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shekhar.kataria: Master | Next Rank: 500 Posts; Posts: 268; Joined: Mon Mar 15, 2010 12:10 am; Thanked: 13 times

by shekhar.kataria » Wed Mar 28, 2012 4:50 am

A password contains at least 8 distinct digits. It takes 12 seconds to try one combination, what is the minimum amount of time required to guarantee access to the database?

[spoiler]Can the first digit of 8 digit password be zero....? Please solve the Question for me also.[/spoiler]

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Source: Beat The GMAT — Problem Solving | Wed Mar 28, 2012 4:50 am

sam2304: Legendary Member; Posts: 1239; Joined: Tue Apr 26, 2011 6:25 amFollowed by: 26 members; Thanked: 233 times; GMAT Score:680

by sam2304 » Wed Mar 28, 2012 5:37 am

Yes. It is a password and not a value.

Since the password can have 8 digits and we have total of 10 digits we have to calculate for every combination. So codes with 0-7 as digits = 10P8
codes with 0-8 as digits = 10P9
codes with 0-9 as digits = 10P10

(10P8 + 10P9 + 10P10)*12

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ronnie1985: Legendary Member; Posts: 626; Joined: Fri Dec 23, 2011 2:50 amFollowed by: 10 members; Location: Ahmedabad; Thanked: 31 times

by ronnie1985 » Wed Mar 28, 2012 7:42 am

At least 8 digits. Assuming that the password is of minimum digits only, the time required = 10P8*12
Similarly for 9 and 10 digits 10P9*12 and 10P10*12.

Since minimum assured time is asked I think the answer is 10P8*12 seconds.

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by [email protected] » Sat Mar 31, 2012 2:26 am

Yes Ronnie said is perfectly right... It shall be 10P8 X 12/60

This will give you the total time taken for the gurrantee of accessing the database.

Also this is a good question as to Can a password start from 0 or no.

I think if not then the question should explicitly state that. Because if it does not then the answers will be wrong..;

Also if the question does not state it explicitely then, the options would be better.

It would be simple to figure out between the options...

Hope this helps...

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Sun Apr 01, 2012 9:06 pm

shekhar.kataria wrote:A password contains at least 8 distinct digits. It takes 12 seconds to try one combination, what is the minimum amount of time required to guarantee access to the database?

[spoiler]Can the first digit of 8 digit password be zero....? Please solve the Question for me also.[/spoiler]

Total number of passwords possible = 10P8
12 seconds = 12/60 = 1/5 minute

Therefore, minimum amount of time required to guarantee access to the database = [spoiler]10P8 * 1/5[/spoiler] minute

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