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# what is the least possible value of k?

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Manager
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what is the least possible value of k? [#permalink]  16 Jan 2010, 04:30
00:00

Difficulty:

(N/A)

Question Stats:

100% (02:06) correct 0% (00:00) wrong based on 7 sessions
For any integer k greater than 1, the symbol k* denotes the product of all integers between 1 and k, inclusive. If k* is a multiple of 3,675, what is the least possible value of k?
(A) 12
(B) 14
(C) 15
(D) 21
(E) 25

OA is
[Reveal] Spoiler:
B

Last edited by apoorvasrivastva on 16 Jan 2010, 23:06, edited 1 time in total.
Senior Manager
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Re: what is the least possible value of k? [#permalink]  16 Jan 2010, 04:38
apoorvasrivastva wrote:
For any integer k greater than 1, the symbol k* denotes the product of all integers between 1 and k, inclusive. If k* is a multiple of 3,675, what is the least possible value of k?
(A) 12
(B) 14
(C) 15
(D) 21
(E) 25

OA is
[Reveal] Spoiler:
E

IMO its should be D,
By factorizing 3675 we get 3*5*5*7*7

Hence, K! should be having at least one 3, two 5's and two 7's.
Intern
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Re: what is the least possible value of k? [#permalink]  16 Jan 2010, 09:15
1
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since 3675= 5*5*7*7*3
my answer is B because in 14! there are 5 and 10 and multiply together they are divisible by 5*5
there are 14 and 7 for the 7*7...
isnt it?
Senior Manager
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Re: what is the least possible value of k? [#permalink]  16 Jan 2010, 09:38
lucalelli88 wrote:
since 3675= 5*5*7*7*3
my answer is B because in 14! there are 5 and 10 and multiply together they are divisible by 5*5
there are 14 and 7 for the 7*7...
isnt it?

oops , yes I guess you are right it should be 14
Manager
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Re: what is the least possible value of k? [#permalink]  16 Jan 2010, 10:07
lucalelli88 wrote:
since 3675= 5*5*7*7*3
my answer is B because in 14! there are 5 and 10 and multiply together they are divisible by 5*5
there are 14 and 7 for the 7*7...
isnt it?

could u please explain the part in red..how did u narrow down on 14!
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Re: what is the least possible value of k? [#permalink]  16 Jan 2010, 10:23
1
KUDOS
apoorvasrivastva wrote:
lucalelli88 wrote:
since 3675= 5*5*7*7*3
my answer is B because in 14! there are 5 and 10 and multiply together they are divisible by 5*5
there are 14 and 7 for the 7*7...
isnt it?

could u please explain the part in red..how did u narrow down on 14!

We basically need 5,5,3,7 and 7 in the number.

14!, has 3, 5, 7, 10, 14

now 10 = 2 x5
14 = 2x 7

hence we get all the numbers which we need.
Manager
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Re: what is the least possible value of k? [#permalink]  16 Jan 2010, 12:02
nitishmahajan wrote:
apoorvasrivastva wrote:
lucalelli88 wrote:
since 3675= 5*5*7*7*3
my answer is B because in 14! there are 5 and 10 and multiply together they are divisible by 5*5
there are 14 and 7 for the 7*7...
isnt it?

could u please explain the part in red..how did u narrow down on 14!

We basically need 5,5,3,7 and 7 in the number.

14!, has 3, 5, 7, 10, 14

now 10 = 2 x5
14 = 2x 7

hence we get all the numbers which we need.

oppps i missed out the on the question stem least possible....arrrgggghhhh...silly me!!

thanks mate for pointing out that
Manager
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Re: what is the least possible value of k? [#permalink]  16 Jan 2010, 17:39
Usually when you see any problems about factors or prime you always need to find the DCM or GCF.
Manager
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Re: what is the least possible value of k? [#permalink]  16 Jan 2010, 18:53
I don't understand how its not B

3675 prime factorization is 3 * 5 * 5 * 7 * 7

so a number would have to have all of those in it.

14 is the first number that does that?
Manager
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Re: what is the least possible value of k? [#permalink]  16 Jan 2010, 23:19
sorry guys the OA is B..please excuse me for the mistype
Senior Manager
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Re: what is the least possible value of k? [#permalink]  31 Jan 2010, 08:17
For any integer k greater than 1, the symbol k* denotes the product of all integers between 1 and k, inclusive. If k* is a multiple of 3,675, what is the least possible value of k?
(A) 12
(B) 14
(C) 15
(D) 21
(E) 25

K! = 3675 * M (M is a postive integer)

K! = 3 * 5 * 5 * 7 * 7

14! has all the numbers above.. therefore B..!
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Re: what is the least possible value of k? [#permalink]  01 Feb 2010, 11:18
Expert's post
I'd be curious to know the source of this question; recently I've seen several questions (like this one) posted on forums which are identical to official questions with one number changed, and I'm interested to know where they're from.
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Re: what is the least possible value of k? [#permalink]  02 Feb 2010, 09:28
Re: what is the least possible value of k?   [#permalink] 02 Feb 2010, 09:28
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