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13! – 11! is divisible by n but not by n^2. What is the range of value

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13! – 11! is divisible by n but not by n^2. What is the range of value  [#permalink]

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New post 27 Jul 2017, 00:38
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Re: 13! – 11! is divisible by n but not by n^2. What is the range of value  [#permalink]

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New post 27 Jul 2017, 00:57
7
13!-11! is simplified as 11!(13*12-11)..
This yield 11!*155 which breaks into 11!*5*31.
Since it's talks about prime numbers , the numbers in this list are 2,3,5,7,11,31. But it also says that it's not divisible by n^2. Therefore the highest value is 31 an the lowest is 7.
31-7=24.
Answer B.

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Re: 13! – 11! is divisible by n but not by n^2. What is the range of value  [#permalink]

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New post 27 Jul 2017, 01:04
kumarparitosh123 wrote:
13!-11! is simplified as 11!(13*12-11)..
This yield 11!*155 which breaks into 11!*5*31.
Since it's talks about prime numbers , the numbers in this list are 2,3,5,7,11,31. But it also says that it's not divisible by n^2. Therefore the highest value is 31 an the lowest is 7.
31-7=24.
Answer B.

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I don't get the last part. Why do you subtract 31 by 7?
and how is "7" to be the lowest?
Why can't 31 be the answer?
Itsn't n is the prime?


Thank you so much
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Re: 13! – 11! is divisible by n but not by n^2. What is the range of value  [#permalink]

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New post 27 Jul 2017, 01:09
kumarparitosh123 wrote:
13!-11! is simplified as 11!(13*12-11)..
This yield 11!*155 which breaks into 11!*5*31.
Since it's talks about prime numbers , the numbers in this list are 2,3,5,7,11,31. But it also says that it's not divisible by n^2. Therefore the highest value is 31 an the lowest is 7.
31-7=24.
Answer B.

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Sorry, I get why do you subtract 31 by 7, because the question is asking the range.
However, why the lowest is not 2? can't it be 31-2 :( :( :(
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Re: 13! – 11! is divisible by n but not by n^2. What is the range of value  [#permalink]

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New post 27 Jul 2017, 01:09
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Because it's talking about RANGE.
Secondly the least prime number is 2 but we cannot consider because as per the questions it must must not be divisible by n^2, so in this case it becomes 4. And the entire set is divisible by 4 . So we discard 2. Similarly we have to discard 3 and 5 also. The only lowest prim number in this case becomes 7 because the nature set is not divisible by square of 7 i.e. 49.
Thus 31-7 becomes answer.

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Re: 13! – 11! is divisible by n but not by n^2. What is the range of value  [#permalink]

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New post 27 Jul 2017, 01:12
kumarparitosh123 wrote:
Because it's talking about RANGE.
Secondly the least prime number is 2 but we cannot consider because as per the questions it must must not be divisible by n^2, so in this case it becomes 4. And the entire set is divisible by 4 . So we discard 2. Similarly we have to discard 3 and 5 also. The only lowest prim number in this case becomes 7 because the nature set is not divisible by square of 7 i.e. 49.
Thus 31-7 becomes answer.

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thank you very much for the very clear explanation.
I got it now
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Re: 13! – 11! is divisible by n but not by n^2. What is the range of value  [#permalink]

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New post 27 Jul 2017, 03:26
Bunuel wrote:
13! – 11! is divisible by n but not by n^2. What is the range of values of n if n is a prime number?

(A) 20

(B) 24

(C) 26

(D) 29

(E) 31


13! – 11! = 11! * 155 = 11! * 31 * 5

If n is a prime number n can take 2, 3, 5, 7, 11, 31

but the above figure is divisible by n but not by n^2 so 2, 3, 5 ruled out only 7, 11 and 31 exist only once
Range will be 31-7 = 24

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13! – 11! is divisible by n but not by n^2. What is the range of value  [#permalink]

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New post 28 Jul 2017, 15:43
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Bunuel wrote:
13! – 11! is divisible by n but not by n^2. What is the range of values of n if n is a prime number?

(A) 20

(B) 24

(C) 26

(D) 29

(E) 31


13! – 11! = 11! (13 *12 -1 ) = 11! * 155 = 11! * 5 *31

It is easy to make clear if we expand 11!

11! * 5 *31 = 2 *3 *4 * 5 * 6 * 7 * 8 * 9 * 10 * 11 * 31 *5

Let n =2...it is clear that expression is divisible by n^2 ................Eliminate

Let n =3...it is clear that expression is divisible by n^2 ................Eliminate

Let n =5...it is clear that expression is divisible by n^2 ................Eliminate

Let n =7...it is clear that expression is NOT divisible by n^2 ................Keep

It clear that biggest number when n = 31.

Range = big value - small value = 31 - 7 = 24

Answer: B
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Re: 13! – 11! is divisible by n but not by n^2. What is the range of value  [#permalink]

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Re: 13! – 11! is divisible by n but not by n^2. What is the range of value   [#permalink] 29 Mar 2020, 04:20

13! – 11! is divisible by n but not by n^2. What is the range of value

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