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# Is b an integer? (1) a^b is an integer (2) a is an integer

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Math Expert
Joined: 02 Sep 2009
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Is b an integer? (1) a^b is an integer (2) a is an integer  [#permalink]

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06 Apr 2018, 04:41
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25% (medium)

Question Stats:

83% (00:47) correct 17% (00:48) wrong based on 48 sessions

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Is b an integer?

(1) a^b is an integer

(2) a is an integer

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Intern
Joined: 16 Mar 2018
Posts: 46
Location: United Kingdom
GMAT 1: 650 Q45 V35
Re: Is b an integer? (1) a^b is an integer (2) a is an integer  [#permalink]

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06 Apr 2018, 04:51
Answer in my opinion B only statement 2 is sufficient.

As in St1 to make a^b integer
a could be 4 and b is 1/2 giving a^b=2 hence b not integer.

Also a could be 1 and b is 1 still giving a^b=1 giving b integer

So ST 1 not sufficient

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Re: Is b an integer? (1) a^b is an integer (2) a is an integer  [#permalink]

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06 Apr 2018, 08:50
St1 a = 4 b= 1/2 so it is integar
a = 2 b= 2 so it is integar
So not sufficient
St2 a = integar
So no infrmation regarding b
Not suuficient

Combined also not sufficient..
So E is answr...

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Is b an integer? (1) a^b is an integer (2) a is an integer  [#permalink]

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06 Apr 2018, 08:52
Bunuel wrote:
Is b an integer?

(1) a^b is an integer

(2) a is an integer

we are looking for whether b is an integer or not.

statement 1: it states that a^b is an integer. let's assume some values for a and b

case 1: a=4
b=2

so, 4^2=16

case 2: a=4 and b= 1/2

(4)^1/2 is also an integer,

thus statement 1 is not sufficient.

statement 2: it tells about the integer value of a. there is no information regarding b. not sufficient.

1+2: it is still not sufficient to answer the question.

thus , the correct answer is E.
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Re: Is b an integer? (1) a^b is an integer (2) a is an integer  [#permalink]

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06 Apr 2018, 22:46
Bunuel wrote:
Is b an integer?

(1) a^b is an integer

(2) a is an integer

In my view, the answer should be E.

Statement 1 - a^b is an integer.
Let say a = 3 and and b = $$\frac{1}{2}$$ (which is not an integer). Then $$a^b$$ = $$3^\frac{1}{2}$$ = $$\sqrt{3}$$. In this case $$a^b$$ is not an integer.

Consider another value where a = 4 and and b = $$\frac{1}{2}$$ (which again is not an integer). Then $$a^b$$ = $$4^\frac{1}{2}$$ = $$\sqrt{4}$$. In this case $$a^b$$ is an integer.

Therefore statement 1 is not sufficient.

Statement 2 - a is an integer
Clearly not sufficient. As in above two examples, we had "a" as an integer so no real value added by the statement.

BOTH statements combined we are still in the same scenario. Therefore none of the statement is sufficient.

Please correct me if I am wrong.
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Re: Is b an integer? (1) a^b is an integer (2) a is an integer   [#permalink] 06 Apr 2018, 22:46
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