Pugalenthi wrote:61) how many integers are there between, but not including, integers r and s?
(1) s -r = 10
(2) there are 9 integers between, but not including r+1 and s+1.

The answer is D.
Here is my question- what is the hint in the question that leads to the integers between s and r are consecutive ?
For e.g., in stmt 1, there could be any number of integers between r and s and s - r could be 10 . What am I missing? Any help would be much appreciated.

Thanks

Hi Pugalenthi,

Let me try to help you.

The question does not have to say that the integers are consecutive because all the integers between r and s are consecutive.

For example:
How many integers are there between 1 and 10, without including either of them?

When the question wants the number of integers between 1 and 10, it wants all of them. We cannot leave out any.

2, 3, 4, 5, 6, 7, 8 and 9 are the integers between 1 and 10.
The question did not have to say that the integers are consecutive. It will be wrong to leave out 5, for example, because 5 is in between 1 and 10.

If the question wants you to choose only certain numbers, say 'even consecutive numbers', 'numbers that are multiples 3', then it will be mentioned clearly.

Let me know if it makes sense.

Makes sense...my follow up question is...how about this range of numbers... -20, -10,0, -10. In my example, s - r would be 10 but the numbers are not consecutive. What am I missing:)?

Pugalenthi wrote:Makes sense...my follow up question is...how about this range of numbers... -20, -10,0, -10. In my example, s - r would be 10 but the numbers are not consecutive. What am I missing:)?

'between' is the word, my friend.

Choose no matter what 'r' and 's' you may want, but then choose the integers that lie between them.

If you choose r = 10 and s = 0, the number of integers between them are {1,2,...,9}. 9 such integers.
If you choose r = 0 and s = -10, the number of integers between them are {-9,-8,...,-1}. 9 such integers.

The number of integers between r and s are 9 no matter what r and s you may choose.

Does this help?