How many three-digit passwords are possible on a home

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BTGmoderatorLU: Moderator; Posts: 2544; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

by BTGmoderatorLU » Sat Mar 31, 2018 2:27 pm

How many three-digit passwords are possible on a home security system keypad that consists of all the digits?

A. 10^3
B. 900
C. 26^3
D. 26*25*25
E. 10*9*8

The OA is A.

The question says it has to be a three-digit number, so should not the first digit just have 9 option than 10?

Likewise, I got 9*10*10 = 900 as the answer.

Can anyone please explain where did I go wrong? Thanks in advance.

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Source: Beat The GMAT — Problem Solving | Sat Mar 31, 2018 2:27 pm

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ErikaPrepScholar: Legendary Member; Posts: 503; Joined: Thu Jul 20, 2017 9:03 amFollowed by: 15 members; Thanked: 86 times; GMAT Score:770

by ErikaPrepScholar » Sat Mar 31, 2018 3:05 pm

Three-digit passwords can begin with 0. So options like 011, 076, 002, and 000 are all valid passwords. This gives 10 options for each digit, or 10*10*10=10^3 possibilities in total.

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Sat Jul 14, 2018 9:57 am

BTGmoderatorLU wrote:How many three-digit passwords are possible on a home security system keypad that consists of all the digits?

A. 10^3
B. 900
C. 26^3
D. 26*25*25
E. 10*9*8

There are ten 1-digit numbers, including 0. Thus, the number of possible 3-digit passwords is 10 x 10 x 10 = 10^3.

Answer: A

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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