gmat prep 2

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jainrahul1985: Master | Next Rank: 500 Posts; Posts: 228; Joined: Sun Aug 17, 2008 8:08 am; Thanked: 4 times

by jainrahul1985 » Tue Jul 26, 2011 12:19 am

If -2x > 3y, is x negative?

(1) y > 0
(2) 2x + 5y - 20 = 0

OA D

1)-2x > 3y
=> x < -(3/2)y
Also y > 0

Therefore x has to be negative

Experts please help me understand why Statement 2 is sufficient

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Source: Beat The GMAT — Data Sufficiency | Tue Jul 26, 2011 12:19 am

Geva@EconomistGMAT: GMAT Instructor; Posts: 905; Joined: Sun Sep 12, 2010 1:38 amFollowed by: 123 members; Thanked: 378 times; GMAT Score:760

by Geva@EconomistGMAT » Tue Jul 26, 2011 12:26 am

jainrahul1985 wrote:If -2x > 3y, is x negative?

(1) y > 0
(2) 2x + 5y - 20 = 0

OA D

1)-2x > 3y
=> x < -(3/2)y
Also y > 0

Therefore x has to be negative

Experts please help me understand why Statement 2 is sufficient

Isolate x:

2x=20-5y

Multiply by -1 to get the -2x from the question stem:

-2x=-(20-5y)
-2x = -20+5y
-2x=5y-20.
Now you know that -2x>3y, so you can say that

5y-20>3y
2y>20
y>10

which means that y is positive, same as (1).

Geva
Senior Instructor
Master GMAT
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https://www.mastergmat.com

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue Jul 26, 2011 12:34 am

jainrahul1985 wrote:If -2x > 3y, is x negative?

(1) y > 0
(2) 2x + 5y - 20 = 0

OA D

1)-2x > 3y
=> x < -(3/2)y
Also y > 0

Therefore x has to be negative

Experts please help me understand why Statement 2 is sufficient

Statement 1: y > 0
Since y > 0, 3y > 0.
Linking together -2x > 3y and 3y > 0, we get:
-2x > 3y > 0
-2x > 0
x < 0.
Sufficient.

Statement 2: 2x + 5y - 20 = 0
Thus, 5y-20 = -2x.
Substituting 5y-20 for -2x in -2x > 3y, we get:
5y-20 > 3y
2y > 20
y > 10.
We saw in statement 1 that y > 0 implies that x < 0.
Sufficient.

The correct answer is D.

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Tue Jul 26, 2011 4:05 am

jainrahul1985 wrote:If -2x > 3y, is x negative?

(1) y > 0
(2) 2x + 5y - 20 = 0

OA D

1)-2x > 3y
=> x < -(3/2)y
Also y > 0

Therefore x has to be negative

Experts please help me understand why Statement 2 is sufficient

Got a PM to reply on this thread.

(1) y > 0 implies 3y > 0, which implies -2x > 0, which means -2x should be a positive value.
For -2x to be positive, x should be a negative value; SUFFICIENT.

(2) 2x + 5y - 20 = 0 or -2x = 5y - 20
Now -2x > 3y implies 5y - 20 > 3y or 2y > 20 or y > 10, which implies y is a positive value. And hence, x should be negative; SUFFICIENT.

The correct answer is D.

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