Is xm < ym ?

[BTGModeratorVI]

Is xm < ym ?

(1) x > y
(2) m < 0

Answer: C
Source: Official Guide

[Brent@GMATPrepNow]

Is xm < ym ?

(1) x > y
(2) m < 0

Answer: C
Source: Official Guide

Target question: Is xm < ym?
Another approach is to rephrase the target question.

Take the inequality and subtract ym from both sides to get: xm - ym < 0
Factor out the m to get m(x - y) < 0
In other words....
REPHRASED target question: Is m(x - y) a NEGATIVE value?

Aside: Here’s a video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100

Statement 1: x > y
Subtract y from both sides to get: x - y > 0
So, x - y is a POSITIVE value
Does this provide enough information to determine whether or not m(x - y) a NEGATIVE value?
No. We still don't know anything about the value of m
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: m < 0
In other words, m is NEGATIVE
Does this provide enough information to determine whether or not m(x - y) a NEGATIVE value?
No. We don't know anything about the value of (x - y)
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that x - y is a POSITIVE value
Statement 2 tells us that m is a NEGATIVE value
So, m(x - y) = (NEGATIVE)(POSITIVE) = some NEGATIVE VALUE
In other words, m(x - y) is definitely a NEGATIVE value
Since we can answer the REPHRASED target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent

[Scott@TargetTestPrep]

Is xm < ym ?

(1) x > y
(2) m < 0

Answer: C
Source: Official Guide

Solution:

We need to determine whether xm < ym.

Statement One Alone:

Statement one alone is not sufficient since we don’t know the value of m. For example, if x = 2, y = 1 and m = -1, then we do have xm < ym. However, if x = 2, y = 1 and m = 1, then we don’t have xm < ym.

Statement Two Alone:

Statement two alone is not sufficient since we don’t know the values of x and y. For example, if x = 2, y = 1 and m = -1, then we do have xm < ym. However, if x = -2, y = -1 and m = -1, then we don’t have xm < ym.

Statements One and Two Together:

Both statements together are sufficient. If we multiply the inequality x > y by m, which is negative, we need to switch the inequality sign and obtain xm < ym.

Answer: C