Section - 8 Problem - 25

[camitava]

Guys need ur help ...

25. How many integers n are there such that
r < n < s?
(1) s – r = 5
(2) r and s are not integers.

[spoiler]OA is C. But why not A only?[/spoiler]

[mschling52]

I agree with C. If we are only given statement (1), we know that s-r = 5 and need to find out how many integers are between r and s. If we say r and s are 0 and 5, then there are 4 integers between them (1,2,3,4). However, if we let r and s be 0.25 and 5.25 then there are 5 integers between them (1,2,3,4,5). Therefore, just knowing the difference between r and s doesn't tell us how many integers lie between them. Specifically, we just know that if r and s are integers themselves, then we will have 4 integers between, but if r and s are not integers, then we will have 5.

[camitava]

mschling52, dnt mind! I am not clear about what u r saying. Can u pls explain this in detail? Now refer my approach -
As we know r - s = 5, so we are sure that there will be 4 integers in between them. Then why not A itself? Yop! I also agree with u that if r and s are not integer, there will be sure that there will be more integer values than the previous condition. But with A only, we can get the result. The Qs is not saying to find the condition where there will be possibility of getting max integer value between r and s. So request u to explain me this, pls!

[samirpandeyit62]

Hi Amitava, u just plot r-s =5 on a number line with both integer & decimal values of r & s u will get the answer

[mschling52]

The answer is not A because just knowing the information in statement 1 (that s-r = 5) is not enough to determine how many integers exist with r<n<s. There could be four OR five integers that satisfy this and we cannot know which is the correct answer.

For example, let r and s be 2 and 7. Then on the number line you can see there are 4 integers n with 2<n<7

-----------2---3---4---5---6---7----------

However, with only the information in Statement 1, r and s could also be 2.5 and 7.5. Plotting this on the number line gives us 5 ingeters with 2.5<n<7.5

------2---2.5---3---4---5---6---7---7.5-------