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

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

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23 Apr 2012, 11:51
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Difficulty:

45% (medium)

Question Stats:

68% (01:34) correct 32% (01:55) wrong based on 135 sessions

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For any integer n greater than 1, n* denotes the product of all the integers from 1 to n, inclusive. How many multiples of 4 are there between 4* and 5*, inclusive?

A. 5
B. 6
C. 20
D. 24
E. 25

Could please someone explain me the logic of the solution for this task since the official explanation isn't clear for me
Math Expert
Joined: 02 Sep 2009
Posts: 58095
Re: For any integer n greater than 1, n* denotes the product of  [#permalink]

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23 Apr 2012, 12:31
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Galiya wrote:
For any integer n greater than 1, n* denotes the product of all the integers from 1 to n, inclusive. How many multiples of 4 are there between 4* and 5*, inclusive?

A. 5
B. 6
C. 20
D. 24
E. 25

Could please someone explain me the logic of the solution for this task since the official explanation isn't clear for me

"n* denotes the product of all the integers from 1 to n, inclusive" means that n*=1*2*3*...*n=n!.

Which means that, 4*=4!=24 and 5*=5!=120. So, the question basically asks "how many multiples of 4 are there between 24 and 120, inclusive"

# of multiples of 4 between 24 and 120, inclusive is (last-first)/multiple+1=(120-24)/4+1=25 (check this: how-many-multiples-of-4-are-there-between-12-and-94862.html).

Hope it helps.
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Re: For any integer n greater than 1, n* denotes the product of  [#permalink]

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23 Apr 2012, 12:42
I'm familiar w this formula, but i need to grasp it
subtracting 24 from 120 we eliminate some multiples of four between 24 and 120: 100, 104, ...112...
Math Expert
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Posts: 58095
Re: For any integer n greater than 1, n* denotes the product of  [#permalink]

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23 Apr 2012, 13:16
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Galiya wrote:
I'm familiar w this formula, but i need to grasp it
subtracting 24 from 120 we eliminate some multiples of four between 24 and 120: 100, 104, ...112...

You can derive it from arithmetic progression formula.

Multiples of 4 represent evenly spaced set (aka arithmetic progression).

Now, if we have $$n$$ terms in arithmetic progression, the first term is $$a_1$$ and the common difference of successive members is $$d$$, then the $$n_{th}$$ term of the sequence is given by: $$a_ n=a_1+d(n-1)$$ --> $$n=\frac{a_ n-a_1}{d}+1$$.

You can see that it's basically the same formula as in my previous post.
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Re: For any integer n greater than 1, n* denotes the product of  [#permalink]

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23 Apr 2012, 16:26
The more I browse the more tricks I learn, this question would have taken me a good 3 minutes. Thanks for the good explanation.
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Re: For any integer n greater than 1, n* denotes the product of  [#permalink]

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31 Aug 2013, 06:26
Bumping for review and further discussion.
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Re: For any integer n greater than 1, n* denotes the product of  [#permalink]

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11 Nov 2013, 21:09
Galiya wrote:
For any integer n greater than 1, n* denotes the product of all the integers from 1 to n, inclusive. How many multiples of 4 are there between 4* and 5*, inclusive?

A. 5
B. 6
C. 20
D. 24
E. 25

Could please someone explain me the logic of the solution for this task since the official explanation isn't clear for me

here, 4* = 4! and 5* = 5!

question is asking no. of terms in an AP whose first term is 24(4!), last term is 120(5!) and common difference is 4.

last term OR nth term = first term +(no. of tems -1)(common difference)
Tn = a + (n-1)d

120 = 24 + (n-1)4
96/4 = n-1

n = 25 .....
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Re: For any integer n greater than 1, n* denotes the product of  [#permalink]

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13 Mar 2017, 00:26
4*=4!=24
5*=5!=120

multiples of b/w 24 and 120= (120-24)/4+1=24+1=25
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Re: For any integer n greater than 1, n* denotes the product of  [#permalink]

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15 Mar 2017, 16:49
1
Galiya wrote:
For any integer n greater than 1, n* denotes the product of all the integers from 1 to n, inclusive. How many multiples of 4 are there between 4* and 5*, inclusive?

A. 5
B. 6
C. 20
D. 24
E. 25

We are given that for any integer n greater than 1, n* denotes the product of all the integers from 1 to n inclusive. Thus the notation n* is same as the notation n!.

Thus, 4* = 4! = 24 and 5* = 5! = 120.

We need to determine how many multiples of 4 are between 24 and 120.

(largest multiple of 4 in the set - smallest multiple of 4 in the set)/4 + 1

(120 - 24)/4 + 1 = 96/4 + 1 = 25

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

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15 Aug 2019, 04:03
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 n greater than 1, n* denotes the product of   [#permalink] 15 Aug 2019, 04:03
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