Data Sufficiency

how many odd integers are greater than integer X and less than the integer y?

1. there are 12 even integers greater than x and less than y

2. there are 24 integers greater than X and less than Y

why is it b?? how can we know how many odd integers are in the 24 integers that is mentioned?? I thought it was c.

Im totally confused, is my train of thought off?

yvonne12 wrote:how many odd integers are greater than integer X and less than the integer y?

1. there are 12 even integers greater than x and less than y

2. there are 24 integers greater than X and less than Y

why is it b?? how can we know how many odd integers are in the 24 integers that is mentioned?? I thought it was c.

Im totally confused, is my train of thought off?

I guess this can be better explained using an example. Take 2 series

X=1, Y=26, the series is 1 2 ... 25 26
X=2, Y=27, the series is 2 3 ... 26 27

In each case, the total number of odd integers is the same.

X=1, Y=26, series : 1 2 ... 25 26
Odd integers are 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25

X=2, Y=27, series : 2 3 ... 26 27
Odd integers are 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25

Hence B

ok, but it does not say whether its consecutive numbers.

thats what throws me off. Please explain further

Look at it this way

B says there are 24 integers between X and Y
So supposing it starts with an even integer then it will end with an odd one
and if it starts with an odd one it will end with an even integer so there are always 12 odd and 12 even integers in abunch of 24 consecutive intyegers

Modifying the above question if it had said that between X and Y there are 25 integers then there would have been different combinations ie 12 odd and 13 even or the converse depending on whether X is even or ODD
So in the above question with statement A and our modified statement B together would have solved the problem

I hope it is clear

can someone explain why statement 1 is not sufficient?

Consider 2,3,4,5 ....... 27 (There are 12 even terms and 12 odd terms)

Consider 3,4,5,6.........27 (There are 12 even terms and 11 odd terms)

Insufficient

Pen it down and check it out.

crackgmat007 wrote:can someone explain why statement 1 is not sufficient?

I had to pen down the whole series and check it. Is there any other quicker way?

yvonne12 wrote:ok, but it does not say whether its consecutive numbers.

thats what throws me off. Please explain further

This is a good question. I dont think we can assume that the integers are consecutive in stmt 2. Can we?

crackgmat007 wrote:

yvonne12 wrote:ok, but it does not say whether its consecutive numbers.

thats what throws me off. Please explain further

This is a good question. I dont think we can assume that the integers are consecutive in stmt 2. Can we?

I dont think it matters whether it says they are consecutive or not.

If I asked you, "how many integers are between 2 and 10?" you could answer it, I do not need to specify how many consecutive integers are between 2 and 10 do I?

Good point!

I dont think it matters whether it says they are consecutive or not.

If I asked you, "how many integers are between 2 and 10?" you could answer it, I do not need to specify how many consecutive integers are between 2 and 10 do I?

So the question does imply that integers are unique, but it does not mention if they are consecutive. So when you are asked for numbers of integers (odd/even) between a range, you consider that a set of consecutive numbers....hmmmm....new information for me.

ashish2104 wrote:

I dont think it matters whether it says they are consecutive or not.

If I asked you, "how many integers are between 2 and 10?" you could answer it, I do not need to specify how many consecutive integers are between 2 and 10 do I?

So the question does imply that integers are unique, but it does not mention if they are consecutive. So when you are asked for numbers of integers (odd/even) between a range, you consider that a set of consecutive numbers....hmmmm....new information for me.

Hi Ashish,

Thinking that the integers are consecutive is thinking far away from required.
If you are asked how many integers are there between 2 and 10, all you need to do is to answer the question direct to the point.
3,4,5,6,7,8,9
The fact they are consecutive is just an additional property/advantage.
It is not because they are consecutive , you are counting them.

Hope this helps!!

Hi! why is it that nobody (and I mean on any forum) has considered X to be a negative integer? If that's the case then the option E would be the clear answer, wouldn't it?