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Between 100 and 200, how many numbers are there in which one digit is

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Between 100 and 200, how many numbers are there in which one digit is  [#permalink]

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New post 25 Nov 2019, 01:16
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Between 100 and 200, how many numbers are there in which one digit is the average of the other two?

A. 11
B. 12
C. 10
D. 8
E. 9


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Between 100 and 200, how many numbers are there in which one digit is  [#permalink]

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New post Updated on: 25 Nov 2019, 03:39
took >2 mins to solve this one .. did it conventional way
possible values
111, 132,153,174,195,123,135,147,159,
IMO E; 9

Bunuel wrote:
Between 100 and 200, how many numbers are there in which one digit is the average of the other two?

A. 11
B. 12
C. 10
D. 8
E. 9


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Originally posted by Archit3110 on 25 Nov 2019, 03:20.
Last edited by Archit3110 on 25 Nov 2019, 03:39, edited 2 times in total.
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Between 100 and 200, how many numbers are there in which one digit is  [#permalink]

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New post Updated on: 25 Nov 2019, 13:08
1
3 digits are in arithmetic progression, and Hundreds digit is always 1.

1. when common difference is 0
three digits are 1,1 and 1 {111}

2. when common difference is 1
three digits are 1,2 and 3 or 0, 1 and 2 {102, 120, 123 or 132}

3. when common difference is 2
three digits are 1,3 and 5 {123 or 132}

4. when common difference is 3
three digits are 1,4 and 7 {147 or 174}

5. when common difference is 4
three digits are 1,5 and 9 {159 or 195}


Total possible numbers= 1+2*5=11



Bunuel wrote:
Between 100 and 200, how many numbers are there in which one digit is the average of the other two?

A. 11
B. 12
C. 10
D. 8
E. 9


Are You Up For the Challenge: 700 Level Questions

Originally posted by nick1816 on 25 Nov 2019, 03:36.
Last edited by nick1816 on 25 Nov 2019, 13:08, edited 2 times in total.
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Between 100 and 200, how many numbers are there in which one digit is  [#permalink]

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New post Updated on: 25 Nov 2019, 08:04
Bunuel wrote:
Between 100 and 200, how many numbers are there in which one digit is the average of the other two?

A. 11
B. 12
C. 10
D. 8
E. 9


Find digits in AP from 100 to 200:
{111}=1
{102},{120}=2
{123},{132}=2
{135},…=2
{147},…=2
{159},…=2

Total=1+2(5)=11

Ans (A)

Originally posted by exc4libur on 25 Nov 2019, 05:28.
Last edited by exc4libur on 25 Nov 2019, 08:04, edited 1 time in total.
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Re: Between 100 and 200, how many numbers are there in which one digit is  [#permalink]

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New post 25 Nov 2019, 08:00
2
102 also fits the criteria [1 = (0+2)/2]. Hence the answer should be 10.
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Re: Between 100 and 200, how many numbers are there in which one digit is  [#permalink]

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New post 25 Nov 2019, 10:25
nick1816

what do you mean by common difference?

could you pls explain in more details? I do not get how you derive the arithmetic progression

Thanks
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Between 100 and 200, how many numbers are there in which one digit is  [#permalink]

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New post 25 Nov 2019, 10:39
1
Camach700
You can write 3 terms of the arithmetic progression as - a, a+k and a+2k, where k is the common difference

Also, you can notice that middle term is the average of first and third term.

\(\frac{a+a+2k}{2}\)= \(\frac{2(a+k)}{2}\)=a+k




Camach700 wrote:
nick1816

what do you mean by common difference?

could you pls explain in more details? I do not get how you derive the arithmetic progression

Thanks
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Re: Between 100 and 200, how many numbers are there in which one digit is  [#permalink]

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New post 25 Nov 2019, 20:51
12.

110,102,120,111,123,132,135,153,149,174,159,195
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Re: Between 100 and 200, how many numbers are there in which one digit is  [#permalink]

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New post 26 Nov 2019, 00:58
dushyantmehra

110 does not fit the given constraints.

[1+0][/2] = 0.5 (average should equal 1) or [1+1][/2] = 1 (average should equal 0).
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Re: Between 100 and 200, how many numbers are there in which one digit is   [#permalink] 26 Nov 2019, 00:58
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