = 68
There are several values of x and y that satisfy statement 2. Here are two cases:
Case a: x = 0 and y = 20. In this case, the answer to the target question is 2x + 2y = 2(0) + 2(20) = 40
Case b: x = 12 and y = 0. In this case, the answer to the target question is 2x + 2y = 2(12) + 2(0) = 24
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that 3x + 5y = 60
Statement 2 tells us that 5x + 3y = 68
If we ADD the two equations we get: 8x + 8y = 128
Divide both sides of the equation by 4 to get: 2x + 2y = 32
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent