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

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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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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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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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