ExplanationTake the task of creating 2-digit numbers and break it into

stages.

Stage 1: Select a digit for the TENS position.

We can choose any digit from 1, 2, 3, 4, 5, 6, 7, 8, or 9

So, we can complete stage 1 in

9 ways

[Aside: we cannot choose 0 for the tens position, because numbers like 03 and 07 are not considered 2-digit numbers]Stage 2: Select a digit for the UNITS position.

In most cases, the UNITS digit can be any of the following: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

HOWEVER, for this question, the units digit must be DIFFERENT from the tens digit we selected in stage 1

So, once select a digit in stage 1, we cannot re-use it in stage 2.

So, we can complete stage 2 in

9 ways

By the Fundamental Counting Principle (FCP), we can complete the 2 stages (and thus create a 2-digit number) in

(9)(9) ways (= 81 ways)

So, we have:

Quantity A: 81

Quantity B: 80

Answer: A

Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.

Cheers,

Brent

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Brent Hanneson – Creator of greenlighttestprep.com

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