Data Sufficiency

VJesus12 wrote: ↑

Sun Oct 03, 2021 10:19 am

If \(x\) and \(y\) are integers, what is the value of \(y?\)

(1) \(xy = 27\)
(2) \(x = y^2\)

Answer: C

Source: Official Guide

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 = 27
Case b: x = 3 and y = 9. In this case, the answer to the target question is y = 9
Since we can’t answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x = y²
There 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 = 1
Case b: x = 4 and y = 2. In this case, the answer to the target question is y = 2
Since 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 = 3

Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent