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- General GMAT Strategies - 7 videos (all free)
- Data Sufficiency - 16 videos (all free)
- Arithmetic - 38 videos (some free)
- Powers and Roots - 36 videos (some free)
- Algebra and Equation Solving - 73 videos (some free)
- Word Problems - 48 videos (some free)
- Geometry - 42 videos (some free)
- Integer Properties - 38 videos (some free)
- Statistics - 20 videos (some free)
- Counting - 27 videos (some free)
- Probability - 23 videos (some free)
- Analytical Writing Assessment - 5 videos (all free)
- Reading Comprehension - 10 videos (all free)
- Critical Reasoning - 38 videos (some free)
- Sentence Correction - 70 videos (some free)
- Integrated Reasoning - 17 videos (some free)

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## Comment on

12 is a divisor of n## what about 108?

## 108 = (2)(2)(3)(3)(3) = (2^2)

108 = (2)(2)(3)(3)(3) = (2^2)(3^3)

If n = (g^h)(h^g), there's no way to assign values to g and h to get (2^2)(3^3).

IF the question were worded so that n = (g^g)(h^h), then 108 would work if we let g = 2 and h = 3. However, the question tells us that n = (g^h)(h^g), in which case there's no way to assign values to g and h to get (2^2)(3^3).

## Brilliant Explanation. Thanks

## What if you chose 720 for n?

## n cannot equal 720.

n cannot equal 720.

To understand why, let's first examine the prime factorization of 720

n = 720

= (2)(2)(2)(2)(3)(3)(5)

= (2^4)(3^2)(5^1)

We're told that n = (g^h)(h^g), where g and h are PRIME

There's no way to assign values to g and h to get (g^h)(h^g)

= (2^4)(3^2)(5^1).

As such, n cannot equal 720

In fact, n cannot equal any number other than 72

Does that help?

Cheers,

Brent

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