Data Sufficiency

BTGModeratorVI wrote: ↑

Fri Apr 03, 2020 9:35 am

Is x > y?

(1) -4x + 2y < y - 3x
(2) wx > wy

Answer: A
Source: Magoosh

Target question: Is x > y?

Statement 1: -4x + 2y < y - 3x
Add 4x to both sides to get: 2y < y + x
Subtract y from both sides to get: y < x
Perfect, the answer to the target question is YES, x IS greater than y
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: wx > wy
ASIDE: We must resist the temptation to divide both sides of the inequality by w to get: x > y, because we don't know whether w is NEGATIVE or POSITIVE.
If we divide both sides of an inequality by a NEGATIVE number, we must REVERSE the direction of the inequality symbol.
To better understand what I mean, consider the following.
There are several values of w, x and y that satisfy statement 2. Here are two:
Case a: w = 1, x = 2 and y = 1. Notice that wx = (1)(2) = 2, and wy = (1)(1) = 1, so wx > wy. In this case, the answer to the target question is YES, x IS greater than y
Case b: w = -1, x = -2 and y = -1. Notice that wx = (-1)(-2) = 2, and wy = (-1)(-1) = 1, so wx > wy. In this case, the answer to the target question is NO, x is NOT greater than y
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent