factorial ds

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rupsk: Master | Next Rank: 500 Posts; Posts: 123; Joined: Mon Feb 07, 2011 12:11 pmFollowed by: 1 member

by rupsk » Sun Nov 13, 2011 5:01 pm

If t is an integer,3^t is a factor of 21!?

(1) t is the product of two distinct single-digit prime numbers that are smaller than 7.

(2) 0 < t < 9

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Source: Beat The GMAT — Quantitative Reasoning | Sun Nov 13, 2011 5:01 pm

neelgandham: Community Manager; Posts: 1060; Joined: Fri May 13, 2011 6:46 amFollowed by: 52 members; Location: Utrecht, The Netherlands; Thanked: 318 times

by neelgandham » Sun Nov 13, 2011 5:50 pm

If t is an integer,3^t is a factor of 21!? The highest power of 3 in 21! is 8(3^8) How ? one each from the numbers in bold.

21! =1*2*3*4*5*6*7*8*9*10*11*12*13*14*15*16*17*18*19*20*21

The question can be rephrased to If t is an integer, Is 0<t<9?

(1) t is the product of two distinct single-digit prime numbers that are smaller than 7.

t can be 2*3 or 2*5 or 3*5.
If t = 6, Is 0<t<9 Yes !
If t = 10, Is Is 0<t<9 No!
Hence Insufficient!

(2) 0 < t < 9

Sufficient!

IMO B

Anil Gandham
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rupsk: Master | Next Rank: 500 Posts; Posts: 123; Joined: Mon Feb 07, 2011 12:11 pmFollowed by: 1 member

by rupsk » Sun Nov 13, 2011 7:10 pm

i got value of t between 0 and 10. so can you explain how you come to the value of 3^8 as for me it is 3^9?

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rooster: Senior | Next Rank: 100 Posts; Posts: 44; Joined: Wed Aug 25, 2010 12:23 am; Thanked: 6 times

by rooster » Sun Nov 13, 2011 7:14 pm

Need to figure out what the question is asking, which is "how many threes are in 21!"?

so, you can list out like this

21 - (3)
18 - (3,3)
15 - (3)
12 - (3)
9 - (3,3)
6 - (3)
3 - (3)

By this, we know we have a total of nine 3s

Now, with that said, we need to see if either can fulfill this.

A- No, since 3*5 would go out of scope

B - Yes, anything less than or equal to 9 works.

ANSWER:
B

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iwillsurvive101: Senior | Next Rank: 100 Posts; Posts: 58; Joined: Mon Nov 07, 2011 7:44 pm; Location: Washington DC; Thanked: 1 times

by iwillsurvive101 » Tue Nov 15, 2011 9:08 am

How did you come up with the following, can you pls explain

Need to figure out what the question is asking, which is "how many threes are in 21!"?

so, you can list out like this

21 - (3)
18 - (3,3)
15 - (3)
12 - (3)
9 - (3,3)
6 - (3)
3 - (3)

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shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 amFollowed by: 21 members; Thanked: 230 times

by shankar.ashwin » Tue Nov 15, 2011 9:59 am

As a short cut you could also do this as shown,

3 | 21
3 | 7 - 0
3 | 2 - 1

Its similar to division but keep dividing the number until it becomes smaller than the divisor (neglect the remainder) So you have 7+2 = 9

iwillsurvive101 wrote:How did you come up with the following, can you pls explain

Need to figure out what the question is asking, which is "how many threes are in 21!"?

so, you can list out like this

21 - (3)
18 - (3,3)
15 - (3)
12 - (3)
9 - (3,3)
6 - (3)
3 - (3)

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