Q. What is the greatest positive integer n such that (2^n) is a factor of (12^10)?
A. 10 ; B. 12 ; C. 16 ; D. 20 ; E. 60
A. 10 ; B. 12 ; C. 16 ; D. 20 ; E. 60
Hi Joy Shaha,
This question comes down to exponent rules and how to 'rewrite' a number raised to a power.
12 = (2)(2)(3)
12^2 = (2^2)(2^2)(3^2) = (2^4)(3^2)
12^3 = (2^3)(2^3)(3^3) = (2^6)(3^3)
Seeing this pattern, you should be able to rewrite 12^10...
12^10 = (2^10)(2^10)(3^10) = (2^20)(3^10)
So the largest 'power of 2' that is a factor of 12^10 is 20.
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
