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# Is a^44 < b^11, given that a =2 and b is an integer ?

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Is a^44 < b^11, given that a =2 and b is an integer ? [#permalink]

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27 Oct 2010, 11:50
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Question Stats:

78% (01:00) correct 22% (01:21) wrong based on 118 sessions

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Is a^44 < b^11, given that a =2 and b is an integer ?

(1) b is even
(2) b is greater than 16
[Reveal] Spoiler: OA

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Last edited by Bunuel on 27 Mar 2015, 05:17, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Is a^44 < b^11, given that a =2 and b is an integer ? [#permalink]

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27 Oct 2010, 14:16
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zerotoinfinite2006 wrote:
Is a^44 < b^11 , given that a =2 and b is an integer ?

I. b is even
II. b is greater than 16

$$2^{44} \lt b^{11}$$
$$16^{11} \lt b^{11}$$

For integral b, this is true if and only if b>16

(1) Insufficient -- doesnt answer our question
(2) Sufficient, tells us b>16

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Re: Is a^44 < b^11, given that a =2 and b is an integer ? [#permalink]

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27 Oct 2010, 14:23
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B.
If b is even it cab be 2,4,6...... 2^44>4^11 - leaves us with B,C,E
B>16 thus B=17,18,19..... 17^11>(2^44=16^11).
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Re: Is a^44 < b^11, given that a =2 and b is an integer ? [#permalink]

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26 Mar 2015, 18:21
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Re: Is a^44 < b^11, given that a =2 and b is an integer ? [#permalink]

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26 Mar 2015, 18:55
Expert's post
Hi All,

This question can be solved with a combination of Exponent Rules and TESTing VALUES.

We're told that B is an INTEGER. We're asked if 2^44 < B^11. This is a YES/NO question.

Fact 1: B is EVEN

IF....
B = 0
Then 2^44 is NOT < 0^11 and the answer to the question is NO

IF....
B = 10,000,0000
Then 2^44 is < 10,000,000^11 and the answer to the question is YES
Fact 1 is INSUFFICIENT

Fact 2: B is greater than 16

This Fact is more about knowing how to 'rewrite' exponents than anything else.

16^11 can be rewritten as (2^4)^11, which is equal to 2^44.

Since we now know that B is GREATER than 16, B^11 will be GREATER than 2^44. The answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT

[Reveal] Spoiler:
B

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Re: Is a^44 < b^11, given that a =2 and b is an integer ?   [#permalink] 26 Mar 2015, 18:55
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