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If a and h are both positive even integers, which of the fol

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If a and h are both positive even integers, which of the fol [#permalink] New post 18 May 2018, 14:54
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If \(a\) and \(b\) are both positive even integers, which of the following must be even?

I. \(a^b\)

II. \((a+1)^b\)

III. \(a^{(b+1)}\)

(A) I only

(B) II only

(C) I and II only

(D) I and III only

(E) I, II, and III
[Reveal] Spoiler: OA

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Re: If a and h are both positive even integers, which of the fol [#permalink] New post 19 May 2018, 06:42
I think the answer should be B .Only 2.

Irrespective of number of times an even number is multiplied by itself, the value would still be even. However in 2, 1 is added and then multiplied b number of times with same snumber. So an odd number power even number would still give an odd number.
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Re: If a and h are both positive even integers, which of the fol [#permalink] New post 22 May 2018, 12:17
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and b are both positive integers. Nothing in the stem says they could be equal or not

A= 2 and b =2

II \((2+1)^2 = 3^2= odd\)

II is not possible
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Re: If a and h are both positive even integers, which of the fol [#permalink] New post 06 Jun 2018, 12:55
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Carcass wrote:
If \(a\) and \(b\) are both positive even integers, which of the following must be even?

I. \(a^b\)

II. \((a+1)^b\)

III. \(a^{(b+1)}\)

(A) I only

(B) II only

(C) I and II only

(D) I and III only

(E) I, II, and III


it's given that a and b are both positive integers.

1. even having an even exponent yields an even . True.
2. even+1=odd. an odd integer having even exponent yields odd.
3. even having odd exponent yields even integer.

Thus , 1+3 is correct. The best answer is D.
Re: If a and h are both positive even integers, which of the fol   [#permalink] 06 Jun 2018, 12:55
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If a and h are both positive even integers, which of the fol

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