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If x is an integer and (x2 -16)(x2 + x -2) < 0, what is the sum of all

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If x is an integer and (x2 -16)(x2 + x -2) < 0, what is the sum of all  [#permalink]

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New post 27 Nov 2018, 11:40
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Difficulty:

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Question Stats:

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If x is an integer and (\(x^2\) - 16)(\(x^2\) + x - 2) < 0, what is the sum of all the possible values of x?

A. -1
B. 0
C. 1
D. 2
E. 3
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Re: If x is an integer and (x2 -16)(x2 + x -2) < 0, what is the sum of all  [#permalink]

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New post 27 Nov 2018, 21:50
rencsee wrote:
If x is an integer and (\(x^2\) - 16)(\(x^2\) + x - 2) < 0, what is the sum of all the possible values of x?

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


To solve such an inequality, one should factorize left hand side; we can rewrite the left hand side as:
\((x-4)(x+4)(x+2)(x-1)<0\)
so, the roots are: -4, -2, +1 & +4.
As you can see, x=-100 yields a positive (+ve) value because of 4 negative values resulted from each parenthesis, while we are looking for a -ve value.

According to attached diagram we can see that integer -ve values are -3, +2 & +3. So the sum of these values equal +2.
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Posts: 7108
Re: If x is an integer and (x2 -16)(x2 + x -2) < 0, what is the sum of all  [#permalink]

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New post 27 Nov 2018, 21:50
rencsee wrote:
If x is an integer and (\(x^2\) - 16)(\(x^2\) + x - 2) < 0, what is the sum of all the possible values of x?

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



Let us factorize (\(x^2\) - 16)(\(x^2\) + x - 2) < 0..
(x+4)(x-4)(x+2)(x-1)<0....
let us write the terms in ascending order..
\((x+4)(x+2)(x-1)(x-4)<0\)..
Now, there are 4 terms and for their product to be NEGATIVE, Odd number should be negative.. so 1 or 3.
Critical points now
(I) x<-4...
all 4 terms negative....NO
(II) -4<x<-2..
x+4 is positive and rest 3 terms negative.. YES
possible value in range -2<x<-4 is -3
(III) -2<x<1
two terms positive and two terms negative.. NO
(IV) 1<x<4
Only x-4 is negative.... YES
possible values in range 1<x<4 is 2 and 3.
(V) x>4
all positive....NO

so all in all possible values are -3, 2, 3 and their sum = 2+3-3=2
D
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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: If x is an integer and (x2 -16)(x2 + x -2) < 0, what is the sum of all  [#permalink]

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New post 27 Nov 2018, 22:02
(x+4)(x+2)(x-1)(x-4) < 0
-4<x<-2 || 1<x<4

-3 + 2 + 3
= 2
Ans D
GMAT Club Bot
Re: If x is an integer and (x2 -16)(x2 + x -2) < 0, what is the sum of all &nbs [#permalink] 27 Nov 2018, 22:02
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