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# If |x| + x = 4, then which one of the following is odd?

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Joined: 02 Sep 2009
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If |x| + x = 4, then which one of the following is odd?  [#permalink]

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02 Apr 2019, 04:03
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5% (low)

Question Stats:

94% (01:04) correct 6% (00:52) wrong based on 47 sessions

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If $$|x| + x = 4$$, then which one of the following is odd?

(A) $$x^2 + 3x$$

(B) $$x^2 + 3x + 2$$

(C) $$x^2 + 4x$$

(D) $$x^2 + 4x + 2$$

(E) $$x^2 + 4x + 3$$

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Re: If |x| + x = 4, then which one of the following is odd?  [#permalink]

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02 Apr 2019, 04:15
Bunuel wrote:
If $$|x| + x = 4$$, then which one of the following is odd?

(A) $$x^2 + 3x$$

(B) $$x^2 + 3x + 2$$

(C) $$x^2 + 4x$$

(D) $$x^2 + 4x + 2$$

(E) $$x^2 + 4x + 3$$

x must be positive. negative x won't work here.

x + x = 4

2x = 4

x = 2.

Option E)

$$2^2 + 4*2 + 3$$ = 12 + 3 = 15.
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Re: If |x| + x = 4, then which one of the following is odd?  [#permalink]

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03 Apr 2019, 03:52
Bunuel wrote:
If $$|x| + x = 4$$, then which one of the following is odd?

(A) $$x^2 + 3x$$

(B) $$x^2 + 3x + 2$$

(C) $$x^2 + 4x$$

(D) $$x^2 + 4x + 2$$

(E) $$x^2 + 4x + 3$$

e+o= o
so $$|x| + x = 4$$
x=2
IMO E is correct
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Re: If |x| + x = 4, then which one of the following is odd?  [#permalink]

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07 Apr 2019, 18:22
Bunuel wrote:
If $$|x| + x = 4$$, then which one of the following is odd?

(A) $$x^2 + 3x$$

(B) $$x^2 + 3x + 2$$

(C) $$x^2 + 4x$$

(D) $$x^2 + 4x + 2$$

(E) $$x^2 + 4x + 3$$

We see that x must be 2.

Thus, x^2 is even, and so is x multiplied by any integer. Of all the answer choices, only x^2 + 4x + 3 is odd (since even + even + odd = odd).

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Re: If |x| + x = 4, then which one of the following is odd?   [#permalink] 07 Apr 2019, 18:22
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