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Is 2 < x < 4?

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Intern
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S
Joined: 26 Feb 2017
Posts: 28

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

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

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New post 23 Oct 2017, 17:42
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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

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Joined: 02 Aug 2009
Posts: 5345

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

Is 2 < x < 4? [#permalink]

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New post 23 Oct 2017, 18:54
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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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Kudos [?]: 6115 [1], given: 121

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Joined: 07 Jun 2017
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Location: India
Concentration: Technology, General Management
GMAT 1: 660 Q46 V38
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WE: Information Technology (Computer Software)
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Re: Is 2 < x < 4? [#permalink]

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New post 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?
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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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