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?
why should we assume consecutive integers?
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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..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?
PS: there is no assumption here.. the question is crystal clear..
- sl750
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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
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
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!saketk wrote: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..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?
PS: there is no assumption here.. the question is crystal clear..
'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
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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We need to determine how many integers are between, but not including, r and s.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.
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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