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A computer is programmed to multiply consecutive even integers 2*4*6*8

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Joined: 26 Jul 2016
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Concentration: Operations, Entrepreneurship
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A computer is programmed to multiply consecutive even integers 2*4*6*8 [#permalink]

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A computer is programmed to multiply consecutive even integers 2*4*6*8*…*n until the product is divisible by 2013, What is the value of n?

A) 22
B) 38
C) 62
D) 122
E) 672
[Reveal] Spoiler: OA

Last edited by Bunuel on 01 Sep 2016, 09:13, edited 1 time in total.
Renamed the topic, edited the question and moved to PS forum.
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Re: A computer is programmed to multiply consecutive even integers 2*4*6*8 [#permalink]

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New post 01 Sep 2016, 08:40
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yashrakhiani wrote:
A computer is programmed to multiply consecutive even integers 2 * 4 * 6 * 8 * … * n until the product is divisible by 2013, What is the value of n?



Factorise 2013.. 3*11*61..
So n has to be a multiple of largest prime number,61..
So n=2*61=122..

Hope this helps you
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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html


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Re: A computer is programmed to multiply consecutive even integers 2*4*6*8 [#permalink]

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New post 30 Oct 2016, 03:35
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yashrakhiani wrote:
A computer is programmed to multiply consecutive even integers 2*4*6*8*…*n until the product is divisible by 2013, What is the value of n?

A) 22
B) 38
C) 62
D) 122
E) 672


Same logic but with application of factorials.
2*4*6*8*...*n = 2(1*2*3*4*...n/2) = 2*(n/2)!
Now we have: 2*(n/2)!/2013=2*(n/2)!/(3×11×61)
For the expression 2*(n/2)! To be divisible by 2013 min value of n/2 should be 61.
So n/2=61 => n=122
Answer D.
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Re: A computer is programmed to multiply consecutive even integers 2*4*6*8 [#permalink]

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New post 10 Dec 2017, 08:28
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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: A computer is programmed to multiply consecutive even integers 2*4*6*8   [#permalink] 10 Dec 2017, 08:28
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