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# Is 2 < x < 4?

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Intern
Joined: 26 Feb 2017
Posts: 28

Kudos [?]: 46 [0], given: 41

Location: Brazil
GMAT 1: 610 Q45 V28
GPA: 3.11
Is 2 < x < 4? [#permalink]

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23 Oct 2017, 17:42
00:00

Difficulty:

65% (hard)

Question Stats:

54% (01:00) correct 46% (01:37) wrong based on 48 sessions

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Is 2 < x < 4?
(1) x^2 – 5x + 6 < 0
(2) 3x^2 – 9x < 0
[Reveal] Spoiler: OA

Kudos [?]: 46 [0], given: 41

Math Expert
Joined: 02 Aug 2009
Posts: 5345

Kudos [?]: 6115 [1], given: 121

Is 2 < x < 4? [#permalink]

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23 Oct 2017, 18:54
1
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Expert's post
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vitorpteixeira wrote:
Is 2 < x < 4?
(1) x^2 – 5x + 6 < 0
(2) 3x^2 – 9x < 0

Hi..
we can substitue values to see if answers match or find the values of x in each case..

$$(1) x^2 – 5x + 6 < 0$$..
$$x^2-5x+6<0....(x-3)(x-2)<0$$
so two cases..
A) $$x-3<0$$ and $$x-2>0$$
that is x<3 and x>2...
2<x<3..
matches with the range
B) $$x-3>0$$ and $$x-2<0$$..
x>3 and x<2...
NOT possible

so ONLY range is 2<x<3
ans is YES

sufficient

(2) 3x^2 – 9x < 0
$$3x(x-3)<0$$..
again two cases
A) $$3x<0$$ and $$x-3>0$$..
x<0 and x>3..
not possible
B) $$3x>0$$ and $$x-3<0$$
x>0 and x<3
range 0<x<3
so if x is 1 ans is NO but if x is 2.5 ans is YES
insuff

A
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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 [?]: 6115 [1], given: 121

Manager
Joined: 07 Jun 2017
Posts: 177

Kudos [?]: 102 [0], given: 59

Location: India
Concentration: Technology, General Management
GMAT 1: 660 Q46 V38
GPA: 3.6
WE: Information Technology (Computer Software)
Re: Is 2 < x < 4? [#permalink]

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23 Oct 2017, 22:00
Is it possible to solve this problem using trail and error
for example putting value of 2, 3 and 4 in each equation and checking whether answer matching?
_________________

Regards,
Naveen
email: nkmungila@gmail.com
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Kudos [?]: 102 [0], given: 59

Re: Is 2 < x < 4?   [#permalink] 23 Oct 2017, 22:00
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