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# if 4 d x d 12, is the tens digit of x! prime? 1) x is even

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if 4 d x d 12, is the tens digit of x! prime? 1) x is even [#permalink]

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18 Jun 2006, 18:21
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if 4 d x d 12, is the tens digit of x! prime?

1) x is even
2) x! has exactly 3 distinct prime factors

I do not understand what does the question mean when it says 4 d x d 12 (Source: Princeton GMAT Test 2)

OA: B
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Joined: 06 May 2006
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19 Jun 2006, 15:43
It is probably 4 < x < 12.

#1. x is even => x = 6, 8, 10. Insufficient
6! = 720 (tens digit prime)
8! = 40320 (tens digit prime)
10! = 3628800 (tens digit not prime)

#2. x! has exactly 3 distinct prime factors
5! = 1*2*3*4*5 (3 prime factors) = 120 (tens digit prime)
6! = 1*2*3*4*5*6 (3 prime factors) = 720 (tens digit prime)
7! = 1*2*3*4*5*6*7 (4 prime factors), and so on...
Sufficient

Now to sleep - 4.20 am here...
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