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How many distinct Prime Factors does a^b^c has 1) a^b has t

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by GMATinsight » Thu Jun 01, 2017 7:17 pm
How many distinct Prime Factors does a^b^c has

1) a^b has three distinct prime factors
2) b^c has four distinct prime factors

Answer: Option A

Source: www.GMATinsight.com
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by susheelh » Thu Jun 01, 2017 8:29 pm
@GMATinsight,

I Tried to solve this in the following way. Please correct me if wrong. (Took a long time though) :(

S1: a^b has 3 distinct prime numbers.
Let the three distinct prime numbers be 2,3,5. Stem can be rewritten as a=(2*3*5). a^b = (2*3*5) * (2*3*5)....b times. Notice that the same three prime factors are repeated each time. infact for any power of a, the same three primes will be repeating. This also means a^b^c will also have 3 distinct primes.
S1 is hence sufficient.

S2: b^c has four distinct prime factors. This says b^c has 4 distinct prime factors. No info on a though. If a = 0 the answer is different as compared to say a = 2
Insuff.

Final answer = A
GMATinsight wrote:How many distinct Prime Factors does a^b^c

1) a^b has three distinct prime factors
2) b^c has four distinct prime factors

Answer: Option A

Source: www.GMATinsight.com
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