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Is 2 < x < 4?

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Intern
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S
Joined: 26 Feb 2017
Posts: 30
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, 18:42
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Question Stats:

56% (01:06) correct 44% (01:32) wrong based on 52 sessions

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Is 2 < x < 4?
(1) x^2 – 5x + 6 < 0
(2) 3x^2 – 9x < 0
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V
Joined: 02 Aug 2009
Posts: 6523
Is 2 < x < 4?  [#permalink]

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New post 23 Oct 2017, 19:54
1
1
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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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: Is 2 < x < 4?  [#permalink]

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New post 23 Oct 2017, 23:00
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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Re: Is 2 < x < 4? &nbs [#permalink] 23 Oct 2017, 23:00
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