How many 3-digit integers between 100 and 200 have a digit

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

Redeem

This topic has expert replies

Post new topic Post Reply

Previous Topic Next Topic

Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 am; Followed by:2 members

How many 3-digit integers between 100 and 200 have a digit

by Gmat_mission » Fri May 25, 2018 12:59 am

Timer

00:00

Your Answer

Global Stats

How many 3-digit integers between 100 and 200 have a digit that is the average (arithmetic mean) of the other 2 digits?

A. 1
B. 7
C. 9
D. 11
E. 19

[spoiler]OA=D[/spoiler].

Could someone tell me how to solve this PS question? I only found 9 numbers. <i class="em em-confused"></i>

Quote

Source: Beat The GMAT — Problem Solving | Fri May 25, 2018 12:59 am

Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pm; Thanked: 6 times; Followed by:5 members

by Vincen » Fri May 25, 2018 1:52 am

Hello Gmat_mission.

Since the numbers are between 100 and 200, then the hundreds digit is 1.

Since the options are small, let's list these numbers:

102; 120

111

132; 123

153; 135

174; 147

195; 159

Hence, there are 11 numbers that satisfy the condition.

Therefore, the correct answer is the option D.

Quote

GMAT/MBA Expert

Scott@TargetTestPrep: 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 » Tue May 29, 2018 8:36 am

Gmat_mission wrote:How many 3-digit integers between 100 and 200 have a digit that is the average (arithmetic mean) of the other 2 digits?

A. 1
B. 7
C. 9
D. 11
E. 19

Let's list them: 102, 111, 123, 135, 147, 159 (if the digits, from left to right, are in ascending order). However, we can see that, except for 111, each of the remaining numbers can have their tens and units digits switched. So we have five more numbers: 120,132, 153, 174, 195. Therefore, we have a total of 11 such numbers.

Answer: D

Scott Woodbury-Stewart
Founder and CEO
[email protected]