How many 3- digit numbers between 100 and 200 have a digit : PS Archive
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# How many 3- digit numbers between 100 and 200 have a digit

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How many 3- digit numbers between 100 and 200 have a digit [#permalink]

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11 Nov 2004, 07:54
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How many 3- digit numbers between 100 and 200 have a digit that is the average of the other 2 digits?

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

Does anyone know of a fast method to solve a problem like this?
Thanks.
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11 Nov 2004, 10:58
"C" it is.

the range is 101 - 199. so one digit out of three must be 1. the second can not be EVEN number bcoz any even + 1 = ODD and any ODD number can not have integer avg.
only possible - 1,3,5,7
by Considering
111,
132 and 123 - 231 / 321 are not possible....

IMHO, such kind of questions demands Hands on experience.

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11 Nov 2004, 12:34
Dharmin wrote:
"C" it is.

the range is 101 - 199. so one digit out of three must be 1. the second can not be EVEN number bcoz any even + 1 = ODD and any ODD number can not have integer avg.
only possible - 1,3,5,7
by Considering
111,
132 and 123 - 231 / 321 are not possible....

Not sure I understand you, Dharmin. Why can't 123 be right?
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11 Nov 2004, 12:38
I will go for D) 11

Dharmin you missed 102 and 120.
Assuming 1ab is the number, one of the possibilities is

(a+b)/ 2 = 1; This is possible if a = b =1 or if a=0 and b=2 or if a=2 and b=0
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11 Nov 2004, 13:16
gayathri wrote:
I will go for D) 11

Dharmin you missed 102 and 120.
Assuming 1ab is the number, one of the possibilities is

(a+b)/ 2 = 1; This is possible if a = b =1 or if a=0 and b=2 or if a=2 and b=0

i accord you gaytri, i missed 102 and 120

to ninomoi,
actually i need to break sentences into two lines
111
132, 123
however, 321 / 231 are not possible.
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11 Nov 2004, 15:41
Agree with you guys. Answer is D

Just for those who need the exact 11 numbers :

102/120
111
123/132
135/153
147/174
159/195
11 Nov 2004, 15:41
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