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
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
How many integers are there between, but not including,
This topic has expert replies
-
BTGmoderatorDC
- Moderator
- Posts: 7187
- Joined: Thu Sep 07, 2017 4:43 pm
- Followed by:23 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
-
GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
Statement 1: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.
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
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
-
deloitte247
- Legendary Member
- Posts: 2214
- Joined: Fri Mar 02, 2018 2:22 pm
- Followed by:5 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
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 $$\ r+1\ and\ s+1$$
$$\left(s+1\right)-\left(r+1\right)-1=9$$
$$s+1-r-1-1=9$$
$$s-r-1=9$$
$$hence\ statement\ 2\ is\ INSUFFICIENT$$
$$\left(s-r\right)+\left(1-2\right)=s-r-1$$
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 $$\ r+1\ and\ s+1$$
$$\left(s+1\right)-\left(r+1\right)-1=9$$
$$s+1-r-1-1=9$$
$$s-r-1=9$$
$$hence\ statement\ 2\ is\ INSUFFICIENT$$
-
fskilnik@GMATH
- GMAT Instructor
- Posts: 1449
- Joined: Sat Oct 09, 2010 2:16 pm
- Thanked: 59 times
- Followed by:33 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
$$?\,\, = \,\,s - r - 1\,\,\,\,\left( {{\rm{the\,\, fingers}}\,\,{\rm{counting}}\,\,{\rm{technique}}} \right)$$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
$$\left( 1 \right)\,\,s - r = 10\,\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 9\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}.\,\,\,\,\,$$
$$\left( 2 \right)\,\,\left( {s + 1} \right) - \left( {r + 1} \right) - 1 = 9\,\,\,\left( {{\rm{same}}\,\,{\rm{technique}}} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 9\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}.\,\,\,\,$$
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
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
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 are there between, but not including, integers r and s ?BTGmoderatorDC wrote: ↑Sat Oct 27, 2018 8:43 pmHow 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
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
