Integer

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Nycgrl: Master | Next Rank: 500 Posts; Posts: 124; Joined: Mon May 19, 2008 1:12 pm; Thanked: 3 times

by Nycgrl » Wed Aug 06, 2008 5:45 pm

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

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Source: Beat The GMAT — Problem Solving | Wed Aug 06, 2008 5:45 pm

parallel_chase: Legendary Member; Posts: 1153; Joined: Wed Jun 20, 2007 6:21 amFollowed by: 2 members; Thanked: 146 times

by parallel_chase » Wed Aug 06, 2008 5:51 pm

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

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vishubn: Legendary Member; Posts: 574; Joined: Sun Jun 01, 2008 8:48 am; Location: Bangalore; Thanked: 28 times

by vishubn » Wed Aug 06, 2008 6:02 pm

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

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

Re: Integer

by Stuart@KaplanGMAT » Wed Aug 06, 2008 7:50 pm

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.

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

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