ps 500 test22 #19

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dunkin77: Master | Next Rank: 500 Posts; Posts: 269; Joined: Sun Apr 01, 2007 5:41 am

ps 500 test22 #19

by dunkin77 » Sun Apr 15, 2007 10:32 am

Hi,

The answer to this is E) but could not figure out why. Can anyone please explain? Thank yoU!

19. 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

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Source: Beat The GMAT — Problem Solving | Sun Apr 15, 2007 10:32 am

jayhawk2001: Community Manager; Posts: 789; Joined: Sun Jan 28, 2007 3:51 pm; Location: Silicon valley, California; Thanked: 30 times; Followed by:1 members

by jayhawk2001 » Sun Apr 15, 2007 12:41 pm

You need to split the number into factors here ...

210 = 2 * 3 * 5 * 7
88 = 8 * 11
75 = 3 * 5 * 5
60 = 5 * 12
34 = 2 * 17

Since we are dealing with the first 12 positive numbers, 17 can't be in
it. Hence 34

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ns88: Senior | Next Rank: 100 Posts; Posts: 33; Joined: Sat Apr 14, 2007 8:29 am

by ns88 » Sun Apr 15, 2007 2:27 pm

Dunkin,

I enjoy the math problems you are posting up. It’s a good way to practice.

In some cases, to save time, I’m trying to solve the questions backwards.

I see that you give away the answer in the first line. Could you please post the answer in the last line after the problem? Or you don’t even have to post the answer, which is even better. I’m sure some math wiz will come up with it.

Thanks.

NS88

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Cybermusings: Legendary Member; Posts: 559; Joined: Tue Mar 27, 2007 1:29 am; Thanked: 5 times; Followed by:2 members

by Cybermusings » Mon Apr 16, 2007 4:54 am

210 = 21*10 = 7*3*5*2 (Hence possible)
88 = 2*2 (or 4)*2*11 (Again possible)
75 = 5*5*3 (Again possible)
60 = 3*2*5*2 (Again possible)
34 = 17*2 (Not possible. 17 is a prime number and it can't be broken down any further)

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BTGmoderatorRO: Moderator; Posts: 772; Joined: Wed Aug 30, 2017 6:29 pm; Followed by:6 members

by BTGmoderatorRO » Sun Dec 24, 2017 5:43 am

The product of the first twelve positive integers is:
1*2*3*4*5*6*7*8*9*10*11*12=12!
For a number to be exactly divisible by 12! it must be a factor.
Considering the options given;
-210
210=3*7*10
3, 7 and 10 can be factored out from 12! without a fractional remainder.
Therefore,210 is a factor.
-88=11*8
11 and 8 can be factored from 12! Thus, 88 is a factor
75 is a factor of 12!
-60 =12*5
12 and 5 can also be factored so 60 is a factor
-34=2*17
2 can be factored but 17 cannot be factored out.
Therefore,34=2*17 cannot be divided by 12!

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Mon Sep 09, 2019 9:49 am

dunkin77 wrote:Hi,

The answer to this is E) but could not figure out why. Can anyone please explain? Thank yoU!

19. 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

Since the product of the first 12 integers does not have a 17 in its prime factorization, that product is not divisible by 34, which is 17 x 2.

Answer: E

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Founder and CEO
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