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# 4 < x^2 + 2x + 1 < 16

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Intern
Joined: 26 Feb 2017
Posts: 25

Kudos [?]: 28 [0], given: 38

4 < x^2 + 2x + 1 < 16 [#permalink]

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23 Oct 2017, 18:25
2
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Difficulty:

85% (hard)

Question Stats:

44% (02:40) correct 56% (01:27) wrong based on 87 sessions

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How many integers satisfy this inequality?
4 < x^2 + 2x + 1 < 16

A - 4
B - 3
C - 2
D - 1
E - 0
[Reveal] Spoiler: OA

Kudos [?]: 28 [0], given: 38

Math Expert
Joined: 02 Aug 2009
Posts: 5214

Kudos [?]: 5861 [0], given: 117

4 < x^2 + 2x + 1 < 16 [#permalink]

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23 Oct 2017, 20:07
Expert's post
1
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vitorpteixeira wrote:
How many integers satisfy this inequality?
4 < x^2 + 2x + 1 < 16

A - 4
B - 3
C - 2
D - 1
E - 0

hi..

so lets solve the equation..
$$4 < x^2 + 2x + 1 < 16......4<(x+1)^2<16......$$
we are looking for integer values..
(x+1) can take two values (x+1)=3 or x+1=-3......
so x=3-1=2 and x=-3-1=-4

so two values : 2 and -4
C
_________________

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 [?]: 5861 [0], given: 117

4 < x^2 + 2x + 1 < 16   [#permalink] 23 Oct 2017, 20:07
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