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# If x^2 + 4x + 3 is odd, then which one of the following cou

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If x^2 + 4x + 3 is odd, then which one of the following cou [#permalink]  18 Apr 2018, 12:00
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If $$x ^2 + 4x + 3$$ is odd, then which one of the following could be the value of x ?

(A) 3
(B) 5
(C) 9
(D) 13
(E) 16
[Reveal] Spoiler: OA

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Re: If x^2 + 4x + 3 is odd, then which one of the following cou [#permalink]  19 Apr 2018, 00:10
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It is good to note that
Odd + Odd = Even
Even + Even = Even
Odd + Even = Odd

&
Odd * Odd = Odd
Even * Even = Even
Even * Odd = Even

Now coming to the question:
It states x^2 + 4x + 3 is ODD

We know that whatever be the value of x, 4x will always be even (Even * Odd (or Even) = Even)
We also know that 3 is Odd

Therfore we can rewrite the expression in the question: x^2 + 4x + 3 is Odd as
x^2 + Even + Odd is Odd

We know (Even + Odd) is Odd

Therefore,
x^2 + Odd is Odd

For the above to be true,
x^2 has to be even and this will happen only when x is EVEN.

The only even number in the answer choice is 16.

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Re: If x^2 + 4x + 3 is odd, then which one of the following cou [#permalink]  19 Apr 2018, 03:21
On solving for z, one value we get for x is -3.

Square of x in that case would be 9. Can this not be the answer?
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Re: If x^2 + 4x + 3 is odd, then which one of the following cou [#permalink]  19 Apr 2018, 03:27
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Hey Mohan,

Did you assume x^2 + 4x + 3 = 0 ??

Note that the question did not mention that x^2+4x+3 is zero. In fact it says, it is some “ odd number”

Hope this helps

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Re: If x^2 + 4x + 3 is odd, then which one of the following cou [#permalink]  17 Jul 2018, 12:33
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Carcass wrote:
If $$x ^2 + 4x + 3$$ is odd, then which one of the following could be the value of x ?

(A) 3
(B) 5
(C) 9
(D) 13
(E) 16

Plugging in the smaller values Such as 1 , 2 etc to watch the pattern.

x = 1 ( odd )

(1)^2 + 4*1 + 3 = 8 ( even ) . It means we have to pick up the even value for x. Let's try:

(2)^2 + 4*2 + 3 = 15 ( odd ) .That fits.

Only even number is 16.

Re: If x^2 + 4x + 3 is odd, then which one of the following cou   [#permalink] 17 Jul 2018, 12:33
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