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

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

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New post Updated on: 01 Sep 2016, 09:13
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A
B
C
D
E

Difficulty:

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Question Stats:

54% (02:04) correct 46% (02:16) wrong based on 105 sessions

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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

Originally posted by yashrakhiani on 01 Sep 2016, 08:30.
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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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
2
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 11 Apr 2020, 10:18
2013=3×11×61
So we need 61 in the given series which will come in 2×61=122
Till 122, 11 and 3 will already be covered.
Option D is the answer

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Re: A computer is programmed to multiply consecutive even integers 2*4*6*8   [#permalink] 11 Apr 2020, 10:18

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

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