Bunuel wrote:

How many different positive factors does the integer n have?

(1) \(n = a^4b^3\), where a and b are different positive prime numbers.

(2) The only positive prime numbers that are factors of n are 5 and 7.

Question: How many different positive factors does the integer n have?Number of factors of a number \(= (p+1)*(q+1)*(r+1)...\)

if, Number \(= a^p*b^q*c^r\)... where a, b, c,... are distinct prine factors of number nStatement 1:\(n = a^4b^3\), where a and b are different positive prime numbers.i.e. Number of factors of \(n = (4+1)*(3+1) = 12\)

SUFFICIENT

Statement 2:The only positive prime numbers that are factors of n are 5 and 7But the exponents of 5 and 7 are unknown hence

NOT SUFFICIENT

Answer: Option A

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