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Is 2x - 3y < x^2?

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Manager
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Is 2x - 3y < x^2? [#permalink] New post 04 Jun 2006, 00:00
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A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

60% (01:58) correct 40% (00:59) wrong based on 91 sessions
Is 2x - 3y < x^2?

(1) 2x - 3y = -2
(2) x > 2 and y > 0

OPEN DISCUSSION OF THIS QUESTION IS HERE: is-2x-3y-x-100596.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 21 Oct 2014, 06:28, edited 2 times in total.
Edited the question and added the OA
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Manager
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Re: Is 2x - 3y < x^2? [#permalink] New post 04 Jun 2006, 02:27
dinesh8 wrote:
Is 2x-3y<x^2?

1. 2x-3y =-2
2. X> 2 and y>0


D

Statement 1
any square value is >= 0 hence x^2 > 2x-3y

Statement2

for x>2 , X^2 >2x, 2x-x^2<0
for y>0, 3y >0

therefore 3y>2x-x^2
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Re: Is 2x - 3y < x^2? [#permalink] New post 11 Jun 2006, 08:32
got D, although did it more by plugging in values.
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Re: Is 2x - 3y < x^2? [#permalink] New post 13 Jun 2006, 00:28
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Will go with D .

1) 2x-3y = -2
A square of any number is > 0 hence 2x-3y<x^2

2) x> 2 and y > 0
Putting any values for x and y and you will see that 2x-3y < x^2
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Re: Is 2x - 3y < x^2? [#permalink] New post 04 Jul 2013, 00:33
dinesh8 wrote:
Is \(2x-3y\)<\(x^2\)?

1. \(2x-3y =-2\)
2. \(x> 2\) and \(y>0\)


How is it D?

I'm getting A

But in choice B there can be multiple cases

for example

X=3 and y=10 in this case its a Yes

but if x=3, y=1

the question becomes is \(X^2 > 3\) we can't answer that?
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Re: Is 2x - 3y < x^2? [#permalink] New post 04 Jul 2013, 00:38
Expert's post
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fozzzy wrote:
dinesh8 wrote:
Is \(2x-3y\)<\(x^2\)?

1. \(2x-3y =-2\)
2. \(x> 2\) and \(y>0\)


How is it D?

I'm getting A

But in choice B there can be multiple cases

for example

X=3 and y=10 in this case its a Yes

but if x=3, y=1

the question becomes is \(X^2 > 3\) we can't answer that?


Is \(2x-3y<x^2\)?

(1) \(2x-3y=-2\) --> question becomes: is \(-2<x^2\)? as square of a number is always non-negative (\(x^2\geq{0}\)) then \(x^2\geq{0}>-2\). Sufficient.

(2) \(x>2\) and \(y>0\) --> is \(2x-3y<x^2\) --> is \(x(x-2)+3y>0\) --> as \(x>2\) then \(x(x-2)\) is a positive number and as \(y>0\) then \(3y\) is also a positive number --> sum of two positive numbers is more than zero, hence \(x(x-2)+3y>0\) is true. Sufficient.

Answer: D.

OPEN DISCUSSION OF THIS QUESTION IS HERE: is-2x-3y-x-100596.html
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Expert Post
Math Expert
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Joined: 02 Sep 2009
Posts: 28731
Followers: 4577

Kudos [?]: 47204 [0], given: 7108

Re: Is 2x - 3y < x^2? [#permalink] New post 04 Jul 2013, 00:42
Expert's post
fozzzy wrote:
dinesh8 wrote:
Is \(2x-3y\)<\(x^2\)?

1. \(2x-3y =-2\)
2. \(x> 2\) and \(y>0\)


How is it D?

I'm getting A

But in choice B there can be multiple cases

for example

X=3 and y=10 in this case its a Yes

but if x=3, y=1

the question becomes is \(X^2 > 3\) we can't answer that?


If x=3 and y=1 we still have an YES answer: 2*3-3*1=3<9=x^2.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. 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.


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Re: Is 2x - 3y < x^2?   [#permalink] 04 Jul 2013, 00:42
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