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

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Manager
Joined: 04 Jan 2013
Posts: 68
How many numbers between 200 and 400 begin or end with 3?  [#permalink]

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Updated on: 21 Mar 2013, 03:23
2
3
00:00

Difficulty:

55% (hard)

Question Stats:

58% (01:14) correct 42% (01:14) wrong based on 290 sessions

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

A. 20
B. 60
C. 100
D. 110
E. 120

Originally posted by chiccufrazer1 on 20 Mar 2013, 18:21.
Last edited by Bunuel on 21 Mar 2013, 03:23, edited 1 time in total.
Renamed the topic and edited the question.
Manager
Joined: 12 Mar 2012
Posts: 78
Location: India
Concentration: Technology, Strategy
GMAT 1: 710 Q49 V36
GPA: 3.2
WE: Information Technology (Computer Software)
Re: how many numbers between 200 and 400  [#permalink]

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20 Mar 2013, 18:35
10
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

Kindly give a kudo if you like my explanation.
##### General Discussion
Manager
Joined: 24 Jan 2013
Posts: 64
Re: How many numbers between 200 and 400 begin or end with 3?  [#permalink]

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23 Mar 2013, 07:41
3
"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.

Manager
Joined: 22 Apr 2013
Posts: 78
Re: how many numbers between 200 and 400  [#permalink]

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17 May 2013, 22:12
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

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.
Veritas Prep GMAT Instructor
Joined: 11 Dec 2012
Posts: 312
Re: how many numbers between 200 and 400  [#permalink]

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17 May 2013, 22:22
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

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!
-Ron
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Manager
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Re: How many numbers between 200 and 400 begin or end with 3?  [#permalink]

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04 Sep 2013, 07:47
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.
Intern
Joined: 09 Jun 2017
Posts: 9
Re: How many numbers between 200 and 400 begin or end with 3?  [#permalink]

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07 Aug 2017, 09:41
Dear all, isn't the question asking for all the numbers that either begin OR end with 3? In this case, shouldn't we be subtracting the numbers which do both, begin AND end with 3? 10 (ten numbers between 200 and 299)+100 (numbers between 300 and 399)-10 (ten numbers between 300 and 399, which begin AND end with 3)?
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Re: How many numbers between 200 and 400 begin or end with 3?  [#permalink]

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17 Mar 2019, 06:40
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: How many numbers between 200 and 400 begin or end with 3?   [#permalink] 17 Mar 2019, 06:40
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