How many integers n are there such that r < n < s ?
1) s - r = 5
2) r and s are not integers
How many integers between r and s?
This topic has expert replies
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
Target question: How many integers n are there such that r < n < s?GmatGreen wrote: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 b: 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
- Patrick_GMATFix
- GMAT Instructor
- Posts: 1052
- Joined: Fri May 21, 2010 1:30 am
- Thanked: 335 times
- Followed by:98 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
IN evaluating statement (1), be careful not to assume that r and s are integers. You'll get different answers for (s,r)=(5,0) and (s,r)=(5.5, 0.5). There are 4 integers between 0 and 5, but 5 integers between 0.5 and 5.5 so we cannot definitively answer the question from (1) alone. We have to merge the statements.
The answer is C. I go through the question in detail in the full solution below (taken from the GMATFix App).
-Patrick
The answer is C. I go through the question in detail in the full solution below (taken from the GMATFix App).
-Patrick
- Check out my site: GMATFix.com
- To prep my students I use this tool >> (screenshots, video)
- Ask me about tutoring.
- Bill@VeritasPrep
- GMAT Instructor
- Posts: 1248
- Joined: Thu Mar 29, 2012 2:57 pm
- Location: Everywhere
- Thanked: 503 times
- Followed by:192 members
- GMAT Score:780
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
Yep, it's a perfect example of how sometimes a statement will provide us a clue about the other one. It's very easy to plug in for R and S and assume that S1 works on its own, but when S2 is something that doesn't seem to help, we have to stop and consider why they would bother providing it. Why is it important that S and R are not integers? From there, it's easier to find the bad assumption in S1.Patrick_GMATFix wrote:IN evaluating statement (1), be careful not to assume that r and s are integers. You'll get different answers for (s,r)=(5,0) and (s,r)=(5.5, 0.5). There are 4 integers between 0 and 5, but 5 integers between 0.5 and 5.5 so we cannot definitively answer the question from (1) alone. We have to merge the statements.
The answer is C. I go through the question in detail in the full solution below (taken from the GMATFix App).
-Patrick
Join Veritas Prep's 2010 Instructor of the Year, Matt Douglas for GMATT Mondays
Visit the Veritas Prep Blog
Try the FREE Veritas Prep Practice Test
Visit the Veritas Prep Blog
Try the FREE Veritas Prep Practice Test
GMAT/MBA Expert
- [email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
Hi GmatGreen,
As everyone else has already mentioned, thinking about how the answer changes when dealing with integers vs. non-integers is necessary on this question.
Going forward with DS questions, here are some things to note:
1) You won't have to consider decimals and fractions all that often (that level of depth is only required on a handful of DS questions)
2) Look for any "clues" (such as how Fact 2 was written) and "limitations" (the phrase X > 0 means that X cannot be 0 or negative, so what's left? - positive integers and positive fractions) appear in the question to guide you.
GMAT assassins aren't born, they're made,
Rich
As everyone else has already mentioned, thinking about how the answer changes when dealing with integers vs. non-integers is necessary on this question.
Going forward with DS questions, here are some things to note:
1) You won't have to consider decimals and fractions all that often (that level of depth is only required on a handful of DS questions)
2) Look for any "clues" (such as how Fact 2 was written) and "limitations" (the phrase X > 0 means that X cannot be 0 or negative, so what's left? - positive integers and positive fractions) appear in the question to guide you.
GMAT assassins aren't born, they're made,
Rich