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# If P = (n)(n 1)(n 2) . . . (1) and n > 2, what is the

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VP
Joined: 13 Jun 2004
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If P = (n)(n 1)(n 2) . . . (1) and n > 2, what is the [#permalink]  05 Sep 2004, 16:16
If P = (n)(n â€“ 1)(n â€“ 2) . . . (1) and n > 2, what
is the largest value of integer n where P has zero
as its last 6 digits and a non-zero digit for its
millions place ?

(A) 29
(B) 30
(C) 34
(D) 35
(E) 39
GMAT Club Legend
Joined: 07 Jul 2004
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Location: Singapore
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I saw this on a previous thread, looking for it now...
VP
Joined: 13 Jun 2004
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sorry I didn't see it before, so I just post it.
Just add the link to the problem and solution if you find it....until that time, you all are free to answer
Manager
Joined: 05 Sep 2004
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The answer to this question is that there is no such integer.

If you notice the product, it's really a factorial of n. If you take the factorial of even the smallest value, 29, the answer comes to a 31 digit number with the last 17 digits being all zero.

If you perform this calculation in Excel using the FACT() function, the value for 21! has five lagging zeros and that for 22! has seven lagging zeros. Even if the answer choices are wrong, their still is no integer that would satisfy this condition.
GMAT Club Legend
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http://www.gmatclub.com/phpbb/viewtopic.php?t=9292
A it is
Beautiful explanation by dookie and ian
_________________

Best Regards,

Paul

Manager
Joined: 05 Sep 2004
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Yep, the refernced solution is right. I knew the pattern of zeros in a factorial but got stumped by Excel's numbers.

Excel only stores and displays 15 significant digits (= converts everything after that to zeros). Whoops!
Director
Joined: 20 Jul 2004
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First I missed that 25 has two 5s and was stuck at n=30.
Then I realised 25 has two 5s and was searching for n=25 (Didn't read "largest value of integer n").

29 it is. Very good problem.
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