It is currently 18 Oct 2017, 00:49

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

3 KUDOS received
Senior Manager
Senior Manager
User avatar
B
Affiliations: SPG
Joined: 15 Nov 2006
Posts: 320

Kudos [?]: 867 [3], given: 28

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

Show Tags

New post 23 May 2010, 00:35
3
This post received
KUDOS
13
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

45% (01:22) correct 55% (01:25) wrong based on 436 sessions

HideShow timer Statistics

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

(1) y > 0
(2) 2x + 5y - 20 = 0
[Reveal] Spoiler: OA

_________________

press kudos, if you like the explanation, appreciate the effort or encourage people to respond.

Download the Ultimate SC Flashcards

Kudos [?]: 867 [3], given: 28

Expert Post
7 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41884

Kudos [?]: 128649 [7], given: 12181

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

Show Tags

New post 23 May 2010, 02:49
7
This post received
KUDOS
Expert's post
4
This post was
BOOKMARKED
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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 128649 [7], given: 12181

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41884

Kudos [?]: 128649 [1], given: 12181

Re: is X negative [#permalink]

Show Tags

New post 23 May 2010, 10:08
1
This post received
KUDOS
Expert's post
onedayill wrote:
Bunuel wrote:
dimitri92 wrote:
If -2x>3y , is X negative

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


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

Answer: D.




Can you please explain stmt. 2 again.
Unable to understand the following stmt---

\(-20+5y>3y\)


(2) \(2x+5y-20=0\) --> \(2x=20-5y\) --> given \(-2x>3y\), substitute \(2x\) --> \(-(20-5y)>3y\) --> \(-20+5y>3y\) --> \(y>10\) --> \(y=positive\), as discussed above if \(y\) is any positive number then \(x\) must be some negative number: \(x<0\). Sufficient.


Hope it's clear.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 128649 [1], given: 12181

1 KUDOS received
SVP
SVP
User avatar
S
Joined: 14 Apr 2009
Posts: 2138

Kudos [?]: 1599 [1], given: 8

Location: New York, NY
Re: If -2x > 3y, is x negative? [#permalink]

Show Tags

New post 27 Nov 2011, 19:48
1
This post received
KUDOS
Patcheko80 wrote:
I got this question in the GMATPrep.
I just not sure how Statement B is also valid. Please help.
Here is it.

if -2X > 3Y, is X negative?
(1) Y > 0
(2) 2X + 5Y - 20 = 0



The key here is knowing whether Y is positive or negative. If Y is positive, then X MUST be negative.
If Y=1, then in order for -2x = 3(1) = 3, then X must be a negative number.

If Y is negative, well - X could go either way. For example, if Y = -2, then x could = 2, in which case you would get

-2X > 3Y
-2X > 3(-2)
-2X > -6
x < 3

But the major point here is that if Y is positive, then X MUST be negative.
We already know (1) is good.
But with (2), what info do we know?

Well, if you combine
-2X > 3Y
with
2X + 5Y > 20

then the 2X cancels the -2X, bring the 3Y to the left and negate it and combine it with 5Y.

5Y - 3Y gets you to 2Y

So you get 2Y > 20
Y>10

OK, so what does that tell you? Well, it tells you that Y is positive! It's essentially a subset of statement (1) where Y>0. So both (1) and (2) basically say that Y is positive. That alone is enough info to answer the original question.

Therefore, when both (1) and (2) are good, we pick answer choice (D).

See more GMAT Pill material for Data Sufficiency.

Kudos [?]: 1599 [1], given: 8

1 KUDOS received
VP
VP
User avatar
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1120

Kudos [?]: 2326 [1], given: 219

Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
GMAT ToolKit User
Re: If -2x > 3y, is x negative? (1) y > 0 (2) 2x + 5y - 20 = 0 [#permalink]

Show Tags

New post 29 Jun 2013, 07:45
1
This post received
KUDOS
fozzzy wrote:

In statement 2 we can write the equation 2x+3y+2y = 20 we know 2x+3y is positive and we get y = 10 hence same as statement 1 is this approach correct?


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

(1) y > 0
-2x > +ve number, hence x is negative.
Sufficient

(2) 2x + 5y - 20 = 0
The area defined by -2x > 3y is the area under the red line. If we know that \(2x + 5y - 20 = 0\) (blue line) (given the initial condition) we can say that x is negative because they intersect when x is negative. (refer to the image)
Sufficient

Your approach is correct. We know that 2x+3y is negative (typo I think), so \(2x + 3y +2y= 20\) can be seen as \(-ve +2y=20\) so y is positive for sure as \(2y=20+(+ve)\)
Attachments

Immagine.JPG
Immagine.JPG [ 23.99 KiB | Viewed 4650 times ]


_________________

It is beyond a doubt that all our knowledge that begins with experience.

Kant , Critique of Pure Reason

Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop
Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant

Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b]

Kudos [?]: 2326 [1], given: 219

Expert Post
1 KUDOS received
Math Revolution GMAT Instructor
User avatar
P
Joined: 16 Aug 2015
Posts: 4121

Kudos [?]: 2885 [1], given: 0

GPA: 3.82
Premium Member CAT Tests
Re: If -2x > 3y, is x negative? [#permalink]

Show Tags

New post 13 Jan 2016, 22:59
1
This post received
KUDOS
Expert's post
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

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

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

In the original condition, there are 2 variables(x,y) and 1 equation(-2x>3y), which should match with the number of equations. So you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer. For 1), when y>0, it becomes 3y>2y. That is, -2x>3y>2y, -2x>2y. -x>y --> -x>y>0, -x>0 therefore x<0, which is yes and sufficient.
For 2), substitute y=(-2/5)x+4 to the equation. It becomes -2x>3(-2/5)x+4 and multiply 5 to both equations. Divide -10x>-6x+20, -4x>20 with -4 and x<-5<0 is also yes and sufficient. Therefore, the answer is D.


-> For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Find a 10% off coupon code for GMAT Club members.
“Receive 5 Math Questions & Solutions Daily”
Unlimited Access to over 120 free video lessons - try it yourself
See our Youtube demo

Kudos [?]: 2885 [1], given: 0

Expert Post
1 KUDOS received
Math Forum Moderator
avatar
P
Joined: 02 Aug 2009
Posts: 4967

Kudos [?]: 5455 [1], given: 112

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

Show Tags

New post 21 Jun 2016, 07:42
1
This post received
KUDOS
Expert's post
Shrivathsan wrote:
If -2x > 3y, is x negative?
(1) y > 0
(2) 2x + 5y - 20 = 0


Hi,
-2x > 3y...
(a)If y<0, x can be both +ive and -ive..
(b)if y>0, x will have to be +ive as 3y is positive and -2x , to be positive, has to have x as -ive..


now lets see the choices..


(1) y > 0
If y>0, x is -ive as proved in (b) above... suff

(2) 2x + 5y - 20 = 0..
this can be written as 2x+3y + 2y -20=0..
now 2x+3y<0, so 2y>20... or y is +ive and therefore x is -ive.... suff

ans D
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 5455 [1], given: 112

Expert Post
Top Contributor
1 KUDOS received
SVP
SVP
User avatar
G
Joined: 12 Sep 2015
Posts: 1794

Kudos [?]: 2447 [1], given: 356

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

Show Tags

New post 29 Sep 2016, 08:33
1
This post received
KUDOS
Expert's post
Top Contributor
dimitri92 wrote:
If -2x > 3y, is x negative?

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


Target question: Is x negative?

Given: -2x > 3y

Statement 1: y > 0
In other words, y is POSITIVE
This means that 3y is POSITIVE
It is given that -2x > 3y
Since 3y is POSITIVE, we can write: -2x > SOME POSITIVE #
If -2x is greater than SOME POSITIVE #, we know that -2x is POSITIVE
If -2x is POSITIVE, then x must be negative
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: 2x + 5y - 20 = 0
IMPORTANT: It is given that -2x > 3y
So, let's take 2x + 5y - 20 = 0 and rewrite it as 5y - 20 = -2x [I have isolated -2x, just like we have in the GIVEN information]
Now, we'll take -2x > 3y, and replace -2x with 5y - 20 to get: 5y - 20 > 3y
Subtract 3y from both sides: 2y - 20 > 0
Add 20 to both sides: 2y > 20
Solve: y > 10
This means that y is POSITIVE
We already saw in statement 1, that when y is positive, x must be negative
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer:
[Reveal] Spoiler:
D


RELATED VIDEO

_________________

Brent Hanneson – Founder of gmatprepnow.com

Image

Kudos [?]: 2447 [1], given: 356

Senior Manager
Senior Manager
User avatar
Joined: 25 Feb 2010
Posts: 450

Kudos [?]: 109 [0], given: 10

Re: is X negative [#permalink]

Show Tags

New post 23 May 2010, 09:54
Bunuel wrote:
dimitri92 wrote:
If -2x>3y , is X negative

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


Given: \(-2x>3y\). Q: is \(x<0\)? (Note here that if \(y\) is any positive number than 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) \(2x+5y-20=0\) --> \(2x=20-5y\) --> \(-20+5y>3y\) --> \(y>10\). Same as above: \(x<0\). Sufficient.

Answer: D.




Can you please explain stmt. 2 again.
Unable to understand the following stmt---

\(-20+5y>3y\)
_________________

GGG (Gym / GMAT / Girl) -- Be Serious

Its your duty to post OA afterwards; some one must be waiting for that...

Kudos [?]: 109 [0], given: 10

Director
Director
avatar
B
Joined: 24 Aug 2009
Posts: 500

Kudos [?]: 839 [0], given: 276

Schools: Harvard, Columbia, Stern, Booth, LSB,
Re: If -2x > 3y, is x negative [#permalink]

Show Tags

New post 25 Aug 2013, 00:04
SUNGMAT710 wrote:
If -2x > 3y, is x negative?
(1) y > 0
(2) 2x + 5y - 20 = 0



-2x > 3y
2x + 3y<0 -----(1)

Statement 1
If y>0
& 2x + 3y<0

Then x must be Negative.
Sufficient

Statement 2
2x + 5y - 20 = 0
2x + 5y = 20
(2x + 3y) + 2y=20
We can write
2y + some negative no = 20
2y = 20 + some Positiveno
y = 10 + some Positiveno/2
This mean that y>10

2x + 3y<0
2x< -3y
x < -1.5 (Positive no) because y is positive

Then x must be Negative.
Sufficient

Answer D
_________________

If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS.
Kudos always maximizes GMATCLUB worth
-Game Theory

If you have any question regarding my post, kindly pm me or else I won't be able to reply

Kudos [?]: 839 [0], given: 276

Verbal Forum Moderator
Verbal Forum Moderator
User avatar
Joined: 10 Oct 2012
Posts: 627

Kudos [?]: 1355 [0], given: 136

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

Show Tags

New post 25 Aug 2013, 00:06
SUNGMAT710 wrote:
If -2x > 3y, is x negative?
(1) y > 0
(2) 2x + 5y - 20 = 0


From F.S 1, we know that -2x>0. Thus, x<0. Sufficient.

From F.S 2, we know that \(y = \frac{20-2x}{5}\) , replacing this value , \(-2x>3*\frac{20-2x}{5} \to\)\(-10x>60-6x \to -4x>60\). Again, x<0.

D.
_________________

All that is equal and not-Deep Dive In-equality

Hit and Trial for Integral Solutions

Kudos [?]: 1355 [0], given: 136

Senior Manager
Senior Manager
User avatar
Joined: 11 Nov 2014
Posts: 363

Kudos [?]: 47 [0], given: 17

Location: India
Concentration: Finance, International Business
WE: Project Management (Telecommunications)
GMAT ToolKit User Premium Member
Re: If -2x > 3y, is x negative? [#permalink]

Show Tags

New post 10 Jan 2016, 05:17
We are given
-2x > 3y
need to find if x is negative?

(1) y > 0
x has to be negative to ensure that -2x > 3y
Suff

(2) 2x + 5y - 20 = 0
substituting y = (20-2x)/5
gives
x>15
Suff


Answer D

Kudos [?]: 47 [0], given: 17

Expert Post
Math Forum Moderator
avatar
P
Joined: 02 Aug 2009
Posts: 4967

Kudos [?]: 5455 [0], given: 112

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

Show Tags

New post 10 Jan 2016, 05:18
NoHalfMeasures wrote:
If -2x > 3y, is x negative?
(1) y > 0
(2) 2x + 5y - 20 = 0


Hi,
-2x > 3y...
(a)If y<0, x can be both +ive and -ive..
(b)if y>0, x will have to be +ive as 3y is positive and -2x , to be positive, has to have x as -ive..

now lets see the choices..
(1) y > 0
If y>0, x is -ive as proved in (b) above... suff

(2) 2x + 5y - 20 = 0..
this can be written as 2x+3y + 2y -20=0..
now 2x+3y<0, so 2y>20... or y is +ive and therefore x is -ive.... suff

ans D
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 5455 [0], given: 112

Senior Manager
Senior Manager
User avatar
Joined: 11 Nov 2014
Posts: 363

Kudos [?]: 47 [0], given: 17

Location: India
Concentration: Finance, International Business
WE: Project Management (Telecommunications)
GMAT ToolKit User Premium Member
Re: If -2x > 3y, is x negative? [#permalink]

Show Tags

New post 10 Jan 2016, 05:58
chetan2u wrote:
NoHalfMeasures wrote:
If -2x > 3y, is x negative?
(1) y > 0
(2) 2x + 5y - 20 = 0


Hi,
-2x > 3y...
(a)If y<0, x can be both +ive and -ive..
(b)if y>0, x will have to be +ive as 3y is positive and -2x , to be positive, has to have x as -ive..

now lets see the choices..
(1) y > 0
If y>0, x is -ive as proved in (b) above... suff

(2) 2x + 5y - 20 = 0..
this can be written as 2x+3y + 2y -20=0..
now 2x+3y<0, so 2y>20... or y is +ive and therefore x is -ive.... suff

ans D



how can you say
2x+3y<0?

Kudos [?]: 47 [0], given: 17

Expert Post
Math Forum Moderator
avatar
P
Joined: 02 Aug 2009
Posts: 4967

Kudos [?]: 5455 [0], given: 112

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

Show Tags

New post 10 Jan 2016, 06:20
paidlukkha wrote:
chetan2u wrote:
NoHalfMeasures wrote:
If -2x > 3y, is x negative?
(1) y > 0
(2) 2x + 5y - 20 = 0


Hi,
-2x > 3y...
(a)If y<0, x can be both +ive and -ive..
(b)if y>0, x will have to be +ive as 3y is positive and -2x , to be positive, has to have x as -ive..

now lets see the choices..
(1) y > 0
If y>0, x is -ive as proved in (b) above... suff

(2) 2x + 5y - 20 = 0..
this can be written as 2x+3y + 2y -20=0..
now 2x+3y<0, so 2y>20... or y is +ive and therefore x is -ive.... suff

ans D



how can you say
2x+3y<0?


Hi,
2x + 3y <0 comes from -2x>3y..
-2x>3y..
add 2x to both sides..
2x-2x>3y+2x..
0>2x+3y...
hope it helps
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 5455 [0], given: 112

Senior Manager
Senior Manager
User avatar
Joined: 11 Nov 2014
Posts: 363

Kudos [?]: 47 [0], given: 17

Location: India
Concentration: Finance, International Business
WE: Project Management (Telecommunications)
GMAT ToolKit User Premium Member
If -2x > 3y, is x negative? [#permalink]

Show Tags

New post 10 Jan 2016, 06:29
Hi,
2x + 3y <0 comes from -2x>3y..
-2x>3y..
add 2x to both sides..
2x-2x>3y+2x..
0>2x+3y...
hope it helps[/quote]


Aye, it does!
Thanks :)

Also, if I understand, <> sign changes in multiplication only!

Btw,
St2 gives me x as +ve
What am I doing wrong?
(2) 2x + 5y - 20 = 0
substituting y = (20-2x)/5
gives
x>15
Suff

Kudos [?]: 47 [0], given: 17

Expert Post
Math Forum Moderator
avatar
P
Joined: 02 Aug 2009
Posts: 4967

Kudos [?]: 5455 [0], given: 112

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

Show Tags

New post 10 Jan 2016, 06:32
paidlukkha wrote:
Hi,
2x + 3y <0 comes from -2x>3y..
-2x>3y..
add 2x to both sides..
2x-2x>3y+2x..
0>2x+3y...
hope it helps



Aye, it does!
Thanks :)

Also, if I understand, <> sign changes in multiplication only![/quote]

hi,
yes you are right , whenever you multiply two sides on either side of equality with a -ive sign or -ive quantity, you are required to change the greater/lesser than sign..
-2x>3y..
2x<-3y..
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 5455 [0], given: 112

Expert Post
Math Forum Moderator
avatar
B
Joined: 20 Mar 2014
Posts: 2676

Kudos [?]: 1722 [0], given: 792

Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
GMAT ToolKit User Premium Member Reviews Badge
If -2x > 3y, is x negative? [#permalink]

Show Tags

New post 13 Jan 2016, 07:42
Sash143 wrote:
If -2x > 3y, is x negative?
(1) y > 0
(2) 2x + 5y - 20 = 0


Given that -2x > 3 y---> x<-1.5 y and the question asks whether x<0.

Per statement 1, y>0 ---> from this statement and the fact that x<-1.5y, clearly we can see that x must be <0. Sufficient.

Per statement 2, 2x + 5y - 20 = 0 ---> y = (20-2x)/5 and from the given fact, y<-2x/3 ---> x < -15. Again sufficient to answer the question asked.

Hence both statements are sufficient to answer the question asked. D is thus the correct answer.

Hope this helps.
_________________

Thursday with Ron updated list as of July 1st, 2015: http://gmatclub.com/forum/consolidated-thursday-with-ron-list-for-all-the-sections-201006.html#p1544515
Rules for Posting in Quant Forums: http://gmatclub.com/forum/rules-for-posting-please-read-this-before-posting-133935.html
Writing Mathematical Formulae in your posts: http://gmatclub.com/forum/rules-for-posting-please-read-this-before-posting-133935.html#p1096628
GMATCLUB Math Book: http://gmatclub.com/forum/gmat-math-book-in-downloadable-pdf-format-130609.html
Everything Related to Inequalities: http://gmatclub.com/forum/inequalities-made-easy-206653.html#p1582891
Inequalities tips: http://gmatclub.com/forum/inequalities-tips-and-hints-175001.html
Debrief, 650 to 750: http://gmatclub.com/forum/650-to-750-a-10-month-journey-to-the-score-203190.html

Kudos [?]: 1722 [0], given: 792

Intern
Intern
avatar
Joined: 28 Sep 2011
Posts: 8

Kudos [?]: 1 [0], given: 43

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

Show Tags

New post 13 Jan 2016, 07:59
Sash143 wrote:
If -2x > 3y, is x negative?
(1) y > 0
(2) 2x + 5y - 20 = 0


It is clear that if x negative, -2x > 0, so we will wish to see whether 3y >0, if so -2x > 3y > 0.

(1) y >0 => clearly, -2x > 3y > 0 => x negative

(2) 2x + 5y - 20 = 0. => 2x + 5y =20
Because -2x > 3y => 2x < -3y
=> 2x + 5y < -3y + 5y =2y
or 20 < 2y => 10<y => -2x > 3y > 30 => x negative

So, answer is D

Kudos [?]: 1 [0], given: 43

Expert Post
Math Forum Moderator
avatar
B
Joined: 20 Mar 2014
Posts: 2676

Kudos [?]: 1722 [0], given: 792

Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
GMAT ToolKit User Premium Member Reviews Badge
Re: If -2x > 3y, is x negative? [#permalink]

Show Tags

New post 13 Jan 2016, 09:32
robu wrote:
Bunuel wrote:
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.


we have 2 equation and two variables so we can calculate . so answer is D.


That is a very dangerous way to look at inequalities question.

Same number of equations and variables MAY OR MAY NOT give you unique values.

Example, 2x+3y=10 and 4x+6y=20, you have 2 equation and 2 variables but still you can not determine UNIQUELY the values of x and y.

Refer to solutions above to understand the correct logic behind D being the correct answer.
_________________

Thursday with Ron updated list as of July 1st, 2015: http://gmatclub.com/forum/consolidated-thursday-with-ron-list-for-all-the-sections-201006.html#p1544515
Rules for Posting in Quant Forums: http://gmatclub.com/forum/rules-for-posting-please-read-this-before-posting-133935.html
Writing Mathematical Formulae in your posts: http://gmatclub.com/forum/rules-for-posting-please-read-this-before-posting-133935.html#p1096628
GMATCLUB Math Book: http://gmatclub.com/forum/gmat-math-book-in-downloadable-pdf-format-130609.html
Everything Related to Inequalities: http://gmatclub.com/forum/inequalities-made-easy-206653.html#p1582891
Inequalities tips: http://gmatclub.com/forum/inequalities-tips-and-hints-175001.html
Debrief, 650 to 750: http://gmatclub.com/forum/650-to-750-a-10-month-journey-to-the-score-203190.html

Kudos [?]: 1722 [0], given: 792

Re: If -2x > 3y, is x negative?   [#permalink] 13 Jan 2016, 09:32

Go to page    1   2    Next  [ 24 posts ] 

Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.