Number of odd integers

Ok, if I had this question on the exam I would have got it wrong. But now that i know the answer here is what I think -

I took a couple of different number sets and made the following observations -

1) If the total number of integers greater than X but less than y is even then you will have an equal number of even and odd integers. So if the total is 24 then no. of off integers will be 24/2

2) If the total number of integers greater than X but less than y is odd then you either the number of even integers will be more than y or vice versa.

Can some one confirm my observation? also how does one figure this out? is there a good book for number properties where this is given? Its too time intensive to find this on the test.

ri2007 wrote:Ok, if I had this question on the exam I would have got it wrong. But now that i know the answer here is what I think -

I took a couple of different number sets and made the following observations -

1) If the total number of integers greater than X but less than y is even then you will have an equal number of even and odd integers. So if the total is 24 then no. of off integers will be 24/2

2) If the total number of integers greater than X but less than y is odd then you either the number of even integers will be more than y or vice versa.

Can some one confirm my observation? also how does one figure this out? is there a good book for number properties where this is given? Its too time intensive to find this on the test.

hi ri2007,

I don't think what you have stated in case 2 needs to be true..
I can have x as some number and y as a bigger number such that between y and x all 24 numbers are odd or all numbers are even. How does it help to find the number of even or odd numbers.

According to (2) the 24 integers can be even as well as odd right gmatrant??

gmatrant

you say

I can have x as some number and y as a bigger number such that between y and x all 24 numbers are odd or all numbers are even. How does it help to find the number of even or odd numbers.

how is this even possible? every alternative number is going to be even and odd in a set of consequitive numbers. Note the language of the question, they do not say S is a set of numbers with x as the lowest and y as the highest or any thing. We are talking about consequitive integers between x and y. At least that the way I read it.

Your comments are always welcome

thanks

if x=7 then y=32 and k is the number of odd integers between 7 and 32 then k=12. if x=8 and y=33 then again k=12. thus in every case k=12, the answer is b

the first part of the question is insufficient because if x=7 and there are 12 even integers between x and y then y=31 and between 7 and 31 there are 12 odd integers but if x=8 and there are 12 even between x and y then y=34 but there are 13 odd integers between them.

IMO B does not require any analysis except that it is a group of 24 consecutive intgegres so it will have 12 odd & 12 even integers the starting pt (even int or odd integer) will not matter at all. the only case where the nos of odd <> even is when the totla nos of integers under examination is odd.