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.
OAD
Please explain statement 2
Many thanks in advance,
Kavin
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integers r and s
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GMATGuruNY
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Statement 1: s = r+10Needgmat 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.
Case 1: r=0 and s=10, with the result that there are 9 integers between r and s.
Case 2: r=1 and s=11, with the result that there are 9 integers between r and s.
Case 3: r=2 and s=12, with the result that there are 9 integers between r and s.
In every case, the number of integers between r and s is 9.
SUFFICIENT.
Statement 2: There are 9 integers between, but not including, r+1 and s+1
Case 1: r+1=0 and s+1=10, with the result that there are 9 integers between r+1 and s+1
Here, r=-1 and s=9, with the result that there are 9 integers between r and s.
Case 2: r+1=1 and s+1=11, with the result that there are 9 integers between r+1 and s+1
Here, r=0 and s=10, with the result that there are 9 integers between r and s.
Case 3: r+1=2 and s+1=12, with the result that there are 9 integers between r+1 and s+1
Here, r=1 and s=11, with the result that there are 9 integers between r and s.
In every case, the number of integers between r and s is 9.
SUFFICIENT.
The correct answer is D.
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Brent@GMATPrepNow
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Here's a related question from the Official Guide.
Statement 1: s - r = 5
There are two cases we need to consider.
Case a: s and r are integers.
For example, s=6 and r=1, in which case there are 4 integers between r and s (2, 3, 4 and 5)
Case b: s and r are not integers.
For example, s=6.1 and r=1.1, in which case there are 5 integers between r and s (2, 3, 4, 5, and 6)
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: r and s are not integers
This is definitely not enough information here to answer the target question.
Consider these 2 cases.
Case a: r=1.1 and s=2.1, in which case there is 1 integer between r and s (2)
Case a: r=1.1 and s=3.1, in which case there are 2 integers between r and s (2 and 3)
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined:
From statement 1, we know that there are either 4 or 5 integers between r and s, depending on whether or not r and s are integers.
Statement 2 rules out the possibility that r and s are integers.
If r and s are non integers, then there must be 5 integers between r and s
Since we can answer the target question with certainty, the combined statements are SUFFICIENT
Answer = C
Cheers,
Brent
Target question: How many integers n are there such that r < n < s? [/color]How many integers n are there such that r < n < s?
(1) s - r = 5
(2) r and s are not integers
Statement 1: s - r = 5
There are two cases we need to consider.
Case a: s and r are integers.
For example, s=6 and r=1, in which case there are 4 integers between r and s (2, 3, 4 and 5)
Case b: s and r are not integers.
For example, s=6.1 and r=1.1, in which case there are 5 integers between r and s (2, 3, 4, 5, and 6)
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: r and s are not integers
This is definitely not enough information here to answer the target question.
Consider these 2 cases.
Case a: r=1.1 and s=2.1, in which case there is 1 integer between r and s (2)
Case a: r=1.1 and s=3.1, in which case there are 2 integers between r and s (2 and 3)
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined:
From statement 1, we know that there are either 4 or 5 integers between r and s, depending on whether or not r and s are integers.
Statement 2 rules out the possibility that r and s are integers.
If r and s are non integers, then there must be 5 integers between r and s
Since we can answer the target question with certainty, the combined statements are SUFFICIENT
Answer = C
Cheers,
Brent
Last edited by Brent@GMATPrepNow on Fri Jul 22, 2016 5:20 am, edited 2 times in total.
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Matt@VeritasPrep
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The second question is craftier and strikes me as a little more likely to appear on the GMAT ... but just out of curiosity, how did it appear in this thread? I can't follow how we got from Q1 to Q2.
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Yes, it's an official GMAT question. It has so many similar qualities to the original question that I inadvertently posted the wrong response.Matt@VeritasPrep wrote:The second question is craftier and strikes me as a little more likely to appear on the GMAT ... but just out of curiosity, how did it appear in this thread? I can't follow how we got from Q1 to Q2.
Cheers,
Brent
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