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# M22-32

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Math Expert
Joined: 02 Sep 2009
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16 Sep 2014, 00:17
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Difficulty:

35% (medium)

Question Stats:

68% (01:17) correct 32% (00:59) wrong based on 149 sessions

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If $$N$$ is a positive integer, is $$N!$$ divisible by 14 ?

(1) $$(N + 1)!$$ is divisible by 15

(2) $$(N + 2)!$$ is divisible by 16

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16 Sep 2014, 00:17
Official Solution:

Statements (1) and (2) combined are insufficient. Consider $$N = 14$$ (the answer is "yes") and $$N = 6$$ (the answer is "no").

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06 Dec 2014, 16:19
1
For N! to be divisible by 14, N have a minimum value of 7
1) insufficient, (N+1)! divisible by 15, it might be that N = 14, or N = 5 or more, both of them are divisible by 15
2) insufficient, (N+2)! divisible by 16, it might be that N = 14, or N = 6 or more, 6! is divisible by 16.

1+2 insufficient
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16 Jan 2016, 01:12
the question basically asks whether integer n >= 7? the statemenets combined do not give a conslusive answer.
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10 Feb 2016, 02:56
I think this is a high-quality question and the explanation isn't clear enough, please elaborate.
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10 Feb 2016, 03:10
1
1
mestrec wrote:
I think this is a high-quality question and the explanation isn't clear enough, please elaborate.

hi,
I'll try to explain it further to you..

Quote:
If N is a positive integer, is N! divisible by 14 ?

(1) (N+1)! is divisible by 15

(2) (N+2)! is divisible by 16

lets first derive the info from the Q..
is N! div by 14, which is 2*7..
the largest prime number in 14 is 7..

SO , the Q basically asks us if N! is div by 7..
and for that N has to be 7 or >7..

now lets see if any statements gives us this info..
(1) (N+1)! is divisible by 15
here 15 is 3*5, so N can be any value >3..
if 4, 4! is not div by 7, hence 14..
if 8, yes..
so insuff..

(2) (N+2)! is divisible by 16
16 is 2^4..
so 6! will be div by 16 and hence N can take any value from 4 onwards..
same as statement 1 ..
insuff
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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09 Mar 2016, 02:16
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Joined: 11 May 2018
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05 Jul 2018, 19:29
can you explain me why 6 is divisible by 15? wont it give reminder of 6 when divisible by 15. and same applies with 2nd statement? Please explain it to me ... i am little bit confused.
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05 Jul 2018, 19:37
1
aravsha wrote:
can you explain me why 6 is divisible by 15? wont it give reminder of 6 when divisible by 15. and same applies with 2nd statement? Please explain it to me ... i am little bit confused.

hi
If N =6 N+1 = 7 and (N+1)!=7!=1*2*3*4*5*6*7 so this div by 15
! or factorial means product of all numbers till N
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: M22-32 &nbs [#permalink] 05 Jul 2018, 19:37
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# M22-32

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