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For any integer n greater than 1, n∗ denotes the product of
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29 Jul 2020, 11:08
29 Jul 2020, 11:08
Expert Reply
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Question Stats:
68% (01:07) correct
32% (01:31) wrong based on 25 sessions
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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
Kudos for the right answer and explanation
(A) 5
(B) 6
(C) 20
(D) 24
(E) 25
Kudos for the right answer and explanation
Re: For any integer n greater than 1, n∗ denotes the product of
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29 Jul 2020, 11:50
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.
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.
Re: For any integer n greater than 1, n∗ denotes the product of
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Updated on: 30 Jul 2020, 02:07
Updated on: 30 Jul 2020, 02:07
2
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
