BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

An integer is said to be “diverse� if no two of its digi

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Moderator
Posts: 2505
Joined: Sun Oct 15, 2017 1:50 pm
Followed by:6 members

An integer is said to be “diverse� if no two of its digi

by BTGmoderatorLU » Wed Sep 11, 2019 2:37 am

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Source: Official Guide

An integer is said to be "diverse" if no two of its digits are the same. For example, 327 is "diverse" but 404 is not. How many "diverse" two digit numbers are there ?

A. 70
B. 72
C. 81
D. 90
E. 91

The OA is C
Top
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Wed Sep 11, 2019 4:24 am
BTGmoderatorLU wrote:Source: Official Guide

An integer is said to be "diverse" if no two of its digits are the same. For example, 327 is "diverse" but 404 is not. How many "diverse" two digit numbers are there ?

A. 70
B. 72
C. 81
D. 90
E. 91

The OA is C
Take the task of creating diverse integers and break it into stages.

Stage 1: Select the tens digit
This digit can be 1, 2, 3, 4, 5, 6, 7, 8, or 9
So, we can complete stage 1 in 9 ways

Stage 2: Select the units digit
This digit can be any digit (from 0 to 9) OTHER than the digit we selected for the tens place
So we can complete this stage in 9 ways.

By the Fundamental Counting Principle (FCP), we can complete the 2 stages (and thus create a diverse integer) in (9)(9) ways (= 81 ways)

Answer: C
--------------------------

Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. For more information about the FCP, watch this free video: https://www.gmatprepnow.com/module/gmat- ... /video/775

You can also watch a demonstration of the FCP in action: https://www.gmatprepnow.com/module/gmat ... /video/776

Then you can try solving the following questions:

EASY
- https://www.beatthegmat.com/what-should- ... 67256.html
- https://www.beatthegmat.com/counting-pro ... 44302.html
- https://www.beatthegmat.com/picking-a-5- ... 73110.html
- https://www.beatthegmat.com/permutation- ... 57412.html
- https://www.beatthegmat.com/simple-one-t270061.html


MEDIUM
- https://www.beatthegmat.com/combinatoric ... 73194.html
- https://www.beatthegmat.com/arabian-hors ... 50703.html
- https://www.beatthegmat.com/sub-sets-pro ... 73337.html
- https://www.beatthegmat.com/combinatoric ... 73180.html
- https://www.beatthegmat.com/digits-numbers-t270127.html
- https://www.beatthegmat.com/doubt-on-sep ... 71047.html
- https://www.beatthegmat.com/combinatoric ... 67079.html


DIFFICULT
- https://www.beatthegmat.com/wonderful-p- ... 71001.html
- https://www.beatthegmat.com/permutation- ... 73915.html
- https://www.beatthegmat.com/permutation-t122873.html
- https://www.beatthegmat.com/no-two-ladie ... 75661.html
- https://www.beatthegmat.com/combinations-t123249.html


Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 8086
Joined: Sat Apr 25, 2015 10:56 am
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members

by Scott@TargetTestPrep » Thu Sep 12, 2019 6:17 pm
BTGmoderatorLU wrote:Source: Official Guide

An integer is said to be "diverse" if no two of its digits are the same. For example, 327 is "diverse" but 404 is not. How many "diverse" two digit numbers are there ?

A. 70
B. 72
C. 81
D. 90
E. 91

The OA is C
There are 90 two-digit numbers (from 10 to 99, inclusive). Of these integers, 9 of them (11, 22, ..., 99) are not "diverse." Therefore, there are 90 - 9 = 81 "diverse" two-digit numbers.

Answer: C

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage
Top
Post new topic Post Reply
• Page 1 of 1