DS - GMAT Prep

[sankruth]

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

[cris]

I think is C. If you put the correct answer under the Spoiler option, then knowing if is the correct answer I will explain it...

:D

[GoMBA]

Can someone please explain how to solve this? I am told that the OA is C

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

[parallel_chase]

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

f = 30!

d is a positive integer

Statement I & II are clearly insufficient alone.

Combining I & II

10^d is a factor of f
d>6

10 = 2*5

Basically we have to count the number of 2's and 5's in 30!
Without even calculating we know that there will be plenty of 2's, therefore we only have to calculate 5's.

30/5 = 6
30/25 = 1

6+1 = 7

we already know that d>6 so 7 is answer.


This means that when 30! will be divided by 10^7 the result will be an integer.

Hence C.

[GoMBA]

Thanks I got it now! I see the mistake i was making.

In 30 there are tens in the form of:

1. 3 tens (10, 20, 30),
2. Multiple twos (2, 4, 8, 12, ...) and 4 fives (5, 15, 25); which together makeup for 4 zeros.

The mistake i was making is that i counted 25 as having only one five.