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

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If t is an integer, is 3^t a factor of 21!? [#permalink]

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If t is an integer, is 3^t 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
[Reveal] Spoiler: OA

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Re: If t is an integer, is 3^t a factor of 21!? [#permalink]

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New post 21 Aug 2014, 10:13
21! has 3,6,9,12,15,18,21 as multiples of 3... which makes 3^9 as the maximum power of 3 which can be a factor of 21!

STAT1
Prime numbers can be 2,3 and 3,5
if its 2,3 then t= 6. So, 3^t will be a factor of 21!
if its 3,5 then t=15. So, 3^t will NOT be a factor of 21!
So, NOT Sufficient

STAT2
for all values of t from 1 to 8 3^t is a factor of 21! as 3^9 is a factor of 21!
So, SUFFICIENT

So, Answer will be B
Hope it helps!
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If t is an integer, is 3^t a factor of 21!? [#permalink]

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

The power of 3 in factorization of 21! is 21/3 + 21/3^2 = 7 + 2 = 9. (Check here: everything-about-factorials-on-the-gmat-85592.html)

(1) t is the product of two distinct single-digit prime numbers that are smaller than 7. If t = 2*3 = 6 < 9, then 3^t will be a factor of 21! but if t = 3*5 = 15 > 9, then 3^t won't be a factor of 21!. Not sufficient.

(2) 0 < t < 9. For any nonnegative t less than or equal to 9, 3^t is a factor of 21!. Sufficient.

Answer: B.

Check Trailing Zeros Questions and Power of a number in a factorial questions in our Special Questions Directory.
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Re: If t is an integer, is 3^t a factor of 21!? [#permalink]

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Re: If t is an integer, is 3^t a factor of 21!? [#permalink]

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New post 05 Apr 2016, 18:28
goodyear2013 wrote:
If t is an integer, is 3^t 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


21! = 1x2x3x4x5x...21
there are 9 factors of 3 here.
question asks is t<9?

1. if 2x3=6 then yes
if 3x5=15 - then no.

A D are out.

2. 0<t<9
basically answers the question. B

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Re: If t is an integer, is 3^t a factor of 21!? [#permalink]

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New post 24 Aug 2017, 13:40
Hello from the GMAT Club BumpBot!

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Re: If t is an integer, is 3^t a factor of 21!?   [#permalink] 24 Aug 2017, 13:40
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