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# Is the value of 27^a/6^b a prime number?

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Math Expert
Joined: 02 Sep 2009
Posts: 55230
Is the value of 27^a/6^b a prime number?  [#permalink]

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11 Sep 2017, 00:24
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Difficulty:

55% (hard)

Question Stats:

68% (01:55) correct 32% (01:56) wrong based on 51 sessions

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Is the value of $$\frac{27^a}{6^b}$$ a prime number?

(1) 3a – b = 1
(2) b is an integer.

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Joined: 02 Nov 2015
Posts: 163
GMAT 1: 640 Q49 V29
Re: Is the value of 27^a/6^b a prime number?  [#permalink]

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11 Sep 2017, 01:25
The question reduces to is 3^(3a-b)/2^b a prime number ??

Statement 1: if b=0 then yes it is a prime number . If b=1 or 2 or 3 or any number , then no.
So insufficient.
Statement 2: not sufficient.

Combined not sufficient. If b=0 then yes it is prime and if b= some other integer then , no.

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Is the value of 27^a/6^b a prime number?  [#permalink]

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11 Sep 2017, 03:34
Find: $$\frac{27^a}{6^b}$$ = prime number?

$$\frac{27^a}{6^b}$$
=> $$\frac{3^(3a)}{2^b * 3^b}$$
=> $$\frac{3^(3a-b)}{2^b}$$

Above number can have only 1 prime value = 3
and for it 3a-b=1 and b=0 is the condition

(1) 3a – b = 1
We don't know anything above b . so we dont know anything about the denominator
Not sufficient

(2) b is an integer.
Here we dont know value of a. and here b can take any value 0,1,2...
Not sufficient

1+2
We get one condition to form prime number ie. 3a-b=1, but we don't know anything about b.
b is an integer.. if b=0 than given number is prime number
if b is any other integer than not a prime number.

Is the value of 27^a/6^b a prime number?   [#permalink] 11 Sep 2017, 03:34
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