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How many factors of 6! are greater than 100?

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Senior Manager
Senior Manager
Joined: 20 May 2014
Posts: 282
Followers: 14

Kudos [?]: 49 [0], given: 220

CAT Tests
How many factors of 6! are greater than 100? [#permalink] New post 05 Nov 2017, 01:59
00:00

Question Stats:

50% (00:02) correct 50% (00:43) wrong based on 2 sessions
How many factors of 6! are greater than 100?

(A) 4

(B) 6

(C) 7

(D) 10

(E) 12

Kudos for correct solution.
[Reveal] Spoiler: OA
Director
Director
Joined: 03 Sep 2017
Posts: 521
Followers: 1

Kudos [?]: 327 [0], given: 66

Re: How many factors of 6! are greater than 100? [#permalink] New post 05 Nov 2017, 07:06
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
Senior Manager
Senior Manager
Joined: 20 May 2014
Posts: 282
Followers: 14

Kudos [?]: 49 [0], given: 220

CAT Tests
Re: How many factors of 6! are greater than 100? [#permalink] New post 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


The OA is 6. Edited the options. Thank you.
Re: How many factors of 6! are greater than 100?   [#permalink] 05 Nov 2017, 08:35
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How many factors of 6! are greater than 100?

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