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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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Bunuel
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If x is an integer and (x)(x^2)(x^3) is positive, which of the followi [#permalink] New post   20 Apr 2016, 01:01
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D
E

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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
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D
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mathiaskeul
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Re: If x is an integer and (x)(x^2)(x^3) is positive, which of the followi [#permalink] New post   20 Apr 2016, 03:04
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!)

Answer is d
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Re: If x is an integer and (x)(x^2)(x^3) is positive, which of the followi [#permalink] New post   20 Apr 2016, 10:48
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)... :-D :lol: :P
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Re: If x is an integer and (x)(x^2)(x^3) is positive, which of the followi [#permalink] New post   20 Apr 2016, 22:12
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)

Answer D.
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Re: If x is an integer and (x)(x^2)(x^3) is positive, which of the followi [#permalink] New post   20 Apr 2016, 22:24
X is negative only when the power is odd.
Hence (d)
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Re: If x is an integer and (x)(x^2)(x^3) is positive, which of the followi [#permalink] New post   18 Apr 2017, 04:16
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] New post   24 Apr 2017, 16:59
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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).

Answer: D
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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, 16:59
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