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

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

How many integers are there between, but not including,

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Moderator
Posts: 7187
Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members
by BTGmoderatorDC » Sat Oct 27, 2018 8:43 pm

Timer

00:00

Answers

A

B

C

D

E

Stats

Difficulty—

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.

OA D

Source: Official Guide
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Data Sufficiency |
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members
Location: New York, NY
Thanked: 13060 times
GMAT Score:790

by GMATGuruNY » Sun Oct 28, 2018 2:54 am
BTGmoderatorDC 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.
Statement 1:
Case 1: r=0 and s=10
Integers between r and s:
1, 2, 3, 4, 5, 6, 7, 8, 9 --> 9 integers

Case 2: r=1 and s=11
Integers between r and s:
2, 3, 4, 5, 6, 7, 8, 9, 10 --> 9 integers

Case 3: r=2 and s=12
Integers between r and s:
3, 4, 5, 6, 7, 8, 9, 10, 11 --> 9 integers

In every case, the number of integers between r and s = 9.
SUFFICIENT.

Statement 2:
On the number line:
...r...r+1...8 integers...s...s+1
Here, the 9 integers in color lie between r+1 and s+1.
As the number line illustrates, between r and s there are a total of 9 integers:
r+1 and the 8 integers in blue.
SUFFICIENT.

The correct answer is D.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Legendary Member
Posts: 2214
Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

by deloitte247 » Sun Oct 28, 2018 9:12 am
Number of integers between two numbers r and s without including r and s can be stated as
$$\left(s-r\right)+\left(1-2\right)=s-r-1$$
Find the value of $$s-r-1$$
$$statement\ 1=\ s-r=10$$
$$from\ s-r-1$$ we have 10-1=9 integers between r and s not including r and s, hence statement 1 is INSUFFICIENT

Statement 2
There are integers between but nut including $$\ r+1\ and\ s+1$$
$$\left(s+1\right)-\left(r+1\right)-1=9$$
$$s+1-r-1-1=9$$
$$s-r-1=9$$
$$hence\ statement\ 2\ is\ INSUFFICIENT$$
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 1449
Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members
Thanked: 59 times

by fskilnik@GMATH » Sun Oct 28, 2018 12:58 pm
BTGmoderatorDC 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.

Source: Official Guide
$$?\,\, = \,\,s - r - 1\,\,\,\,\left( {{\rm{the\,\, fingers}}\,\,{\rm{counting}}\,\,{\rm{technique}}} \right)$$
$$\left( 1 \right)\,\,s - r = 10\,\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 9\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}.\,\,\,\,\,$$
$$\left( 2 \right)\,\,\left( {s + 1} \right) - \left( {r + 1} \right) - 1 = 9\,\,\,\left( {{\rm{same}}\,\,{\rm{technique}}} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 9\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}.\,\,\,\,$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members
Location: Vancouver, BC
Thanked: 5254 times
GMAT Score:770

Re: How many integers are there between, but not including,

by Brent@GMATPrepNow » Mon Feb 10, 2020 7:59 am
BTGmoderatorDC wrote: ↑
Sat Oct 27, 2018 8:43 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.

OA D

Source: Official Guide
Target question: How many integers are there between, but not including, integers r and s ?

Statement 1: s - r = 10
First of all, this tells us that s is greater than r
So, on the number line, we have: ------r------------s----

Also notice that, if we take the given equation and add r to both sides, we get s = r+10
So, we can replace s with r+10 to get: ------r------------(r+10)----

Since r is an integer, we know that r+1 is an integer, and r+2 is an integer, and r+3 is an integer, etc.
If we add all of these values to our number line we get: ------r--(r+1)--(r+2)--(r+3)--(r+4)--(r+5)--(r+6)--(r+7)--(r+8)--(r+9)--(r+10)----
We can see that there are 9 integers between r and s
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: There are 9 integers between, but not including, r + 1 and s + 1.
The key here is to recognize that the number of integers between r + 1 and s + 1 IS THE SAME AS the number of integers between r and s

For example, we know that there are three integers between 5 and 9 (the integers are 6, 7 and 8)
If we add one to 5 and 9, we get 6 and 10
Notice that there are also three integers between 6 and 10 (the integers are 7, 8 and 9)

So, if there are 9 integers between r + 1 and s + 1, then we can also conclude that there are 9 integers between r and s
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1