Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND EditionIf x and y are integers, what is the value of y ?
(1) xy = 27
(2) x = y²
Given: x and y are integers Target question: What is the value of y ? Statement 1: xy = 27 There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 1 and y = 27. In this case, the answer to the target question is
y = 27Case b: x = 3 and y = 9. In this case, the answer to the target question is
y = 9Since we can’t answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: x = y²There are several values of x and y that satisfy statement 2. Here are two:
Case a: x = 1 and y = 1. In this case, the answer to the target question is
y = 1Case b: x = 4 and y = 2. In this case, the answer to the target question is
y = 2Since we can’t answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined Statement 1 tells us that xy = 27.
If we divide both sides of the equation by y, we get: x = 27/y
Statement 2 tells us that x = y²
Since both equations (x = 27/y and x = y²) are set equal to x, we can set them equal to each other to get: 27/y = y²
Now multiply both sides of the equation by y to get: 27 = y³
At this point, we can see that the equation has only one solution:
y = 3Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent
_________________
Brent Hanneson – Creator of gmatprepnow.com
I’ve spent the last 20 years helping students overcome their difficulties with GMAT math, and the biggest thing I’ve learned is…
Many students fail to maximize their quant score NOT because they lack the skills to solve certain questions but because they don’t understand what the GMAT is truly testing -
Learn more