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How many factors of 6! are greater than 100?
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05 Nov 2017, 01:59
05 Nov 2017, 01:59
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Question Stats:
26% (01:20) correct
73% (01:29) wrong based on 26 sessions
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How many factors of 6! are greater than 100?
(A) 4
(B) 6
(C) 7
(D) 10
(E) 12
Kudos for correct solution.
(A) 4
(B) 6
(C) 7
(D) 10
(E) 12
Kudos for correct solution.
Re: How many factors of 6! are greater than 100?
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05 Nov 2017, 07:06
05 Nov 2017, 07:06
1
I found no other way than checking the possible multiplication among factors of 6!.
I start with the greatest factor down to the smallest factor greater than 100.
6! = 6*5*4*3*2.
Case 1: Combine 5 of the values to yield a product greater than 100
6*5*4*3*2
Total options = 1.
Case 2: Combine 4 of the values to yield a product greater than 100
6*5*4*3
6*5*4*2
6*5*3*2
6*4*3*2
5*4*3*2
Total options = 5.
Total options = Case 1 + Case 2 = 1+5 = 6.
6 is not among the answers. I think there is something wrong
I start with the greatest factor down to the smallest factor greater than 100.
6! = 6*5*4*3*2.
Case 1: Combine 5 of the values to yield a product greater than 100
6*5*4*3*2
Total options = 1.
Case 2: Combine 4 of the values to yield a product greater than 100
6*5*4*3
6*5*4*2
6*5*3*2
6*4*3*2
5*4*3*2
Total options = 5.
Total options = Case 1 + Case 2 = 1+5 = 6.
6 is not among the answers. I think there is something wrong
Re: How many factors of 6! are greater than 100?
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05 Nov 2017, 08:35
05 Nov 2017, 08:35
IlCreatore wrote:
I found no other way than checking the possible multiplication among factors of 6!.
I start with the greatest factor down to the smallest factor greater than 100.
6! = 6*5*4*3*2.
Case 1: Combine 5 of the values to yield a product greater than 100
6*5*4*3*2
Total options = 1.
Case 2: Combine 4 of the values to yield a product greater than 100
6*5*4*3
6*5*4*2
6*5*3*2
6*4*3*2
5*4*3*2
Total options = 5.
Total options = Case 1 + Case 2 = 1+5 = 6.
6 is not among the answers. I think there is something wrong
I start with the greatest factor down to the smallest factor greater than 100.
6! = 6*5*4*3*2.
Case 1: Combine 5 of the values to yield a product greater than 100
6*5*4*3*2
Total options = 1.
Case 2: Combine 4 of the values to yield a product greater than 100
6*5*4*3
6*5*4*2
6*5*3*2
6*4*3*2
5*4*3*2
Total options = 5.
Total options = Case 1 + Case 2 = 1+5 = 6.
6 is not among the answers. I think there is something wrong
The OA is 6. Edited the options. Thank you.
