Data Sufficiency

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

1. 10sq<d> is a factor of f
2. d>6

I took me more than 4 mins to answer this.

Which would be the fastest way to find how many times is 10 a factor of 30! ?

Finding out how many times 10 is a factor of 30! should be easier if you consider that 10 = 2*5. You obviously have enough 2's in 30! (at least one in every even number), so the question comes down to figuring how many 5's there are. There will be 6+1 = 7 fives in 30! (30/5 = 6 and add another one for 25), which means that 10^7 is a factor of 30.

I don't understand your notation, though... What is 10sq<d>? 10*sqrt(d) by any chance?

Hi Dana

Sorry I meant base 10, exponent d
10^d

Oh ok then. That means that 1 is insufficient. d could be anything from 1 to 7 inclusive.
2 is insufficient as well, since d could be anything from 6 to 30.
However, taken together the two statements are sufficient, since only 7 is consistent with both restrictions.

if we look at the product of the first 30 positive integers we get 5 as a factor seven times so IMO statement 1 is sufficient

and the answer should be A

if we look at the product of the first 30 positive integers we get 5 as a factor seven times so IMO statement 1 is sufficient

and the answer should be A

if we look at the product of the first 30 positive integers we get 5 as a factor seven times so IMO statement 1 is sufficient

and the answer should be A

The official answer is C

Refer here https://www.beatthegmat.com/consecutive- ... 22927.html

Let me know if there are any questions also and I will more than happy to explain. ddo, there is a shortcut that I came across in this forum which I have explained also. Ian has provided an explanation on why the shortcut works in one of his posts(trying to find that also).

DanaJ, u r absolutely correct on C and your explanation. Keep up the good work on your solutions...

Hope this helps!