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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]  29 Jul 2020, 11:08
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63% (01:02) correct 36% (01:15) wrong based on 11 sessions
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]  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

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Re: For any integer n greater than 1, n∗ denotes the product of [#permalink]  30 Jul 2020, 00:07
1
KUDOS
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]  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
Intern
Joined: 09 Nov 2018
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Re: For any integer n greater than 1, n∗ denotes the product of [#permalink]  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
_________________

Inspired by great content in some best books on GRE, I have created my own YouTube channel-QUANT MADE EASY!
Here, I cover important topics for better conceptual understanding. Subscribe to my channel for your Quant preparation!
All the Best!

Manager
Joined: 22 Jan 2020
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Re: For any integer n greater than 1, n∗ denotes the product of [#permalink]  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

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