If -2x>3y, is x negative : GMAT Data Sufficiency (DS)
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If -2x>3y, is x negative

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If -2x>3y, is x negative [#permalink]

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

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

Could any one please tell me why the second one works? Thanks so much again!

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Last edited by Bunuel on 17 Jul 2014, 04:38, edited 1 time in total.
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Re: If -2x>3y, is x negative [#permalink]

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YTT wrote:
Could any one please tell me why the second one works? Thanks so much again!


(2) \(2x+5y-20=0\) --> \(y=4-\frac{2}{5}x\), substitute \(y\) --> \(-2x>3(4-\frac{2}{5}x)\) --> \(-2x>12-\frac{6}{5}x\) --> \(-12>\frac{4}{5}x\) --> \(x<-15\). Obviously if \(x<-15\) it's negative. Sufficient.

Hope it helps.
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Re: If -2x>3y, is x negative [#permalink]

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New post 15 Feb 2010, 14:26
Ques x < 0 ?

Given -2x > 3y

S1: y > 0... implies 3y > 0
Therefore -2x > 0.... this can only happen if x < 0.. Hence SUFF

S2: 2x + 5y = 20
5y - 20 = 2x

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

Therefore -2x > 30.... this can only be possible if x < 0... Hence SUFF..

Therefore D..
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Re: If -2x>3y, is x negative [#permalink]

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New post 12 Mar 2010, 03:49
-2x > 3y

stmt1: y>0 if y>0 => 3y>0 => -2x>0 => 2x<0 => x< 0 so suff to answer

stmt2: 2x+5y-20 = 0 => 2x+5y = 20 => 5y = 20 - 2x => y = (20-2x)/5
replace y in first -2x>3y

-2x>3(20-2x)/5
=> -10x>60-6x
=>-4x>60
=>-x>15
=>x<-15 (multiply by -1 both the sides and change the inequalities)
if x<-15 it is sure that x<0 also so suff
hence, both alone can determine the answer
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Re: If -2x>3y, is x negative [#permalink]

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Re: If -2x>3y, is x negative [#permalink]

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New post 17 Jul 2014, 02:57
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Re: If -2x>3y, is x negative [#permalink]

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New post 17 Jul 2014, 04:20
YTT wrote:
Could any one please tell me why the second one works? Thanks so much again!



Statement I is sufficient:

If y is positive and -2x > positive hence x has to be negative

Statement II is sufficient:
2x + 5y = 20

-2x > 3y

-2x > 3(20 - 2x)/5

-10x > 60 - 6x

-4x>60
-x > 15
x<-15

Hence the answer is D.
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Re: If -2x>3y, is x negative [#permalink]

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New post 17 Jul 2014, 04:40
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If -2x>3y , is x negative

Given: \(-2x>3y\).
Question: is \(x<0\)? (Note here that if \(y\) is any positive number then we would have \(-2x>positive\), and in order that to be true \(x\) must be some negative number).

(1) \(y>0\) --> \(-2x>3y>0\) --> \(x<0\). Sufficient.

(2) \(2x+5y-20=0\) --> \(2x=20-5y\) --> \(-20+5y>3y\) --> \(y>10\). The same as above: \(x<0\). Sufficient.

Answer: D.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-2x-3y-is-x-negative-94665.html
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Resources:
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: If -2x>3y, is x negative   [#permalink] 17 Jul 2014, 04:40
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