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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 ..
_________________

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

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 ..
_________________

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

Add the quotients: 26
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

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

Add the quotients: 26 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