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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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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?

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

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

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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?

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?

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!

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

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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!

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!!

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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29 Mar 2016, 09:26

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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

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

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 StoneCold
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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.

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!