Factor Problem

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neoshichhadva: Newbie | Next Rank: 10 Posts; Posts: 9; Joined: Wed May 25, 2011 10:51 pm

by neoshichhadva » Mon Sep 19, 2011 9:40 am

If 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

[spoiler]Answer: C[/spoiler]

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Source: Beat The GMAT — Data Sufficiency | Mon Sep 19, 2011 9:40 am

cans: Legendary Member; Posts: 1309; Joined: Mon Apr 04, 2011 5:34 amFollowed by: 123 members; Location: India; Thanked: 310 times; GMAT Score:750

by cans » Mon Sep 19, 2011 9:46 am

f=30!
A) 10^d is factor of 30!
d=1, true, d=2, true. Insufficient
B) d>6 d=7,8,... insufficient
A&B) 30! = (10)^7 * n where n is not multiple of 10.
d>6.
d=7, 10^7 is factor of 30!
10^8 is not....
Sufficient
d=7
IMO C

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sl750: Master | Next Rank: 500 Posts; Posts: 496; Joined: Tue Jun 07, 2011 5:34 amFollowed by: 1 member; Thanked: 38 times

by sl750 » Mon Sep 19, 2011 10:07 am

f = 30!

Statement 1

30!/10^d = Integer. d=1,2,3,4,5,6. Insufficient

Statement 2. d>6 Insufficient

1+2

d>6
Look at the factors of 5 in 30! 5, 10,15,20,25,30. There are a total of 7 5's in 30!. There are sufficient 2's as well to ensure that we obtain an integer
Therefore in order for 30!/(2^d)(5^d) to be an integer. d=7 Sufficient

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