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How many odd integers between 200 and 600 are there such

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aliky
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How many odd integers between 200 and 600 are there such [#permalink] New post   Updated on: 09 Sep 2012, 03:49
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How many odd integers between 200 and 600 are there such that their tens digit is even?

A. 20
B. 25
C. 100
D. 150
E. 200

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C

Originally posted by aliky on 18 Nov 2009, 12:57.
Last edited by Bunuel on 09 Sep 2012, 03:49, edited 1 time in total.
Renamed the topic and edited the question.
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Re: How many odd integers between 200 and 600 are there such [#permalink] New post   09 Sep 2012, 03:50
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How many odd integers between 200 and 600 are there such that their tens digit is even?

A. 20
B. 25
C. 100
D. 150
E. 200

The hundreds digit can take 4 values: 2, 3, 4 and 5;
The tens digit can take 5 values: 0, 2, 4, 6 and 8;
The units digit can take 5 values: 1, 3, 5, 7 and 9;

Total: 4*5*5=100.

Answer: C.
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sriharimurthy
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Re: How many odd integers between 200 and 600 are there such [#permalink] New post   18 Nov 2009, 13:06
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The definition of even and odd covers all integers such that :
(a) Any number which, when divided by 2, leaves a remainder 0 is EVEN.
(b) Any number which, when divided by 2, leaves a remainder 1 is ODD.

Thus 0, being an integer and satisfying condition (a), is an EVEN number.
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Re: How many odd integers between 200 and 600 are there such [#permalink] New post   08 Sep 2012, 23:36
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I guess the easier way to do this would be.

400 numbers between - 200 & 600
Out of which half would be even, half odd.
Number of odd = 200. Of this.. the one with even tenth digit would be half again. hence 100.
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Re: How many odd integers between 200 and 600 are there such [#permalink] New post   04 Jan 2013, 08:04
This has got nothing to do with the question, however according to the Sum formula aren't there 399 numbers between 200 and 600, i.e. 599-201 = 398 + 1 = 399????
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Re: How many odd integers between 200 and 600 are there such [#permalink] New post   04 Jan 2013, 08:09
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KevinBrink wrote:
This has got nothing to do with the question, however according to the Sum formula aren't there 399 numbers between 200 and 600, i.e. 599-201 = 398 + 1 = 399????


It depends whether we include 200 and 600.

There are 401 integers from 200 to 600, both inclusive;
There are 400 integers from 200 to 600, including 600 or 200.
There are 399 integers from 200 to 600, both exclusive.

Hope it's clear.
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Re: How many odd integers between 200 and 600 are there such [#permalink] New post   04 Jan 2013, 08:15
Yes thank you that is what I thought also, but then Asax is wrong? Isn't he or she?!
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Re: How many odd integers between 200 and 600 are there such [#permalink] New post   04 Jan 2013, 08:20
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KevinBrink wrote:
Yes thank you that is what I thought also, but then Asax is wrong? Isn't he or she?!


I guess asax meant that there are 400 integers from 201 to 600, both inclusive.
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Re: How many odd integers between 200 and 600 are there such [#permalink] New post   04 Jan 2013, 08:25
Ok thanks Bunuel for the clear explanation!
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Re: How many odd integers between 200 and 600 are there such [#permalink] New post   04 Jan 2013, 14:18
KevinBrink wrote:
Yes thank you that is what I thought also, but then Asax is wrong? Isn't he or she?!


even when you exclude 200 and 600 there will be 200 odd numbers and 100 out of which will have tenths digit as even
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Re: How many odd integers between 200 and 600 are there such [#permalink] New post   28 Jan 2021, 20:04
Total brain fart. Ever get those instances where your brain just stares blankly at the page and nothing is being processed? 6 minutes.

Pattern recognition is key here.

Tens digit is even means 0,2,4,6,8
3-digit integer must also be odd

201 202 203 204 205 206 207 208 209 <--- Only 5 of these satisfy the condition.
221 222 223... <--- Only 5 of these satisfy

For every X00 series where X is 2,3,4,5 there are a total of 25 digits that satisfy the condition

4 x 25 = 100

Answer is C.
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Re: How many odd integers between 200 and 600 are there such [#permalink] New post   26 Mar 2023, 05:21
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Re: How many odd integers between 200 and 600 are there such [#permalink]
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