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If a, b, c and n are positive integers and m=a^4∗b^3∗c^n

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If a, b, c and n are positive integers and m=a^4∗b^3∗c^n

by Mo2men » Thu Mar 23, 2017 1:08 pm
If a, b, c and n are positive integers and m= a^4 * b^3 * c^n, how many factors does m have?

1) a, b, and c are prime numbers

2) n=2

OA: E

Source: Math revolution

General question: When it is mentioned a, b, c, does it mean those are distinct? Could be a=b=c (regardless of the question above)?
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Thu Mar 23, 2017 1:24 pm
Mo2men wrote: General question: When it is mentioned a, b, c, does it mean those are distinct? Could be a=b=c (regardless of the question above)?
We cannot assume that a, b and c have distinct (different values), unless it's stated somewhere.

Cheers,
Brent
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by Mo2men » Thu Mar 23, 2017 1:26 pm
Brent@GMATPrepNow wrote:
Mo2men wrote: General question: When it is mentioned a, b, c, does it mean those are distinct? Could be a=b=c (regardless of the question above)?
We cannot assume that a, b and c have distinct (different values), unless it's stated somewhere.

Cheers,
Brent
Thanks Brent. This is what i thought but need it some confirmation.
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by Brent@GMATPrepNow » Thu Mar 23, 2017 1:31 pm
Mo2men wrote:If a, b, c and n are positive integers and m = a^4 * b^3 * c^n, how many factors does m have?

1) a, b, and c are prime numbers

2) n=2

OA: E
Target question: How many factors does m have?

Given: m = (a^4)(b^3)(c^n)

The two statements seem to provide a lot of information, so I'm going to jump straight to..

Statements 1 and 2 combined
There are several values of a, b, c, and n that satisfy BOTH statements. Here are two:
Case a: a = 2, b = 2, c = 2 and n = 2, in which case m = (2^4)(2^3)(2^2) = 2^9. In this case, m has 10 factors.
Case b: a = 3, b = 3, c = 2 and n = 2, in which case m = (3^4)(3^3)(2^2) = (3^7)(2^2). In this case, m has 24 factors.
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

---------ASIDE---------------
To determine the number of factors of m, I used the following rule:

If N = (p^a)(q^b)(r^c)..., where p, q, r,...(etc.) are prime numbers, then the total number of positive divisors of N is equal to (a+1)(b+1)(c+1)...

Example: 14000 = (2^4)(5^3)(7^1)
So, the number of positive divisors of 14000 = (4+1)(3+1)(1+1) = (5)(4)(2) = 40
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