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How many numbers between 200 and 400 begin or end with 3?

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How many numbers between 200 and 400 begin or end with 3? [#permalink] New post 20 Mar 2013, 17:21
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Question Stats:

47% (01:43) correct 53% (00:45) wrong based on 183 sessions
How many numbers between 200 and 400 begin or end with 3?

A. 20
B. 60
C. 100
D. 110
E. 120
[Reveal] Spoiler: OA

Last edited by Bunuel on 21 Mar 2013, 02:23, edited 1 time in total.
Renamed the topic and edited the question.
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Re: how many numbers between 200 and 400 [#permalink] New post 20 Mar 2013, 17:35
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There will be 10 numbers from 200 to 299 that will end with 3 ( 203, 213, 223........ 293 ).
There will be 100 numbers from 300 to 400 that will begin with 3, we will not count the numbers that will end with because they will be repeated.
Total numbers = 10 + 100 = 110
Answer is D.

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Re: How many numbers between 200 and 400 begin or end with 3? [#permalink] New post 23 Mar 2013, 06:41
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"How many numbers between 200 and 400 begin or end with 3?"

Just think that those numbers are:

i) The ones ending in 3: 203, 213, 223, ... , 393 --> 20 numbers

ii) The ones beginning in 3: 300, 301, 302, 303, ... , 393, ... , 399 --> 100 numbers

BUT 10 out of the first 20 numbers are repeated in the second set.

THEREFORE, the solution is 110 numbers.

Answer: D
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Re: how many numbers between 200 and 400 [#permalink] New post 17 May 2013, 21:12
Abhii46 wrote:
There will be 10 numbers from 200 to 299 that will end with 3 ( 203, 213, 223........ 293 ).
There will be 100 numbers from 300 to 400 that will begin with 3, we will not count the numbers that will end with because they will be repeated.
Total numbers = 10 + 100 = 110
Answer is D.

Kindly give a kudo if you like my explanation.


I would have fallen into a trap on that one...I was thinking units and tens positions.
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Re: how many numbers between 200 and 400 [#permalink] New post 17 May 2013, 21:22
Expert's post
MzJavert wrote:
Abhii46 wrote:
There will be 10 numbers from 200 to 299 that will end with 3 ( 203, 213, 223........ 293 ).
There will be 100 numbers from 300 to 400 that will begin with 3, we will not count the numbers that will end with because they will be repeated.
Total numbers = 10 + 100 = 110
Answer is D.


I would have fallen into a trap on that one...I was thinking units and tens positions.


I agree, it's pretty easy to see that all the 300s will count, so the answer needs to be 100 or more, but then a lot of people will fall into the trap of picking 120 instead of 110. The 230s don't count (except for 233), but there could have easily been a question asking how many of these numbers contain at least one 3. Always important to reread the question before answering in order to avoid falling into some of the traps the exam has laid out for you.

Hope this helps!
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Re: How many numbers between 200 and 400 begin or end with 3? [#permalink] New post 04 Sep 2013, 06:47
The first number is 203, thereafter only possible case is numbers ending with 3. 3 repeats itself after every 10 digits
so between 200 and 299, periodicity of numbers ending with 3 is 10, so there are 10 such numbers 303,313......393

All numbers between 300-399, are starting with 3, so a total of 99-0+1 = 100 numbers.
So total numbers is 110.
Re: How many numbers between 200 and 400 begin or end with 3?   [#permalink] 04 Sep 2013, 06:47
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