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# 1(1!) + 2(2!) + 3(3!) + 4(4!)………….50(50!) is a multiple of prime P

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Intern
Joined: 26 Jun 2019
Posts: 31
Location: India
GMAT 1: 660 Q51 V29
GPA: 3.3
1(1!) + 2(2!) + 3(3!) + 4(4!)………….50(50!) is a multiple of prime P  [#permalink]

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28 Jun 2019, 13:32
2
10
00:00

Difficulty:

65% (hard)

Question Stats:

56% (02:12) correct 44% (01:56) wrong based on 36 sessions

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1(1!) + 2(2!) + 3(3!) + 4(4!)………….50(50!) is a multiple of prime P. P lies in the range........?

A. 30 < P < 40
B. 10 < P < 15
C. 30 < P < 40
D. P > 40
E. 15 < P < 20
Manager
Joined: 15 Jul 2018
Posts: 62
Re: 1(1!) + 2(2!) + 3(3!) + 4(4!)………….50(50!) is a multiple of prime P  [#permalink]

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28 Jun 2019, 14:01
The above expression can be written as n*n! n is between 1 and 50(both inclusive) and it can be rewritten as(n+1)!-n! ,which will give answer as 51!-1!, which may be a multiple of prime P >40

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Director
Joined: 19 Oct 2018
Posts: 961
Location: India
Re: 1(1!) + 2(2!) + 3(3!) + 4(4!)………….50(50!) is a multiple of prime P  [#permalink]

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28 Jun 2019, 19:08
1
n(n!)= (n+1-1)*n!
n(n!)= (n+1)*n!- 1*n!
n(n!= (n+1)! - (n)!

1(1!) + 2(2!) + 3(3!) + 4(4!)………….50(50!)
= (2!-1!)+(3!-2!)+........+(50!-49!)+(51!-50!)
=51!-1!

prime factor of 51!-1 must be greater than 47.
Option D

utkarshg97 wrote:
1(1!) + 2(2!) + 3(3!) + 4(4!)………….50(50!) is a multiple of prime P. P lies in the range........?

A. 30 < P < 40
B. 10 < P < 15
C. 30 < P < 40
D. P > 40
E. 15 < P < 20
Re: 1(1!) + 2(2!) + 3(3!) + 4(4!)………….50(50!) is a multiple of prime P   [#permalink] 28 Jun 2019, 19:08
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