yogami wrote:My bad. Here is the actual 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
Definitely not the toughest but unlikely in GMAT
the answer is at the following link
https://www.beatthegmat.com/manhattan-ch ... tml#156357
Thanks for the link again. Those questions are good bro:)
So the primes of 264600 are 2, 2, 2, 3, 3, 3, 5, 5, 7, 7
combinations that don't make 6 are (a) the 2s 5s 7s (b) 3s 5s 7s
(a) 2^3 * 5^2 * 7^2 = 36 combinations
(b) 3^3 * 5^2 * 7^2 = 36 combinations
so total is 72. This rules out A and B
But there are duplicates e.g. the combinations of 5^2 and 7^2 but I don't know how to remove them. So i know the answer is less than 72 and definitely not 9 or 36. So it is between 51 and 63... Intuituvely, 51 seems a little low coz that'd mean there were 21 duplicates so I'd guess the answer to be 63 but I am not sure.
You are right this is a tough one to do in 2 mins coz you have to prime factorize and then do combinations excluding 6 and then remove duplicates = three layers... definitely a question I think I'd solve up till I got to 72 but then I'd be stuck and have to guess...