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M13 Q 32

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Manager
Joined: 13 May 2010
Posts: 122

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M13 Q 32 [#permalink]

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23 Jan 2012, 21:09
Is $$a^b \gt b^a$$ ?

1. $$a \gt b \gt 1$$
2. $$a = b + 1$$

* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
* Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
* BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
* EACH statement ALONE is sufficient
* Statements (1) and (2) TOGETHER are NOT sufficient

Ans (E)

Can someone please provide suitable set of numbers for testing these statements? I used number testing approach but had a hard time coming up with the right set of numbers? How do you figure what type of numbers should you be testing for these types of questions?

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Math Expert
Joined: 02 Sep 2009
Posts: 42539

Kudos [?]: 135203 [0], given: 12673

Re: M13 Q 32 [#permalink]

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24 Jan 2012, 03:40
teal wrote:
Is $$a^b \gt b^a$$ ?

1. $$a \gt b \gt 1$$
2. $$a = b + 1$$

Ans (E)

Can someone please provide suitable set of numbers for testing these statements? I used number testing approach but had a hard time coming up with the right set of numbers? How do you figure what type of numbers should you be testing for these types of questions?

On DS questions when plugging numbers, your goal is to prove that the statement is not sufficient. So you should try to get an YES answer with one chosen number(s) and a NO with another.

Is $$a^b \gt b^a$$ ?

(1) $$a \gt b \gt 1$$ --> first try minimum possible integers for $$a$$ and $$b$$: if $$a=3$$ and $$b=2$$ then $$a^b=9>8=b^a$$ and the answer is YES. Now, increase $$a$$ and $$b$$ and try: $$a=4$$ and $$b=3$$ then $$a^b=64<81=b^a$$, so in this case the answer is NO.

(2) $$a = b + 1$$. The same set of numbers works for this statement as well. Not sufficient.

(1)+(2) Again, two sets of numbers considered, satisfy both statements and give different answer to the question. Not sufficient.

Hope it's clear.
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Kudos [?]: 135203 [0], given: 12673

Manager
Joined: 13 May 2010
Posts: 122

Kudos [?]: 24 [0], given: 4

Re: M13 Q 32 [#permalink]

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26 Jan 2012, 15:39
Thanks a lot, Bunuel!

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Re: M13 Q 32   [#permalink] 26 Jan 2012, 15:39
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M13 Q 32

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Moderator: Bunuel

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