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

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Intern
Joined: 14 Oct 2004
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How many 3- digit numbers between 100 and 200 have a digit [#permalink]  11 Nov 2004, 07:54
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Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
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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Victory always starts in the head. It's a state of mind

Senior Manager
Joined: 06 Dec 2003
Posts: 366
Location: India
Followers: 1

Kudos [?]: 4 [0], given: 0

"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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Perseverance, Hard Work and self confidence

Manager
Joined: 09 Sep 2004
Posts: 166
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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?
Director
Joined: 07 Nov 2004
Posts: 694
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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
Senior Manager
Joined: 06 Dec 2003
Posts: 366
Location: India
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Kudos [?]: 4 [0], given: 0

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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Perseverance, Hard Work and self confidence

Director
Joined: 31 Aug 2004
Posts: 606
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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
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# How many 3- digit numbers between 100 and 200 have a digit

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