Problem Solving

The product of the first twelve positive integers is divisible by all of the following EXCEPT
(A) 210
(B) 88
(C) 75
(D) 60
(E) 34


IS THERE ANY FORMULA SO SOLVE THIS

I dont think there is formula for this. 34 is the answer.

210 = 3*7*2*5
88 = 8*11
75 = 5*5*3
60 = 2*3*10
34 = 2*17

product of first 12 integers is same to say it is 12!

now we just have to see if any of the answer choices is the factor in 12 !

let me break up !( u dont have to do this but start eleminating right away )

210=12*10 ( product in 12!)--elliminate
88=11*8 ( product in 12!)--elliminate
75= here i do a bit of calculation to elliminate ! -
first 75 is reduced to 15 when divided by 5
then to 5 divided by 3
then 10 is divisble opf 5 so i know now 12! is divisble of 75
60=12*5 ( product in 12!)--elliminate
34- answer

calcualtion looks clunsy trust me its not


Vishu

Nycgrl wrote:The product of the first twelve positive integers is divisible by all of the following EXCEPT
(A) 210
(B) 88
(C) 75
(D) 60
(E) 34


IS THERE ANY FORMULA SO SOLVE THIS

Basically, we want to find the choice with a prime factor greater than 12. There are other possible answers as well (for example, 49 would be correct, since 12! will only have 1 "7" among its factors), but that's the most likely candidate on the GMAT.

Only (e) has a prime factor greater than 12 (34 = 2 * 17), so that's the right choice.