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If n is an integer and (9!+ 8!+7!)/3^n is an integer, what is the

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Bunuel
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If n is an integer and (9!+ 8!+7!)/3^n is an integer, what is the [#permalink] New post   02 May 2016, 22:16
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If n is an integer and (9! + 8! +7!)/3^n is an integer, what is the largest possible value of n?

A. 6
B. 5
C. 4
D. 3
E. 2



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A
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chetan2u
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Re: If n is an integer and (9!+ 8!+7!)/3^n is an integer, what is the [#permalink] New post   02 May 2016, 22:36
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Bunuel wrote:
If n is an integer and (9! + 8! +7!)/3^n is an integer, what is the largest possible value of n?

A. 6
B. 5
C. 4
D. 3
E. 2



Hi all,
As I had mentioned in a similar type of Q, do NOT find the minimum of three in any single term and take the answer..
here in that case we will have 3s least in 7! or 8! so 7/3 =2.. ans would be 2.. BUT we have to add and take out COMMON factor to see if by addition is there any extra 3s being added..

so (9! + 8! +7!) = 7!(9*8+8+1) = 7!*81 ..
so number of 3s in 7!*81 = 2+4 = 6------ 2 in 7! and 4 in 81
ans 6..
A

Abhishek009 refer that healthy discssion on 49! and 50!, where there was a post that take the lowest as it was an easy approach...
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Re: If n is an integer and (9!+ 8!+7!)/3^n is an integer, what is the [#permalink] New post   04 May 2016, 12:39
chetan2u wrote:
Bunuel wrote:
If n is an integer and (9! + 8! +7!)/3^n is an integer, what is the largest possible value of n?

A. 6
B. 5
C. 4
D. 3
E. 2



Hi all,
As I had mentioned in a similar type of Q, do NOT find the minimum of three in any single term and take the answer..
here in that case we will have 3s least in 7! or 8! so 7/3 =2.. ans would be 2.. BUT we have to add and take out COMMON factor to see if by addition is there any extra 3s being added..

so (9! + 8! +7!) = 7!(9*8+8+1) = 7!*81 ..
so number of 3s in 7!*18 = 2+4 = 6------ 2 in 7! and 4 in 81
ans 6..
A

Abhishek009 refer that healthy discssion on 49! and 50!, where there was a post that take the lowest as it was an easy approach...


How did you get 18??? (red part above) I tried solving this question by finding the maximum nos. of 3 in any one. Can you please explain this? Thank you.!
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Re: If n is an integer and (9!+ 8!+7!)/3^n is an integer, what is the [#permalink] New post   04 May 2016, 12:42
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MeghaP wrote:
chetan2u wrote:
Bunuel wrote:
If n is an integer and (9! + 8! +7!)/3^n is an integer, what is the largest possible value of n?

A. 6
B. 5
C. 4
D. 3
E. 2



Hi all,
As I had mentioned in a similar type of Q, do NOT find the minimum of three in any single term and take the answer..
here in that case we will have 3s least in 7! or 8! so 7/3 =2.. ans would be 2.. BUT we have to add and take out COMMON factor to see if by addition is there any extra 3s being added..

so (9! + 8! +7!) = 7!(9*8+8+1) = 7!*81 ..
so number of 3s in 7!*18 = 2+4 = 6------ 2 in 7! and 4 in 81
ans 6..
A

Abhishek009 refer that healthy discssion on 49! and 50!, where there was a post that take the lowest as it was an easy approach...


How did you get 18??? (red part above) I tried solving this question by finding the maximum nos. of 3 in any one. Can you please explain this? Thank you.!


It's a typo should be 81.
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Alex75PAris
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Re: If n is an integer and (9!+ 8!+7!)/3^n is an integer, what is the [#permalink] New post   04 May 2016, 12:44
(9! + 8! +7!) = 7! (9 x 8 + 8 + 1) = 7! (72 + 8 + 1) = 7! x 81 = 7 x 6 x 5 x 4 x 3 x 2 x 9 x 9
= 7 x 3 x 2 x 5 x 4 x 3 x 2 x 3 x 3 x 3 x 3

So 6, answer choice A
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Re: If n is an integer and (9!+ 8!+7!)/3^n is an integer, what is the [#permalink] New post   06 May 2016, 20:21
7!(9*8+8+1)/3^n
7! *81 /3^n
to make this expression integer n must be 6

Ans A



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Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
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Re: If n is an integer and (9!+ 8!+7!)/3^n is an integer, what is the [#permalink]
06 May 2016, 20:21
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