Problem Solving

Hi camitava,

This question can be solved by figuring out the "pattern" behind the math and/or using Prime Factorization.

First, a number that's divisible by 8 can be broken down into prime factors and will have at least three 2s among the primes.

For example,
16 is divisible by 8 because 16 = (2)(2)(2)(2) ..... it has three 2s in it.
18 is NOT divisible by 8 because 18 = (2)(3)(3) .... it has only one 2 in it.

So, we need to figure out if a number has three 2s in it or not, and we need to do so quickly. Let's see if we can figure out a pattern in this sequence of numbers....It's INTERESTING that we're dealing with 1 to 96, inclusive (and not 1 to 100); 96 is divisible by 8.....

If....
N=1 then 1(2)(3) does NOT divide by 8
N=2 then 2(3)(4) DOES divide by 8
N=3 then 3(4)(5) does NOT
N=4 then 4(5)(6) DOES
N=5 then 5(6)(7) does NOT
N=6 then 6(7)(8) DOES
N=7 then 7(8)(9) DOES
N=8 then 8(9)(10) DOES

Of the first 8 options, 5/8 of them are divisible by 8

Looking a bit deeper at the pattern, the fraction becomes a bit more obvious. An option is divisible by 8 if one of the following occurs:
1) A multiple of 8 is there.
2) Any two even numbers are there.

The above pattern will continue with every ensuing set of 8 terms; out of every 8, 5 of them will have what is necessary to divide by 8.

Final Answer: D

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