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

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

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

(1) b is even
b can be any large even integer. Is a^44 < b^11? answer will be yes.
but if b=2 . answer will be no. insufficient
(2) b is greater than 16
so, B=17,18,19..... 17^11>(2^44=16^11). sufficient

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