adthedaddy wrote:How many integers 'n' are there such that r<n<s ?
(1) s-r=5
(2) r & s are not integers

In the OG Quant guide, the ans is given as C. In my opinion, the ans should be E.
Plz suggest.

combining both the statements

r & s are not integers
So let s = 6.5

s-r = 5 (from the first statement)
=> r = 6.5 - 5 = 1.5

set of integer n such that r<n<s = {2,3,4,5,6}
# of integers n = 5 , hence sufficient

the answer is C

Hi,
Plz explain how you calculated set of integer n={2,3,4,5,6}

The range of nos fulfilling the condition s-r=5 can be innumerable.

adthedaddy wrote:Hi,
Plz explain how you calculated set of integer n={2,3,4,5,6}

The range of nos fulfilling the condition s-r=5 can be innumerable.

Well s-r = 5 and r<n<s can have 2 situations.

Case a - where s and r are integers and therefore there will be 4 integers in between. Eg: 10-5 = 5 and satisfies 5<10 (r<s) and therefore the set will be 6,7,8,9

Case b - where s and r are non-integers and therefore there will be 5 integers in between. Eg: 10.5-5.5 = 5 and satisfies 5.5<10.5 (r<s) and therefore the set will be 6,7,8,9 and 10.

Through statement 1, you can have case a and b - Insufficient.
Through statement 2, just mentions that they are non-integers but does not mention any relationship.

Combining statement 1 and 2, you can confirm that there will be 5 integers. Therefore C.

Regards
Anup

Hi Anup,

You're getting the set as 6,7,8,9 while earlier another member solved it ans got it as {2,3,4,5,6}
Which one should be correct ?

In my opinion, there cannot be any fixed value for which you can get s-r=5 where r,s are non-integers
e.g. 10.1-5.1=5
10.2-5.2=5
10.3-5.3=5,... and so on... the count is unlimited.

How are you able to get a fixed range of nos viz. {6,7,8,9,10} or {2,3,4,5,6} ??

Hi,

I thought the question was how many integers there were and not the specific set of integers. So although the set varies, the number of integers in the sets remains the same.

Regards
Anup

anuprajan5 wrote:Hi,

I thought the question was how many integers there were and not the specific set of integers. So although the set varies, the number of integers in the sets remains the same.

Regards
Anup

Ok.. My query is the same - how can we find the 5 integers which you've quoted. I am asking thus because I am still not able to understand how the integer count is limited to 5.
Would be grateful if you can elaborate a bit.

adthedaddy wrote:How many integers 'n' are there such that r<n<s ?
(1) s-r=5
(2) r & s are not integers

In the OG Quant guide, the ans is given as C. In my opinion, the ans should be E.
Plz suggest.

Why does statement 2 require that r and s not be integers?
Because this condition likely affects STATEMENT 1.
Thus, when we evaluate statement 1, we must be sure to consider both INTEGER and NON-INTEGER values.

Statement 1: s = r+5.
Case 1: r and s are INTEGERS
If r=0, then s=5, yielding 4 possible values for n: 1, 2, 3, 4.
Case 2: r and s are NON-INTEGERS
If r=.5, then s=5.5, yielding 5 possible values for n: 1, 2, 3, 4, 5.
INSUFFICIENT.

Statement 2: r and s are not integers
Since r and s could be ANY non-integers such that r<s, INSUFFICIENT.

Statements 1 and 2 combined:
As we saw in case 2, if r and s are non-integer values such that s=r+5, there will be 5 integer values between them.
To illustrate:
If r=7.2, then s=12.2, yielding 5 possible values for n: 8, 9, 10, 11, 12.
If r=1003.1, then s=1008.1, yielding 5 possible values for n: 1004, 1005, 1006, 1007, 1008.
Since in each case there are 5 integers between r and s, SUFFICIENT.

The correct answer is C.

adthedaddy wrote:Hi Anup,

You're getting the set as 6,7,8,9 while earlier another member solved it ans got it as {2,3,4,5,6}
Which one should be correct ?

In my opinion, there cannot be any fixed value for which you can get s-r=5 where r,s are non-integers
e.g. 10.1-5.1=5
10.2-5.2=5
10.3-5.3=5,... and so on... the count is unlimited.

How are you able to get a fixed range of nos viz. {6,7,8,9,10} or {2,3,4,5,6} ??

Taking your examples, on the number line, the integers between 5.1 and 10.1 are 6,7,8,9 and 10.
Similar for 5.2 and 10.2 and so on.

If you had 2 integers for r and s, then the number of integers between them would only be 4. For example between 5 and 10, the integers would be 6,7,8 and 9.

Hence it was essential for statement 2 to tell us that r and s were non integers and for statement 1 to define the relationship between r and s.

Regards
Anup