Question: Divisor of 86420

Comment on Divisor of 86420

Hi just trying to assess how much time to spend on questions of this type. What level difficulty level would you say this is?
gmat-admin's picture

This is a SUPER HARD question. It's definitely 750+

Hi Brent, if we consider any negative value for n for example n = -2
We get 72/(6^-2) = 72/(1\36) = (72)(36)
This makes 6^-2 a divisor of 72, in the same way for the above ques we can consider any -ve value for n?
gmat-admin's picture

That's a great idea, but we can't say that 6^(-2) a divisor of 72.
Divisors must be INTEGERS, and 6^(-2) = 1/16 (which is not an integer)


Good question
gmat-admin's picture

I'm glad you like it :-)

Please let me know if this is a valid way to solve: i took the prime factorization of 86420 and got:
2 x 2 x 5 x 11 x 17 x 23
By recognizing there is no 3 in the prime factorization, i concluded 6 (nor any multiple of 6 i.e 6^n) is not a divisor of 86420, meaning n must equal 0, knowing that the question is not flawed. by assuming n is 0, i solved and got 1.
gmat-admin's picture

That approach is perfect (yet time consuming).

minor point: Although the approach is 100% valid, your prime factorization is a little off.
86,420 = 2 x 2 x 5 x 29 x 149 (still no 3's! ;-)


Hi Brent,

I solved this using the following logic:

86420 = 8 + 6 + 4 + 2 + 0 = 20.

A number divisible by 6 should have the sum of its digits divisible by 3 and be even. 86420 is even but its digits do not add up to be number divisible by 3.

The only way 6^n can be divisible is if n = 0, in which case 2^n - n^2 = 1

Hence, B

Took me less than 1.5 minutes :)
gmat-admin's picture

Perfect solution - nice work Karaan!

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