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
Brent Hanneson - Creator of GMATPrepNow.com
