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

Question

If x = 2y, what is the value of xy ?

(1) x > Y
(2) 3x - 2y = 14

elonsmusk · Answer

If x = 2y, what is the value of xy ?

(1) x > Y
(2) 3x - 2y = 14

Statement 1:
 x > y
We do not know a single value. Insuff.

Statement 2:
 Plug in x for 2y
3x - x = 14
2x = 14
x = 7
y = 3.5
xy = 7*3.5
 Suff

Kinshook · Answer

(1) x > y
x = 2y > y -> x & y > 0
But value of xy may not be derived from the information
NOT SUFFICIENT

(2) 3x - 2y = 14
6y - 2y = 14
4y = 14
y = 3.5
x = 7
xy = 3.5 * 7 = 24.5
SUFFICIENT

IMO B

MathRevolution · Answer

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. Visit https://www.mathrevolution.com/gmat/lesson for details. 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.

BrentGMATPrepNow · Answer

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

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