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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]  18 May 2018, 14:54
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Question Stats:

96% (00:31) correct 3% (00:32) wrong based on 29 sessions
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]  19 May 2018, 06:42
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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.
Founder
Joined: 18 Apr 2015
Posts: 13908
GRE 1: Q160 V160
Followers: 313

Kudos [?]: 3678 [0], given: 12922

Re: If a and h are both positive even integers, which of the fol [#permalink]  22 May 2018, 12:17
Expert's post
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]  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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