Manhattan Challenge Problem

[Saurabh Malpani]

12/01/03
Question
How many numbers that are not divisible by 6 divide evenly into 264,600?

(A) 9
(B) 36
(C) 51
(D) 63
(E) 72


I understand the the solution except the last part where the answer is arrived at by Subtracting the 81 from 144 (I mean I understand what are the steps followed but I don't understand why My answer is wrong)

My Apporach was:

As known that to be multiple of 6 we need to have atleast one 2 and one 3. In my apporach I try to calculate, just as we do in Combinations,the number of factors when I have ONLY 2s and Only 3s in additon to 5 and 7
2^4 * 5^2 *7^2 --- i.e multipy 3*3*3 =27

2^4 * 5^2 *7^2------- i.e multipy 3*3*3 =27

Sum them up I get 54.

So what's wrong with my apporach..???

[Saurabh Malpani]

Well as I was typing the problem the solution clicked to me the problem in my apporach is that i am not adding 7^2 * 5^2---3*3=9 . 9+ 54 =63 which is the correct answer.

Thanks
Saurabh Malpani

[StaceyKoprince]

Great! It's always the best when you figure it out for yourself! (And do remember - the challenge problems are likely to be harder than anything, or almost anything, you'll see on the test. Just make sure you've mastered absolutely everything else - otherwise, it's not a wise use of your time to use these extensively.)

[atayamir]

i don't get it?

[jnelson0612]

There is an explanation at this link: how-many-numbers-that-are-not-divisible-t4234.html