Source: Official Guide for GMAT Review 2016 Problem Solving; #117

5

A three-digit code for certain locks uses

A three-digit code for certain locks uses the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 according to the following constraints. The first digit cannot be 0 or 1, the second digit must be 0 or 1, and the second and third digits cannot both be 0 in the same code. How many different codes are possible?

1 Explanation

1

Jeffrey Braganza

3 digit Code: X Y Z

If Y is 0:
X – cannot have 0 or 1, so we can have 2 to 9 inclusive, 8 possible numbers
Y – 0, so 1 possible no
Z – if Y is 0, Z cannot be 0, so Z can be 1 to 9 inclusive, 9 possible nos

OR

If Y is 1:
X – cannot have 0 or 1, so we can have 2 to 9 inclusive, 8 possible numbers
Y – 1, so 1 possible no
Z – if Y is 1, Z can be 0 to 9 inclusive, 10 possible nos

(8*1*9) + (8*1*10) = 72 + 80 = 152

Jan 17, 2016 • Comment

Cydney Seigerman, Magoosh Tutor

Great job! Thanks for posting your solution :)

Jan 19, 2016 • Reply

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Official Guide for GMAT Review 2016

Official Guide for the GMAT 2015 14th Ed.

Official Guide for the GMAT 13th Ed.

Official Guide for the GMAT 12th Ed.

Revised GRE PDF 2nd Ed.


Section 5.3 Problem Solving

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