Consecutive Integer Problem

[hypik21]

Whats the quickest way to solve this?

If D is a positive integer and F is the product of the first 30 integers, what is the calue of D.

1. 10^d is a factor of F
2. d> 6

OA: c

[cramya]

10 can be split in to 5 * 2

In 30! 5 is the bottle neck that will limit 10's powers and not 2 since there are more 2's (every 2nd number is divisible by 2 whereas only every 5 the number is divisible by 5)

There is kind of a shortcut to finding this.
Divide 30 by increasing powers of 5 till u get 0 as the integer quotient and add all the integer quotients in the process
i.e 30/5 + 30/5^2 +30/5^3
= 6 + 1 + 0 (we stop here)= 7

Refer to this post (it will be more clear) - https://www.beatthegmat.com/ps-confused- ... html#92483. Ian has provided an explanation to this shortcut



Now to the actual problem:

Stmt I

10^ d is factor of F = 30!

By doing what I mentioned in bold above we see 10^7 is the highest power of 10 that will divide 30! (d can be any number from 0 to 7)

INSUFF

Stmt II

d>6

We have no idea how D relates to F

INSUFF

Combining I and II

we know d = 7

SUFF

C)

[iamcste]

Whats the quickest way to solve this?

If D is a positive integer and F is the product of the first 30 integers, what is the calue of D.

1. 10^d is a factor of F
2. d> 6

OA: c

https://www.manhattangmat.com/forums/if- ... t2234.html

This is the expert way!