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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] New post 29 Jul 2020, 11:08
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For any integer n greater than 1, \(n\ast\) denotes the product of all the integers from 1 to n, inclusive. How many multiples of 4 are there between \(4\ast\) and \(5\ast\), inclusive?

(A) 5
(B) 6
(C) 20
(D) 24
(E) 25


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[Reveal] Spoiler: OA

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Re: For any integer n greater than 1, n∗ denotes the product of [#permalink] New post 29 Jul 2020, 11:50
n* is factorial of n.
4* = 1x2x3x4 = 24
5* = 5x4* = 120

Let there be x multiples of 4 between 24 and 120 inclusive.
We can treat this as an AP with first term 24 and xth term as 120.

=> 120 = 24 + 4*(x - 1)
=> 96 = 4*(x - 1)
=> 24 = x - 1
=> 25 = x

So, the answer is E.
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Re: For any integer n greater than 1, n∗ denotes the product of [#permalink] New post 30 Jul 2020, 00:07
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Quote:
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?

Step 1: Understanding the question
As n∗ denotes the product of all the integers from 1 to n, inclusive, value of 4* is 4*3*2*1 = 24 and value of 5* is 5*4*3*2*1 = 120
Difference between 104 and 24 to be calculated to find number of multiples of 4.

Step 2: Calculation
Difference between 120 and 24 = 96

Hence, numbers of multiples between 120 and 24, inclusive, are \(\frac{96}{4}\) + 1 = 24 + 1 = 25

E is correct


Link to my video on the topic: Factorial
https://youtu.be/mLDlYRAr2sA
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Last edited by kapil1 on 30 Jul 2020, 02:07, edited 1 time in total.
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Re: For any integer n greater than 1, n∗ denotes the product of [#permalink] New post 30 Jul 2020, 01:20
kapil1 wrote:
Quote:
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?

Step 1: Understanding the question
As n∗ denotes the product of all the integers from 1 to n, inclusive, value of 4* is 4*3*2*1 = 24 and value of 5* is 5*4*3*2*1 = 120
Difference between 104 and 24 to be calculated to find number of multiples of 4.

Step 2: Calculation
Difference between 120 and 24 = 96

Hence, numbers of multiples between 120 and 24, not inclusive, are \(\frac{96}{4}\) -1 = 26 - 1 = 25

E is correct


Link to my video on the topic: Factorial
https://youtu.be/mLDlYRAr2sA


\(\frac{96}{4}\) is 24 and not 26. So your final answer should be 23.
Also it is stated in the question that it is inclusive of 24 and 120.
Thus, \(\frac{96 }{ 4}\) + 1 = 25
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Re: For any integer n greater than 1, n∗ denotes the product of [#permalink] New post 30 Jul 2020, 02:08
sukrut96 wrote:
kapil1 wrote:
Quote:
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?

Step 1: Understanding the question
As n∗ denotes the product of all the integers from 1 to n, inclusive, value of 4* is 4*3*2*1 = 24 and value of 5* is 5*4*3*2*1 = 120
Difference between 104 and 24 to be calculated to find number of multiples of 4.

Step 2: Calculation
Difference between 120 and 24 = 96

Hence, numbers of multiples between 120 and 24, not inclusive, are \(\frac{96}{4}\) -1 = 26 - 1 = 25

E is correct


Link to my video on the topic: Factorial
https://youtu.be/mLDlYRAr2sA


\(\frac{96}{4}\) is 24 and not 26. So your final answer should be 23.
Also it is stated in the question that it is inclusive of 24 and 120.
Thus, \(\frac{96 }{ 4}\) + 1 = 25

Thanks! Edited :)
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Here, I cover important topics for better conceptual understanding. Subscribe to my channel for your Quant preparation!
All the Best!
https://www.youtube.com/channel/UCvdY0kJNbnJzPEOsT5PMFRQ

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Re: For any integer n greater than 1, n∗ denotes the product of [#permalink] New post 05 Aug 2020, 05:44
n* = n!

4*= 4!= 24
5*= 5!= 120

Multiples of 4 in 24 is 24/4=6
Multiples of 4 in 120 is 120/4=30

To get the multiples of 4 between 5! and 4!
it is the same as counting the number of integers between 6 and 30 inclusive

Namely: 30-6+1=25

Final Answer: E
Re: For any integer n greater than 1, n∗ denotes the product of   [#permalink] 05 Aug 2020, 05:44
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