Is xy > 0?

This topic has expert replies
Moderator
Posts: 7187
Joined: Thu Sep 07, 2017 4:43 pm
Followed by:23 members

Is xy > 0?

by BTGmoderatorDC » Mon Apr 15, 2019 10:11 pm

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Is xy > 0?

(1) x - y > -2
(2) x - 2y < -6

OA C

Source: GMAT Prep

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Tue Apr 16, 2019 6:36 am

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

BTGmoderatorDC wrote:Is xy > 0?

(1) x - y > -2
(2) x - 2y < -6
Target question: Is xy > 0?

Statement 1: x - y > -2
Let's TEST some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 5 and y = 1. In this case, xy = (5)(1) = 5. So, the answer to the target question is YES, xy IS greater than 0
Case b: x = 5 and y = -1. In this case, xy = (5)(-1) = -5. So, the answer to the target question is NO, xy is NOT greater than 0
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x - 2y < -6
Let's TEST some values again.
There are several values of x and y that satisfy statement 2. Here are two:
Case a: x = 1 and y = 10. In this case, xy = (1)(10) = 10. So, the answer to the target question is YES, xy IS greater than 0
Case b: x = -1 and y = 10. In this case, xy = (-1)(10) = -10. So, the answer to the target question is NO, xy is NOT greater than 0
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
IMPORTANT: There's a useful inequality property that says If two inequalities have their inequality symbols facing the same way, we can ADD the inequalities.
We have:
x - y > -2
x - 2y < -6

Take the BOTTOM equation and multiply both sides by -1 to get:
x - y > -2
-x + 2y > 6 [since we multiplied both sides by a NEGATIVE value, we REVERSED the direction of the inequality symbol]

Now ADD the equations to get: y > 4
In other words, y is POSITIVE

Now take:
x - y > -2
-x + 2y > 6

Take the TOP equation and multiply both sides by 2 to get:
2x - 2y > -4
-x + 2y > 6

Now ADD the equations to get: x > 2
In other words, x is POSITIVE

Since x and y are both POSITIVE, we know that xy IS positive
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image