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

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

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

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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>

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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 pmFollowed by: 5 members; Thanked: 6 times

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.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8136; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

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

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Founder and CEO
[email protected]

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