sandy wrote:
Quantity A |
Quantity B |
Number of two digit positive integers for which the unit digit is not equal to the tens digit |
80 |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Take 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
_________________
Brent Hanneson – Creator of greenlighttestprep.com
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