Scott Woodbury-Stewart

GMAT OFFICIAL GUIDE PS – A three digit code for certain logs uses…

A three digit code for certain logs uses…

Solution:

We are given the following constraints for a 3-digit code:

The first number 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. Thus, we must create two different scenarios for our digits.

Scenario One (second digit is zero) 

1st digit: 8 values (since it can be any digit from 2 to 9, inclusive)

2nd digit: 0

3rd digit: 9 values (since it can’t be 0 again but it can be any digit from 1 to 9, inclusive)

Thus, in scenario one there are 8 x 1 x 9 = 72 ways to create the 3-digit code.

Scenario Two (second digit is 1) 

1st digit: 8 values (since it can be any digit from 2 to 9, inclusive)

2nd digit: 1

3rd digit: 10 values (since it can be any digit from 0 to 9, inclusive)

Thus in scenario two there are 8 x 1 x 10 = 80 ways to create the 3-digit code

Combining our scenarios there are 72 + 80 = 152 ways to create the 3-digit code.

Answer: B 

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