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# PowerPrep DS - Factors

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PowerPrep DS - Factors [#permalink]  27 Aug 2006, 08:36
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Can someone show me a quick way to solve this ds question from PowerPrep?

If d is a positive integer and f is the prodcut 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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it should be C ...
using both the options we can find that d is infact 7 ...
soln:
from first we find the value of d to be anything from the set { 1,2,3,4,5,6,7} ..
because the gretaest power of 5 in 30! is 7 ... that means we can have at maximum 10^7 in 30! ...
from second st
d>6 ..
thus d is 7 ..
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Thanks for responding. A little more help.. I'm not seeing how you get from the greatest power of 5 in 30! is 7 (I can see this but not how it relates to the 10) therefore max 10^7 in 30!. Can you explain? Thanks again.

from first we find the value of d to be anything from the set { 1,2,3,4,5,6,7} ..
because the gretaest power of 5 in 30! is 7 ... that means we can have at maximum 10^7 in 30! ...
from second st
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Is it because 5 is the highest factor of 10 (1 and 2 being the lowest)? so therefore (5*2)^7 must be contained?
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yup you are thinking in the right directions,
10 = 5 * 2 ...
=>10^x = 5^x * 2^x ..
here we need to identify the largest value of x in 30! ..
the largest power of 2 power of 2 will be greater than largest power of 5 in 30! .. so we need to find a number which satisfies both 5 as well as 2 .. thus in effect we need tro find the largest power of 5 only ..
hope it helps ..
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Right. It helps indeed. Thanks again.
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Intuitively I can get (C) here, but can't quite figure out how. Anybody know where the OE for this problem is? Can't seem to find it in the OG.

Thanx
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Good question, I need to hit the number properties book again....

To find the highest power of 10 in 30!, we have to find the highest powers of the factors of 10, and then take the lowest power of the factor.

In this case, the highest power of 2 in 30! is as follows:-

30/2=15 ignore the remainder
15/2=7
7/2=3
3/2=1

This means that the highest power of 2 in 30! is 26

The highest power of 5 in 30! is as follows:-

30/5=6
6/5=1
Total =7

The highest power of 10 is the lowest power of its factors, in this case 7.
So the max value of d is 10^7, but it could be any value from 1 thru 7. hence 1 is insuff.

From 2, we know that d > 7...combine with 1, we get the answer...hence C
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Futuristic wrote:
Good question, I need to hit the number properties book again....

To find the highest power of 10 in 30!, we have to find the highest powers of the factors of 10, and then take the lowest power of the factor.

In this case, the highest power of 2 in 30! is as follows:-

30/2=15 ignore the remainder
15/2=7
7/2=3
3/2=1

This means that the highest power of 2 in 30! is 26

The highest power of 5 in 30! is as follows:-

30/5=6
6/5=1
Total =7

The highest power of 10 is the lowest power of its factors, in this case 7.
So the max value of d is 10^7, but it could be any value from 1 thru 7. hence 1 is insuff.

From 2, we know that d > 7...combine with 1, we get the answer...hence C

Which book are you referring to?
Director
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4gmat number properties e-book.

And sorry for the typo, I meant >6 not >7
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Re: PowerPrep DS - Factors [#permalink]  01 Sep 2006, 08:58
lets see..F=30!

ie. 1*2*3*4*....*30

lets see prime factors of 10=2*5; 2^a * 5^b

1) says 10^d is a factor of 30!

well d can 1, 2, ...and so on Inusff

2) say D>6...well, it can be 7, 8, 9, 10, 11..and so on..Insuff

lets take em together

lets see prime factors of 10=2*5; 2^a * 5^b;
and we know that 10^(to something) is a factor of 30! and we know this something is greater than 6...

in other words the power of 5^b will determine the power of 10....cause depends on how many 5s are there in the 30!

lets see 30/5=6
plus 1 one more from 25;

so in total there are 7 5s...

we now Know that we have 5^7 s in the 30!

we therfore also now know that the power of 10 will be 7...

C it sufficient...

THIS IS A GOOD QUESTION TO TEST 650+ QUant level questions..

mathec wrote:
Can someone show me a quick way to solve this ds question from PowerPrep?

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

(1) 10^d is a factor of f
(2) d > 6
Re: PowerPrep DS - Factors   [#permalink] 01 Sep 2006, 08:58
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