If -13 < 7a + 1 < 29 and 19 < 2 - b < 23, what is the maximum possible integer value of a + b?
A) -14
B) -13
c) -23
D) -12
E) -18
Answer is B) -13
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
can somebody please help with this problem
This topic has expert replies
-
amandeep.hora
- Senior | Next Rank: 100 Posts
- Posts: 31
- Joined: Sun Jul 12, 2009 10:11 am
- Thanked: 1 times
GMAT/MBA Expert
-
Anju@Gurome
- GMAT Instructor
- Posts: 511
- Joined: Wed Aug 11, 2010 9:47 am
- Location: Delhi, India
- Thanked: 344 times
- Followed by:86 members
-13 < 7a + 1 < 29 ---> -14 < 7a < 28 ---> -2 < a < 4amandeep.hora wrote:If -13 < 7a + 1 < 29 and 19 < 2 - b < 23, what is the maximum possible integer value of a + b?
19 < 2 - b < 23 ---> 17 < -b < 21 ---> -21 < b < -17
Hence, (a + b) < 4 + (-17) ---> (a + b) < -13
Maximum possible integral value of (a + b) is -14
Anju Agarwal
Quant Expert, Gurome
Backup Methods : General guide on plugging, estimation etc.
Wavy Curve Method : Solving complex inequalities in a matter of seconds.
§ GMAT with Gurome § Admissions with Gurome § Career Advising with Gurome §
Quant Expert, Gurome
Backup Methods : General guide on plugging, estimation etc.
Wavy Curve Method : Solving complex inequalities in a matter of seconds.
§ GMAT with Gurome § Admissions with Gurome § Career Advising with Gurome §
-
amandeep.hora
- Senior | Next Rank: 100 Posts
- Posts: 31
- Joined: Sun Jul 12, 2009 10:11 am
- Thanked: 1 times
thanks for taking the time to reply Anju !!
I still have a doubt though ,
I followed the below steps
-13 < 7a + 1 < 29 ---> -14 < 7a < 28 ---> -2 < a < 4
19 < 2 - b < 23 ---> 17 < -b < 21 ---> -21 < b < -17
then I chose -16 as the highest value that b can have and +3 highest integer value that a can have then their sum comes as -13 .
Still wondering what is wrong in my approach
really appreciate your help
Cheers,
Aman
I still have a doubt though ,
I followed the below steps
-13 < 7a + 1 < 29 ---> -14 < 7a < 28 ---> -2 < a < 4
19 < 2 - b < 23 ---> 17 < -b < 21 ---> -21 < b < -17
then I chose -16 as the highest value that b can have and +3 highest integer value that a can have then their sum comes as -13 .
Still wondering what is wrong in my approach
really appreciate your help
Cheers,
Aman
Regards
Aman
Aman
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
First, the question doesn't say that a and b are integers. It says that a+b is an integer.amandeep.hora wrote:thanks for taking the time to reply Anju !!
I still have a doubt though ,
I followed the below steps
-13 < 7a + 1 < 29 ---> -14 < 7a < 28 ---> -2 < a < 4
19 < 2 - b < 23 ---> 17 < -b < 21 ---> -21 < b < -17
then I chose -16 as the highest value that b can have and +3 highest integer value that a can have then their sum comes as -13 .
Still wondering what is wrong in my approach
really appreciate your help
Cheers,
Aman
Second, if -21 < b < -17, then b cannot equal -16
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
