Hard PS gmatprep question

Hi Rakesh,

This question has LOTS of details that you have notice if you're going to answer it correctly. You'll notice that the answers have 8 as a common denominator (this provides an interesting hint to how the "math" will work. You should also notice that the question stem asks you to consider the numbers from 1 to 96, inclusive (and it's interesting that 96 is a multiple of 8...).

The prompt asks you to think about (n)(n+1)(n+2), so you'll be dealing with 3 consecutive integers multiplied together. For a number to be divisible by 8, it must include at least three 2's when the number is broken down using prime factorization:

For example: (1)(2)(3) = 6 which is NOT divisible by 8 (obviously), but you'll notice that there's just ONE 2.
For example: (2)(3)(4) = 24 which IS divisible by 8; you'll notice that there ARE THREE 2s (the 2 has one and the 4 has two).

So, we're looking for all the options that have three 2s in them...

Any option that is (even)(odd)(even) will include three 2s
Any option that has (odd)(multiple of 8)(odd) will also include three 2s

If you consider the first 8 possibilities
(1)(2)(3) = NO
(2)(3)(4) = YES
(3)(4)(5) = NO
(4)(5)(6) = YES
(5)(6)(7) = NO
(6)(7)(8) = YES
(7)(8)(9) = YES
(8)(9)(10) = YES

5/8 are what we're looking for. This pattern continues through every "set of 8", so the final answer is D

GMAT assassins aren't born, they're made,
Rich

If you're interested, you can practice what you've learned by tackling this similar DS question: https://www.beatthegmat.com/divisibility-t221510.html

Cheers,
Brent

rakeshd347 wrote:
Hi Brent,

What do you think would be the difficulty level of this question. 700+

Yeah, I think the linked question is 700+ question.

Cheers,
Brent