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

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

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