hard prep question

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jamesk486: Master | Next Rank: 500 Posts; Posts: 141; Joined: Wed Mar 28, 2007 9:24 pmFollowed by: 1 member; Thanked: 2 times

by jamesk486 » Sun Apr 22, 2007 9:18 pm

x=0.000999999, then what is the smallest number that n can be in x*10^n>100 ??

the answer is 6..confused..

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Source: Beat The GMAT — Problem Solving | Sun Apr 22, 2007 9:18 pm

jayhawk2001: Community Manager; Posts: 789; Joined: Sun Jan 28, 2007 3:51 pmFollowed by: 1 member; Location: Silicon valley, California; Thanked: 30 times

Re: hard prep question

by jayhawk2001 » Sun Apr 22, 2007 9:40 pm

jamesk486 wrote:x=0.000999999, then what is the smallest number that n can be in x*10^n>100 ??

the answer is 6..confused..

For n=5, x*10^5 = 99.999 which is less than 100.

For n=6, we get 999.999 which is > 100.

Hence 6.

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Cybermusings: Legendary Member; Posts: 559; Joined: Tue Mar 27, 2007 1:29 amFollowed by: 2 members; Thanked: 5 times

by Cybermusings » Sun Apr 22, 2007 11:06 pm

x=.000999999
When is x*(10^n)>100
.000999999*(10^5)=99.9999 which is less than 100
Hence we have to multiply it by 10 one more time
So .000999999*(10^6)=999.999 which is greater than 100
Hence minimum value of n has to be 6

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