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# If x is an integer and (x)(x^2)(x^3) is positive, which of the followi

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Math Expert
Joined: 02 Sep 2009
Posts: 43896
If x is an integer and (x)(x^2)(x^3) is positive, which of the followi [#permalink]

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20 Apr 2016, 00:01
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90% (00:33) correct 10% (00:22) wrong based on 82 sessions

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If x is an integer and (x)(x^2)(x^3) is positive, which of the following could be negative?

A. x^4
B. (x)(x^3)
C. (x)(x)
D. x + x^3
E. 3x^2
[Reveal] Spoiler: OA

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Manager
Joined: 10 Apr 2016
Posts: 55
Concentration: Strategy, Entrepreneurship
GMAT 1: 520 Q29 V30
GPA: 3.01
Re: If x is an integer and (x)(x^2)(x^3) is positive, which of the followi [#permalink]

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20 Apr 2016, 02:04
Assuming) x is negative (makes it easier)

(-2)(-2^2)(-2^3)

(-2)^3.(-2)^3

The two negative numbers will remain negative, so they will both cancel out.
So we need an equation where x^n with n being odd.

a) not sufficient -> will always be positive
b) not sufficient -> equals x^4 which will always be positive
c) not sufficient -> equals x^2 which will always be positive
d) -2+-8 = -10!!!
e) 3*4=12 is positive (pemdas!)

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Re: If x is an integer and (x)(x^2)(x^3) is positive, which of the followi [#permalink]

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20 Apr 2016, 09:48
Bunuel wrote:
If x is an integer and (x)(x^2)(x^3) is positive,which of the following could be negative?

A. x^4
B. (x)(x^3)
C. (x)(x)
D. x + x^3
E. 3x^2

$$x^y$$ can be negative only when y is odd...

This $$x^3$$ will be negative

Further (-ve ) + (-ve ) = (-ve )

Only (D) follows ( because all others are x^ even numbers , resulting in a +ve number)...
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Manager
Joined: 29 Jul 2015
Posts: 64
Location: Australia
GMAT 1: 680 Q49 V33
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Re: If x is an integer and (x)(x^2)(x^3) is positive, which of the followi [#permalink]

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20 Apr 2016, 21:12
If x is an integer and (x)(x^2)(x^3) is positive, which of the following could be negative?

A. x^4
B. (x)(x^3)
C. (x)(x)
D. x + x^3
E. 3x^2

A) X^4 - always positive (or 0).
B) X(X^3) = X^4 - Again always positive (or 0).
C) (x)(x) = X^2 - Again always positive (or 0).
D) x+x^3 - Could be -ve if x is -ve.
E) 3X^2 - again always positive (or 0)

Manager
Joined: 16 Feb 2016
Posts: 53
Concentration: Other, Other
Re: If x is an integer and (x)(x^2)(x^3) is positive, which of the followi [#permalink]

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20 Apr 2016, 21:24
X is negative only when the power is odd.
Hence (d)
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Posts: 207
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Re: If x is an integer and (x)(x^2)(x^3) is positive, which of the followi [#permalink]

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18 Apr 2017, 03:16
Bunuel wrote:
If x is an integer and (x)(x^2)(x^3) is positive, which of the following could be negative?

A. x^4
B. (x)(x^3)
C. (x)(x)
D. x + x^3
E. 3x^2

Time Taken: 1:09
As per statement
two condition either
(-)(-)^2(-)^3=+ve
(+)(+)^2(+)^3=+ve
Now start check
Option A: Since Power is even so always positive
Option B: Sum of Power even so always positive
Option C: Sum of power even so always Positive
Option E: Power even so always positive
For option D take -1
(-1)+(-1)^3=-2
Option: D is correct
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Re: If x is an integer and (x)(x^2)(x^3) is positive, which of the followi [#permalink]

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24 Apr 2017, 15:59
1
KUDOS
Expert's post
Bunuel wrote:
If x is an integer and (x)(x^2)(x^3) is positive, which of the following could be negative?

A. x^4
B. (x)(x^3)
C. (x)(x)
D. x + x^3
E. 3x^2

Observe that (x)(x^2)(x^3) = x^6, which is always nonnegative regardless of the value of x. Similarly, observe that x is (or simplified to be) raised to an even power in choices A, B, C, and E, so their respective expression will also be nonnegative. Thus, the only expression that could be negative is choice D (e.g., let x = -1, then x + x^3 = -2).

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Re: If x is an integer and (x)(x^2)(x^3) is positive, which of the followi   [#permalink] 24 Apr 2017, 15:59
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