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# For any integer k greater than 1, the symbol k* denotes the product of

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Manager
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For any integer k greater than 1, the symbol k* denotes the product of [#permalink]

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16 Jan 2010, 05:30
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Difficulty:

65% (hard)

Question Stats:

58% (01:30) correct 42% (01:44) wrong based on 276 sessions

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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
[Reveal] Spoiler: OA

Last edited by Bunuel on 29 Mar 2016, 11:49, edited 2 times in total.
Renamed the topic and edited the question.

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Senior Manager
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Re: For any integer k greater than 1, the symbol k* denotes the product of [#permalink]

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16 Jan 2010, 05:38
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.

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Intern
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Re: For any integer k greater than 1, the symbol k* denotes the product of [#permalink]

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16 Jan 2010, 10:15
2
KUDOS
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?

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Re: For any integer k greater than 1, the symbol k* denotes the product of [#permalink]

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16 Jan 2010, 10:38
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

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Manager
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Re: For any integer k greater than 1, the symbol k* denotes the product of [#permalink]

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16 Jan 2010, 11:07
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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Senior Manager
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Re: For any integer k greater than 1, the symbol k* denotes the product of [#permalink]

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16 Jan 2010, 11:23
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.

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Manager
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Re: For any integer k greater than 1, the symbol k* denotes the product of [#permalink]

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16 Jan 2010, 13:02
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

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Re: For any integer k greater than 1, the symbol k* denotes the product of [#permalink]

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16 Jan 2010, 18:39
Usually when you see any problems about factors or prime you always need to find the DCM or GCF.

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Re: For any integer k greater than 1, the symbol k* denotes the product of [#permalink]

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16 Jan 2010, 19:53
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?

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Manager
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Re: For any integer k greater than 1, the symbol k* denotes the product of [#permalink]

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17 Jan 2010, 00:19
sorry guys the OA is B..please excuse me for the mistype

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Senior Manager
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Re: For any integer k greater than 1, the symbol k* denotes the product of [#permalink]

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31 Jan 2010, 09:17
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: For any integer k greater than 1, the symbol k* denotes the product of [#permalink]

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01 Feb 2010, 12:18
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: For any integer k greater than 1, the symbol k* denotes the product of [#permalink]

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02 Feb 2010, 10:28
Yes should be 14 only/
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Re: For any integer k greater than 1, the symbol k* denotes the product of [#permalink]

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29 Mar 2016, 09:26
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: For any integer k greater than 1, the symbol k* denotes the product of [#permalink]

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06 Apr 2016, 23:17
jeeteshsingh 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

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

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

14! has all the numbers above.. therefore B..!

How did you conclude that 14! has all the numbers (and why not any other option). I don't know how to solve such questions. Please suggest

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Re: For any integer k greater than 1, the symbol k* denotes the product of [#permalink]

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07 Apr 2016, 23:25
MeghaP wrote:
jeeteshsingh 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

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

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

14! has all the numbers above.. therefore B..!

How did you conclude that 14! has all the numbers (and why not any other option). I don't know how to solve such questions. Please suggest

See here in order to get 3675 we need two sevens and two fives and one two in the factorial
here two sevens will happen only at 14 and 14 contains all the multiples needed

Thanks ..

Kudos if you like my post..

Regards
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Re: For any integer k greater than 1, the symbol k* denotes the product of [#permalink]

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27 Apr 2016, 17:18
At what level do you guys think youd start to see this level of difficulty? 700-740? 750+?

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Re: For any integer k greater than 1, the symbol k* denotes the product of [#permalink]

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27 Apr 2016, 17:22
sunnypatel wrote:
At what level do you guys think your start to see this level of difficulty? 700-740? 750+?

I am not Gmat Expert ; But maybe Around 650-680
P.S => Continue to practise these Questions on the gmatclub ..Try a few others of the same category and after a few weeks you will be saying that this question has 600 level of difficulty.
Regards
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Re: For any integer k greater than 1, the symbol k* denotes the product of [#permalink]

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16 Jun 2016, 11:18
K* is a multiple of 3675 means 3675 multiple by some no. N = K* (3675 x N = K*).

To find N, K* should be divisible by 3675.

So 1x2x3x4....xK should be divisible by 3675

Prime factorisation of 3675 is 5*5*7*7*3 (LCM)

So 1x2x3x4....xK should be divisible by (5*5*7*7*3)

Thus nos. in 1x2x3x4....xK should contain at least 2 smallest nos. which can be divided by two 5s (5 and 10 will do so)
nos. in 1x2x3x4....xK should contain at least 2 smallest nos. which can be divided by two 7s (7 and 14 will do so)
nos. in 1x2x3x4....xK should contain at least 1 smallest no. which can be divided by the single 3 ( 3 will do so).

The sequence 1x2x3x4x5x6x7x8x9x10x11x12x13x14 is the smallest sequence that contains at least one multiple of 3, 2 multiples of 5 and 2 multiples of 7.

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Re: For any integer k greater than 1, the symbol k* denotes the product of [#permalink]

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18 Jul 2016, 06:43
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

Quote:
Hi Bunuel,
Can you please provide a detailed explanation of the solution to this problem?
Thanks again!

Regards,
Yosita

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Re: For any integer k greater than 1, the symbol k* denotes the product of   [#permalink] 18 Jul 2016, 06:43

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