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why should we assume consecutive integers?

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by n@resh » Fri Sep 09, 2011 8:50 pm
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?
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Source: — Data Sufficiency |
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by saketk » Fri Sep 09, 2011 9:37 pm
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..
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by sl750 » Fri Sep 09, 2011 11:15 pm
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
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by n@resh » Sat Sep 10, 2011 8:36 am
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!
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by pavand » Sat Sep 10, 2011 11:45 am
'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
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by Scott@TargetTestPrep » Tue Oct 30, 2018 10:26 am
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.
We need to determine how many integers are between, but not including, r and s.

To find the number of integers between two integers (not including them), we subtract 1 from the difference of the two integers.

To illustrate, let's say the two integers r and s are 4 and 10, respectively; then, the number of integers between 4 and 10 (not including them) is 10 - 4 - 1 = 5. Sure enough, there are 5 integers between 4 and 10, namely 5, 6, 7, 8 and 9.

Thus, in this question we need to determine the value of s - r - 1.

Statement One Alone:

s - r = 10

Since s - r = 10, then s - r - 1 = 9. Thus, there are 9 integers between s and r. Statement one alone is sufficient to answer the question.
Statement Two Alone:

There are 9 integers between, but not including, r + 1 and s + 1.

Since we are given the number of integers that are between r + 1 and s + 1, we can create the following equation:

s + 1 - (r + 1) - 1 = 9

s + 1 - r - 1 - 1 = 9

s - r - 1 = 9

We again see that there are 9 integers between r and s. Statement two alone is also sufficient to answer the question.

Answer: D

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