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# Is 2 < x < 4? 1) x - 5x + 6 < 0 2) 5x - 25x > 0

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Current Student
Joined: 11 May 2008
Posts: 553
Is 2 < x < 4? 1) x - 5x + 6 < 0 2) 5x - 25x > 0 [#permalink]

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28 Jul 2008, 05:03
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Is 2 < x < 4?
1) x² - 5x + 6 < 0
2) 5x² - 25x > 0
SVP
Joined: 07 Nov 2007
Posts: 1789
Location: New York
Re: how to solve inequality [#permalink]

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28 Jul 2008, 05:33
arjtryarjtry wrote:
Is 2 < x < 4?
1) x² - 5x + 6 < 0
2) 5x² - 25x > 0

1)
x² - 5x + 6 < 0
= x² - 3x -2x+ 6 < 0
= (x-3) (x-2)<0

assume x=3.5 .. --> LEADS to >0
assume x=2.5 --> LEADS to <0
So, state (1) is not suffcient

2) 5x² - 25x > 0
5x (x-5)>0
assume x=3 --> LEADS to <0
that is incorrect.

BOTH statements are not sufficient..
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Director
Joined: 27 May 2008
Posts: 540
Re: how to solve inequality [#permalink]

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28 Jul 2008, 05:37
arjtryarjtry wrote:
Is 2 < x < 4?
1) x² - 5x + 6 < 0
2) 5x² - 25x > 0

refer thread 7-t67336 for the same question, interesting discussion..
SVP
Joined: 07 Nov 2007
Posts: 1789
Location: New York
Re: how to solve inequality [#permalink]

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28 Jul 2008, 06:11
durgesh79 wrote:
arjtryarjtry wrote:
Is 2 < x < 4?
1) x² - 5x + 6 < 0
2) 5x² - 25x > 0

refer thread 7-t67336 for the same question, interesting discussion..

thanks.. good question.
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Smiling wins more friends than frowning

Senior Manager
Joined: 19 Mar 2008
Posts: 351
Re: how to solve inequality [#permalink]

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28 Jul 2008, 06:48
arjtryarjtry wrote:
Is 2 < x < 4?
1) x² - 5x + 6 < 0
2) 5x² - 25x > 0

Is 2 < x < 4?

1) x² - 5x + 6 < 0
(x-3)(x-2) < 0
2 < x < 3
(1) alone is sufficient

2) 5x² - 25x > 0
x(x-5) > 0
x < 0 or x > 5
so we can prove that 2 < x < 4 is NOT true
so (2) alone is sufficient

D
Re: how to solve inequality   [#permalink] 28 Jul 2008, 06:48
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# Is 2 < x < 4? 1) x - 5x + 6 < 0 2) 5x - 25x > 0

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