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Is 2 < x < 4?

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Intern
Joined: 26 Feb 2017
Posts: 30
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:

50% (02:00) correct 50% (02:11) wrong based on 55 sessions

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Is 2 < x < 4?
(1) x^2 – 5x + 6 < 0
(2) 3x^2 – 9x < 0
Math Expert
Joined: 02 Aug 2009
Posts: 7035
Is 2 < x < 4?  [#permalink]

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23 Oct 2017, 18:54
1
2
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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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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Regards,
Naveen
email: nkmungila@gmail.com
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Re: Is 2 < x < 4? &nbs [#permalink] 23 Oct 2017, 22:00
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