n@resh wrote: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.


Above Question, why should we assume integers as consecutive there's nothing explicitly mentioned!
why can't be ans B?

the answer should be D.. i.e. we can answer this question using each statement alone.. I am in a hurry right now , so will post the solution in couple of hours time..

PS: there is no assumption here.. the question is crystal clear..

We have to find out the number of integers between two integer, but not including the integers themselves

In statement 1, we have s=10+r, let's say r=1, then s=11, the number of integers between 1 and 11 is 9 excluding 1 and 11 itself. No matter what integer you pick for r, the number of integers between r and s excluding will be fixed. Sufficient

In statement 2, we have to find the number of integers between r+1 and s+1. We are told that the number of integers between r+1 and s+1 is 9 excluding r+1 and s+1. Let's say r=1,r+1=2, so s+1 must be 9 integers away from r+1 in order to satisfy the condition.i,e, s+1=12 Sufficient

saketk wrote:

n@resh wrote: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.


Above Question, why should we assume integers as consecutive there's nothing explicitly mentioned!
why can't be ans B?

the answer should be D.. i.e. we can answer this question using each statement alone.. I am in a hurry right now , so will post the solution in couple of hours time..

PS: there is no assumption here.. the question is crystal clear..

well, you know what, i know ans can be D but the point is between 1 and 11 ...why you think only 9 integers i.e. 2,3,4,5,6,7,8,9 ?? that's because those integers must be consecutive which was an implicit deduction! what if, i assume those are not in consecutive!

'How many integers' itself means consecutive integers. For example, to calculate how many integers are there between 1 and 9, excluding both, we count all consecutive integers that is 2,3,4,5,6,7,8. The answer is 7
The formula for number of consecutive integers:

a) For FIRST TERM OR LAST TERM INCLUDED...(LAST TERM - FIRST TERM)
E.g: 1 to 9, answer = 1,2,3,4,5,6,7,8 (9-1)

b) Where BOTH FIRST TERM AND LAST TERM ARE INCLUDED...(LAST TERM - FIRST TERM + 1)
E.g: 1 to 9, answer = 1,2,3,4,5,6,7,8,9 (9-1+1)

c) Where NEITHER FIRST TERM NOR LAST TERM IS INCLUDED...(LAST TERM - FIRST TERM - 1)
E.g: 1 to 9, answer = 2,3,4,5,6,7,8 (9-1-1)

Your question relates to (c)
(1) s-r=10
s-r-1=10-1
s-r-1=9 (Required equation as per (c))
SUFFICIENT

(2) (s+1) - (r+1) - 1 = 9
s+1-r-1-1=9
s-r-1=9 (Required equation as per (c))
SUFFICIENT
On the other hand, the number of integers between r and s will be equal to number of integers between r+1 and s+1 (with the same inclusion/exclusion rule). For example, no. of integers between 31 and 35 both included is 5 and the no. of integers between 32 and 36 both included is again 5
SUFFICIENT

Answer is (D)

Integers with no adjectives like odd or even are consecutive integers