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If x is an integer, which of the following must be an odd integer?

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Bunuel
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If x is an integer, which of the following must be an odd integer? [#permalink] New post   14 Oct 2019, 08:17
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If x is an integer, which of the following must be an odd integer?

A. 2x + 2
B. 4x + 3
C. 12x-6
D. 13x
E. 14x
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B
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BrentGMATPrepNow
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Re: If x is an integer, which of the following must be an odd integer? [#permalink] New post   14 Oct 2019, 08:23
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Bunuel wrote:
If x is an integer, which of the following must be an odd integer?

A. 2x + 2
B. 4x + 3
C. 12x-6
D. 13x
E. 14x


Let's test a nice easy value of x.
How about x = 0

We get...
A. 2(0) + 2 = 2, which is EVEN
B. 4(0) + 3 = 3, which is ODD
C. 12(0) - 6 = 12, which is EVEN
D. 13(0) = 0, which is EVEN
E. 14(0) = 0, which is EVEN

Answer: B

Cheers,
Brent
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Re: If x is an integer, which of the following must be an odd integer? [#permalink] New post   14 Oct 2019, 09:43
Bunuel wrote:
If x is an integer, which of the following must be an odd integer?

A. 2x + 2
B. 4x + 3
C. 12x-6
D. 13x
E. 14x


(A) If x is Odd 2x is even & 2x + 2 will hence be Even ; If x is even then 2x is even & 2x + 2 will hence be Even.
(B) If x is Odd 4x is even & 4x + 3 will hence be Odd ; If x is even then 4x is even & 4x + 3 will hence be Odd.
(C) If x is Odd 12x is even & 12x - 6 will hence be Even ; If x is even then 12x is even & 12x - 6 will hence be Even.
(D) If x is Odd 13x is Odd ; If x is even then 13 x is even
(E) If x is Odd 14x is Even ; If x is even then 14 x is even

Hence , Answer must be (B) as for either odd/even value of x the result is always Odd.
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Re: If x is an integer, which of the following must be an odd integer? [#permalink] New post   17 Dec 2020, 11:17
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Bunuel wrote:
If x is an integer, which of the following must be an odd integer?

A. 2x + 2
B. 4x + 3
C. 12x-6
D. 13x
E. 14x


Multiple of an EVEN number is always even and if an odd number is added with an even number then the result is must be odd.

The answer is B
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Re: If x is an integer, which of the following must be an odd integer? [#permalink] New post   18 Dec 2020, 05:55
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A. 2x + 2 : even(2x) + even(2) = even

B. 4x + 3 : even(2x) + even(2x) + odd = odd

C. 12x - 6: even(12x) - even(6) = even

D. 13x: 13 * 1 = odd; 13 * 2 = even

E. 14x: even(14) * x = even

Answer B
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Re: If x is an integer, which of the following must be an odd integer? [#permalink] New post   20 Dec 2020, 04:39
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Bunuel wrote:
If x is an integer, which of the following must be an odd integer?

A. 2x + 2
B. 4x + 3
C. 12x-6
D. 13x
E. 14x

Solution:

Since 4x is even regardless of what integer x is and 3 is odd, 4x + 3 = even + odd = odd.

Answer: B
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Re: If x is an integer, which of the following must be an odd integer? [#permalink]
20 Dec 2020, 04:39
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