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# How many factors of 6! are greater than 100?

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Math Expert
Joined: 02 Sep 2009
Posts: 42571

Kudos [?]: 135380 [0], given: 12691

How many factors of 6! are greater than 100? [#permalink]

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05 Nov 2017, 02:06
Expert's post
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Difficulty:

55% (hard)

Question Stats:

51% (08:29) correct 49% (01:35) wrong based on 47 sessions

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How many factors of 6! are greater than 100?

(A) 4

(B) 6

(C) 7

(D) 10

(E) 12
[Reveal] Spoiler: OA

_________________

Kudos [?]: 135380 [0], given: 12691

Math Expert
Joined: 02 Aug 2009
Posts: 5341

Kudos [?]: 6107 [1], given: 121

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

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05 Nov 2017, 04:30
1
KUDOS
Expert's post
Bunuel wrote:
How many factors of 6! are greater than 100?

(A) 4

(B) 5

(C) 7

(D) 10

(E) 12

A good Q and not a very easy one ...

$$6! =1*2*3*4*5*6 = 2^4*3^2*5=720$$
now the trick is NOT to try and find the ONES greater than 100 BUT the ones that are required to be multiplied by factors above 100 to get 6!
the lowest factors are 1,2,3,4,5,6 which can be seen from 6! if we check 6... $$\frac{6!}{6}=2*3*4*5=120>100$$
next will be 2*4=8 and $$\frac{2*3*4*5*6}{2*4}=3*5*6=90<100$$
so our answer is 1,2,3,4,5,6 so 6 values

Realized, missed out on 1....
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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 6107 [1], given: 121

Intern
Joined: 27 Mar 2017
Posts: 1

Kudos [?]: 1 [1], given: 0

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

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05 Nov 2017, 06:03
1
KUDOS
6!= 6*5*4*3*2
What combination of numbers is over 100?
1. 6*5*4
2. 6*5*4*3
3. 6*5*4*3*2
4. 6*5*4*2
5. 6*5*3*2

Note: 5*4*3*2 is over 100, but it can be written as (3*2)*5*4, which is equal 6*5*4

Ans: B

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Director
Joined: 25 Feb 2013
Posts: 619

Kudos [?]: 304 [1], given: 39

Location: India
GPA: 3.82
Re: How many factors of 6! are greater than 100? [#permalink]

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05 Nov 2017, 06:38
1
KUDOS
Bunuel wrote:
How many factors of 6! are greater than 100?

(A) 4

(B) 5

(C) 7

(D) 10

(E) 12

6! = 6*5*4*3*2

Now number of factors that are greater than 100 are -

1) 6*5*4*3*2 = 720

2) 6*5*4*3 = 360

3) 6*5*4*2 = 240

4) 6*5*3*2 = 180

5) 6*4*3*2 = 144

6) 5*4*3*2 = 120

IMO number of factors should be 6 but there is no such option

Hi Bunuel

Can you confirm whether the OAs are correct or point out the EXTRA factor in my method?

Kudos [?]: 304 [1], given: 39

Math Expert
Joined: 02 Sep 2009
Posts: 42571

Kudos [?]: 135380 [0], given: 12691

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

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05 Nov 2017, 08:35
chetan2u wrote:
Bunuel wrote:
How many factors of 6! are greater than 100?

(A) 4

(B) 5

(C) 7

(D) 10

(E) 12

A good Q and not a very easy one ...

$$6! =1*2*3*4*5*6 = 2^4*3^2*5=720$$
now the trick is NOT to try and find the ONES greater than 100 BUT the ones that are required to be multiplied by factors above 100 to get 6!
the lowest factors are 1,2,3,4,5,6 which can be seen from 6! if we check 6... $$\frac{6!}{6}=2*3*4*5=120>100$$
next will be 2*4=8 and $$\frac{2*3*4*5*6}{2*4}=3*5*6=90<100$$
so our answer is 1,2,3,4,5,6 so 6 values

Realized, missed out on 1....

The OA is 6. Edited the options. Thank you.
_________________

Kudos [?]: 135380 [0], given: 12691

Re: How many factors of 6! are greater than 100?   [#permalink] 05 Nov 2017, 08:35
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