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lcpanam: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Thu Jan 29, 2015 8:10 am

by lcpanam » Thu Jan 29, 2015 8:15 am

I am stuck and need help in solving.
A company wants to assign its employees ID numbers that have x digits each. The firm has 800 employees, what is the smallest number of digits the firm can use for each ID number. Repeats are allowed.

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Source: Beat The GMAT — Problem Solving | Thu Jan 29, 2015 8:15 am

DavidG@VeritasPrep: Legendary Member; Posts: 2663; Joined: Wed Jan 14, 2015 8:25 amFollowed by: 128 members; Location: Boston, MA; Thanked: 1153 times; GMAT Score:770

by DavidG@VeritasPrep » Thu Jan 29, 2015 8:23 am

Hi, Icpanam.

Just imagine that x = 1. Well, in that case, you could assign any digit between 0 and 9, so you'd have 10 options

If x = 2, the first digit could be anything between 0 and 9, and because repeats are allowed, the second digit, could also be anything between 0 and 9. Now we're up to 10*10 = 100 options.

If x = 3, any of the first 3 digits could be anything between 0 and 9, giving us 10*10*10 = 1000 options. That'll cover all the employees.

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by GMATinsight » Thu Jan 29, 2015 8:30 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Thu Jan 29, 2015 10:16 am

lcpanam wrote:I am stuck and need help in solving.
A company wants to assign its employees ID numbers that have x digits each. The firm has 800 employees, what is the smallest number of digits the firm can use for each ID number. Repeats are allowed.

You don't really need to apply any counting techniques here.

With 1 digit, you can assign values from 0 to 9 (10 possibilities)
With 2 digits, you can assign values from 00 to 99 (100 possibilities)
With 3 digits, you can assign values from 000 to 999 (1000 possibilities)

So, 3-digit ID numbers will accommodate the 800 employees.

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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