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Bunuel
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If x is an integer and x + x^2 + x^3 is odd, which of the following 12 Apr 2016, 02:23
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E
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85% (01:15) correct 15% (01:26) wrong based on 191 sessions

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If x is an integer and x + x^2 + x^3 is odd, which of the following must be even?

A. x
B. x^2
C. x^3
D. 3x
E. x + x^2
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E
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OptimusPrepJanielle
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If x is an integer and x + x^2 + x^3 is odd, which of the following 12 Apr 2016, 03:33
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Bunuel
If x is an integer and x + x^2 + x^3 is odd, which of the following must be even?

A. x
B. x^2
C. x^3
D. 3x
E. x + x^2

x + x^2 + x^3 = odd
Since each is a power of x, x has to be odd

On checking the options, only
x + x^2 = odd + odd = even
Correct option: E
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If x is an integer and x + x^2 + x^3 is odd, which of the following 22 Jan 2017, 11:54
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We actually don't need the even/odd nature of x.
Irrespective of x being even or odd=>x+x^2 will always be even.

Hence E.
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If x is an integer and x + x^2 + x^3 is odd, which of the following 25 Jan 2017, 11:16
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Bunuel
If x is an integer and x + x^2 + x^3 is odd, which of the following must be even?

A. x
B. x^2
C. x^3
D. 3x
E. x + x^2

We are given that x + x^2 + x^3 = odd

We can factor out an x:

x(1 + x + x^2) = odd

Since the product of two odd numbers = odd number, x MUST BE odd. Since x is odd, x^2 MUST BE odd also. Since odd + odd = even, we see that only answer choice E, x + x^2, is even.

Alternate solution:

When the sum of three integers is odd, EITHER each one is odd OR two of them are even and one of them is odd. However, since any integer raised to a power has the same parity (the fact of being odd or even), x, x^2, and x^3 must be ALL odd. Since odd + odd = even, we see that only answer choice E, x + x^2, is even.

Answer: E
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If x is an integer and x + x^2 + x^3 is odd, which of the following 26 Mar 2017, 03:15
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Bunuel
If x is an integer and x + x^2 + x^3 is odd, which of the following must be even?

A. x
B. x^2
C. x^3
D. 3x
E. x + x^2

I solved for x to be odd and selected A. I want to shoot myself.
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If x is an integer and x + x^2 + x^3 is odd, which of the following 01 Jan 2023, 00:55
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Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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