If x = 2y, what is the value of xy ? (1) x > Y (2) 3x - 2y = 14

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Since we have 2 variables (x and y) and 1 equation, D is most likely to be the answer. So, we should consider each condition on its own first.

Condition 1)

If x = 2, y = 1, then we have xy = 2.
If x = 4, y = 2, then we have xy = 8.

Since condition 1) does not yield a unique solution, it is not sufficient

Condition 2)
We have 3x - 2y = 3x - x = 2x = 14 or x = 4, y = 2 since x = 2y.

Since condition 2) yields a unique solution, it is sufficient


Therefore, B is the answer.

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.­

Given: x = 2y

Target question: What is the value of xy?

Statement 1: x > y
There are several values of x and y that satisfy statement 1 (and the given equation, x = 2y). Here are two:
Case a: x = 2 and y = 1. In this case, the answer to the target question is xy = (2)(1) = 2
Case b: x = 6 and y = 3. In this case, the answer to the target question is xy = (6)(3) = 18
Since we can't answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 3x - 2y = 14
When we combine this equation with the given equation, x = 2y, we see that we have a system of 2 different linear equations with 2 variables.
This means we COULD solve the system for x and y, which means we COULD determine the value of xy (although we would never waste valuable time on test day performing such calculations)
Since we COULD answer the target question with certainty, statement 2 is SUFFICIENT

Aside: if you want to solve the system of equations for "fun," you'll find that the solution is x = 7 and y = 3.5, which means xy = 24.5

Answer: B

Cheers,
Brent

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