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# If d is a positive integer and f is the product of the first

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Manager
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Re: DS : product of first 30 positive integers [#permalink]

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14 Aug 2010, 09:06
thanks for the tip on trailing zeroes bunuel.

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Re: DS : product of first 30 positive integers [#permalink]

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12 Jan 2011, 23:42
awesome bunuel. Trailing Zero is a very interesting concept that will be helpful =)

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Number properties question - factorials [#permalink]

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30 Apr 2011, 23:50
Question:

If d is a positive integer and f is the product of the first 30 positive integers, what is the value of d?

(1) 10^(d) is a factor of f
(2) d > 6

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Re: Number properties question - factorials [#permalink]

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01 May 2011, 00:01
chloeholding wrote:
Question:

If d is a positive integer and f is the product of the first 30 positive integers, what is the value of d?

(1) 10^(d) is a factor of f
(2) d > 6

gmatprep-ds-product-of-first-30-integers-87454.html

 ! Please post PS questions in the PS sub-forum: gmat-problem-solving-ps-140/Please post DS questions in the DS sub-forum: gmat-data-sufficiency-ds-141/No posting of PS/DS questions is allowed in the main Math forum.

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Re: Number Properties from GMATPrep [#permalink]

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12 Sep 2011, 06:22
Thanks for this explanation Bunuel.

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Re: DS: GMAT Prep - What is the value of d? [#permalink]

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13 Sep 2011, 08:27
A nice question, here is my approach.

F=1*2*3......*30
Now F would have Seven 5's.

Thus from 10^1 till 10^7 is possible.
a. A doesnt help in reducing this.
b. Useless all alone.

Combining both we get that the value has to be 10^7.

And thus the answer is C.

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17 Sep 2011, 06:12
richardj wrote:
The maximum value of d = int(d/5) + int (d/(5^2)) + ....

d = int(30/5) + int(30/25) + ... = 6 + 1 + 0 = 7

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Re: DS: GMAT Prep - What is the value of d? [#permalink]

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18 Sep 2011, 21:52
Clear C it is.

The key to this problems is to look for no of 5's in the given product.

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Re: DS: GMAT Prep - What is the value of d? [#permalink]

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23 Sep 2011, 17:00
zoom wrote:
If $$d$$ is a positive integer and $$f$$ is the product of the first $$30$$ positive integers, what is the value of $$d$$?

1) $$10^d$$ is a factor of $$f$$
2) $$d > 6$$

Image:
Attachment:
GPrep_d_is_a_positive_integer.png

d = 30!
f = a positive integer

1) f = k(10^d) where k is an integer
30! = k (10^d)

Since d is a positive integer, how many 10s are in 30!?

30/5 = 6
30/25 = 1

so there are seven 10s in 30! and d could be 0, 1, .......7. NSF.

2) d > 6,m so what ? nothing because we do not know the relationship between d and f. NSF..

1 & 2) Oh yeah... now we has relationship between d and f. Also we know the exact value of d i.e. 7.

Sufficient.. D = 7.

Then it is C.

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Re: DS: GMAT Prep - What is the value of d? [#permalink]

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29 Sep 2011, 07:15
zoom wrote:
If $$d$$ is a positive integer and $$f$$ is the product of the first $$30$$ positive integers, what is the value of $$d$$?

1) $$10^d$$ is a factor of $$f$$
2) $$d > 6$$

Image:
Attachment:
GPrep_d_is_a_positive_integer.png

d = +ve
f = 30!
Q: d=?

1)
max. powers of 10 in 30!
int(30/5) + int(30/25) = 7
but, does not tell value of d
0 <= d <= 7
Insufficient

2) Insufficient

3) Combining
0 <= d <= 7 ===> from (1)
d > 6 ===> from (2)
we get d =7
Sufficient, hence (C)
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GM.

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Re: DS: GMAT Prep - What is the value of d?   [#permalink] 29 Sep 2011, 07:15

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