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can somebody please help with this problem

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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by Anju@Gurome » Sun Apr 07, 2013 9:59 am
amandeep.hora wrote:If -13 < 7a + 1 < 29 and 19 < 2 - b < 23, what is the maximum possible integer value of a + b?
-13 < 7a + 1 < 29 ---> -14 < 7a < 28 ---> -2 < a < 4
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
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by amandeep.hora » Sun Apr 07, 2013 1:37 pm
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
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by Brent@GMATPrepNow » Mon Apr 08, 2013 5:13 am
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
First, the question doesn't say that a and b are integers. It says that a+b is an integer.
Second, if -21 < b < -17, then b cannot equal -16

Cheers,
Brent
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