Question: 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

Correct Answer: D
Solution and Explanation:
Approach Solution 1:

It has asked to find out the greatest positive integer n such that 2^n is a factor of 12 ^ 10.
Exponent rules and the proper way to "rewrite" a number raised to a power are key to answering this query.

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)

You should be able to rewrite 12 ^ 10 once you recognize this pattern.

12^10 = (2^10)(2^10)(3^10) = (2^20)(3^10)
Therefore, 20 is the biggest "power of 2," which is a factor of 12 ^ 10.

D is the correct answer.

Approach Solution 2:

It has asked to find out the greatest positive integer n such that 2^n is a factor of 12 ^ 10.
We have to factorize the number into prime numbers to find the answer.
12^10=(2^2∗3)^10=2^20∗3^10

The greatest value of n such that 2^n is a factor of 12^10 is 20.
These are the more common and slightly more complicated factorial questions. What is the biggest positive number n, for instance, such that 2^n is a factor of 12!

D is the correct answer.

“What is greatest positive integer n such that 2^n is a factor of 12^10?" - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.

To understand GMAT Problem Solving questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and a list of possible responses.

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