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Different prime numbers

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Different prime numbers

by rahulvsd » Sun Nov 06, 2011 5:21 am
How many different prime numbers are factors of positive integer B?

1. 5 different prime numbers are factors of B^3 (Bcube).
2. 5 different prime numbers are factors of 3B.

[spoiler]OA: A[/spoiler]
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by shankar.ashwin » Sun Nov 06, 2011 5:56 am
A IMO.

Statement 1:

If B has 5 different prime factors say (2,3,5,7,11). then B^3 would still have the same 5 prime factors and vice versa. Sufficient.

Statement 2:

3B has 5 prime factors. Now if 'B' does not have 3 as factor it is possible then B has 4 prime factors and 3B would have 5 in that case (since 3 is prime) Insuff
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by neelgandham » Sun Nov 06, 2011 10:56 am
How many different prime numbers are factors of positive integer B?

1. 5 different prime numbers are factors of B^3 (Bcube).

Let
B = 6, # of different prime factors of B = 2 (2,3)
B^2 = 36 ((2^2)*(3^2)), # of different prime factors of B = 2 (2,3)
B^3 = 216 ((2^3)*(3^3)), # of different prime factors of B = 2 (2,3)
B^n = ((2^n)*(3^n)), # of different prime factors of B = 2 (2,3)

So, if B^n has X prime factors, then B has the same number of prime factors

Answer = 5 Sufficient

Sufficient!

2. 5 different prime numbers are factors of 3B.

Let B = 2*3*4*5*7, then 3B = 2*3*4*5*7*3
# of Prime factors of 3B = 5
# of Prime factors of B = 5

Let B = 2*4*5*7*11, then 3B = 2*4*5*7*11*3
# of Prime factors of 3B = 6
# of Prime factors of B = 5

Insufficient!

[spoiler]OA: A[/spoiler]
Anil Gandham
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