BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

QR #49: How many integers n are there such that r<n<s

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 37
Joined: Tue Aug 16, 2011 12:41 pm

QR #49: How many integers n are there such that r<n<s

by saintforlife » Sun Nov 04, 2012 12:59 pm
How many integers n are there such that r < n < s?

(1) s - r = 5
(2) r and s are not integers

OA = C

I read the answer explanation in the Quant Review #2 book, but I don't understand something.

By combining both, if you say that the number of integers n=5 between r and s, doesn't the example they give in Statement 1 solution violate the inequality?

They say if r=6.5 and s=11.5, then n=5. Doesn't this violate r<n<s inequality because clearly n=5 < r=6.5?

I know it works for cases such as r=0.1 and s=5.1, then n=5. Here the inequality r<n<s holds, but for the above case, it doesn't.

Can somebody weigh-in? What am I missing?
Top
Source: — Data Sufficiency |
Legendary Member
Posts: 1084
Joined: Fri Apr 15, 2011 2:33 pm
Thanked: 158 times
Followed by:21 members

by pemdas » Sun Nov 04, 2012 5:36 pm
did you understand the logic behind this question?
why to ask about this gibberish by official explanation

if we knew about s and r (integers or not integers) our task would be simplified to st(1) Suff. Since we know nothing about s and r, there could be always four integers (case when s and r are integers) or five integers (when s or r is not integer)

st(2) helps with assigning type for our numbers (s and r), but we know nothing about values

combined st(1&2) supports our previously inquired data, i.e. s and r are not integers, hence the number of integers in the given interval will always be 5.

answer c)
Success doesn't come overnight!
Top
Senior | Next Rank: 100 Posts
Posts: 49
Joined: Thu Dec 01, 2011 2:59 am
Thanked: 4 times

by kullayappayenugula » Sun Nov 04, 2012 10:15 pm
hi...you got the question wrong. The n is not the number of integers but the integers themsleves.

How many integers n are there such that r < n < s?
Top

GMAT/MBA Expert

User avatar
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

by Brent@GMATPrepNow » Sun Nov 04, 2012 10:19 pm
saintforlife wrote:How many integers n are there such that r < n < s?
(1) s - r = 5
(2) r and s are not integers
Target question: How many integers n are there such that r < n < s? [/color]

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
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
User avatar
Newbie | Next Rank: 10 Posts
Posts: 1
Joined: Tue Mar 16, 2010 8:10 am

by vsri1987 » Sun Sep 22, 2013 1:47 am
Hi Brent,

s - r = 5

If s=3 and r=-2 then we will have 0 as well in the integer list(count will be 5), isn't it?
Also, it is nowhere mentioned that these are positive integers or do we just assume this in GMAT, please suggest?


Regards,
Vishal
Top

GMAT/MBA Expert

User avatar
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

by Brent@GMATPrepNow » Sun Sep 22, 2013 5:49 am
vsri1987 wrote:Hi Brent,

s - r = 5

If s=3 and r=-2 then we will have 0 as well in the integer list(count will be 5), isn't it?
Also, it is nowhere mentioned that these are positive integers or do we just assume this in GMAT, please suggest?


Regards,
Vishal
Good question.

If s=3 and r=-2, then -1, 0, 1, and 2 (4 values) are the only integers between r and s.

To answer your main question, there is nothing in the original question that tells us that r and s must be positive.
In fact there are MANY (an infinite number actually) different values for r and s (both positive and negative) that we can use to demonstrate that statement 1 is not sufficient.
I happened to use positive numbers to demonstrate this, but I could have also used negative numbers.
The bottom line is that, for statement 1, there will be either 4 or 5 integers that are between r and s.
As such, we cannot answer the target question with certainty.

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
User avatar
Legendary Member
Posts: 1556
Joined: Tue Aug 14, 2012 11:18 pm
Thanked: 448 times
Followed by:34 members
GMAT Score:650

by theCodeToGMAT » Sun Sep 22, 2013 6:41 am
s > n > r

1. s - r = 5
if r & s are integers .. then 4 integers.
(0.1) and (5.1) --> 5 integers..
INSUFFICIENT

2. r & s are not integers
INSUFFiCIENT since there is not relation..


Combining...

SUFFICIENT

ANSWER [spoiler][C][/spoiler]
R A H U L
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 8083
Joined: Sat Apr 25, 2015 10:56 am
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members

Re: QR #49: How many integers n are there such that r<n<s

by Scott@TargetTestPrep » Mon Jul 05, 2021 5:20 am
saintforlife wrote: ↑
Sun Nov 04, 2012 12:59 pm
 How many integers n are there such that r < n < s?

(1) s - r = 5
(2) r and s are not integers

OA = C

Solution:

Question Stem Analysis:

We need to determine the number of integers between r and s.

Statement One Alone:

Statement one alone is not sufficient. For example, if r = 1 and s = 6, then there are 4 integers between r and s, namely, 2, 3, 4, and 5. However, if r = 1.1 and s = 6.1, then there are 5 integers between r and s, namely 2, 3, 4, 5 and 6.

Statement Two Alone:

Statement two alone is not sufficient. For example, if r = 1.1 and s = 2.1, then there is 1 integer between r and s, namely, 2. However, if r = 1.1 and s = 3.1, then there are 2 integers between r and s, namely 2 and 3.

Statements One and Two Together:

Both statements together are sufficient since there will be 5 integers between r and s when they are not integers themselves as we can see from the analysis from Statement One Alone when r = 1.1 and s = 6.1. We can prove this as follows:

Let [r] be the greatest integer less than or equal to r. Since r is not an integer, [r] < r. Since s - r = 5, s = r + 5, so the integers between r and s (or r + 5) are [r] + 1, [r] + 2, [r] + 3, [r] + 4 and [r] + 5. Therefore, there are 5 integers.

Answer: C

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage
Top
Post new topic Post Reply
• Page 1 of 1