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Number of two digit positive integers for which the unit

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GRE 1: Q167 V156
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Kudos [?]: 1615 [1] , given: 376

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Number of two digit positive integers for which the unit [#permalink] New post 13 Jun 2016, 17:34
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Question Stats:

57% (00:43) correct 42% (00:42) wrong based on 40 sessions
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.



Practice Questions
Question: 4
Page: 119
[Reveal] Spoiler: OA

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1 KUDOS received
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4711
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 91

Kudos [?]: 1615 [1] , given: 376

CAT Tests
Re: Number of two digit positive integers for which the unit [#permalink] New post 13 Jun 2016, 17:36
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Explanation

The two-digit positive integers are the integers from 10 to 99. There are 90 such integers. In 9 of these integers, namely, 11, 22, 33, …, 99, the units digit and tens digit are equal. Hence, Quantity A, the number of two-digit positive integers for which the units digit is not equal to the tens digit, is 90 – 9, or 81. Since Quantity B is 80, the correct answer is Choice A.
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Re: Number of two digit positive integers for which the unit [#permalink] New post 22 Mar 2018, 12:06
Expert's post
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
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Re: Number of two digit positive integers for which the unit   [#permalink] 22 Mar 2018, 12:06
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