If -13 < 7a + 1 < 29 and 19 < 2 - b < 23, what is the

Solving for the ranges of a and b, we see that

-23 < a+b < -13.

However, notice that a and b do NOT have to be integers themselves. Since the max of a and b is strictly less than -13, it can never actually reach -13, and thus the maximum integer value is -14.

Answer: C.

Because the question does not state that a and b are integers it follows:

-2<a<4

-17>b>-21

We are looking for the maximum value of a+b, i.e. if a is 3.999999 and b is -16.999999, then the maximum integer value is -13.

Any doubts? I do not have official answer.

reto, it should be -14, C and NOT D.

-13<7a+1<29 ---> -14<7a<28---> -2<a<4 ...(1)

19<2-b<23 ---> 17<-b<21 ---> -21<b<-17 ...(2)

Thus from 1 and 2 , -23<a+b<-13 ---> the greatest INTEGER value is -14. C is the correct answer.

You cannot assume b =-16.99999999 as -17>b>-21, and -16.999999 is > -17.

Please use GMATLCUB search function to search for already posted questions. This question has already been discussed before.

Topics merged.

Thanks. Very careless error. I gotta be more careful.

If -13 < 7a + 1 < 29 and 19 < 2 - b < 23, what is the maximum possible integer value of a + b?

A. -23
B. -18
C. -14
D. -13
E. -12

Solving the question stem gives

-2 < a < 4

-21< b < -17

Add both equations

-23 < a+b < -13

Highest integer less than -13 in answer choices is -14.

C


Sent from my iPhone using GMAT Club Forum mobile app

-13 < 7a + 1 < 29 and 19 < 2 - b < 23

-14 < 7a < 28 and 17 < - b < 21

-2 < a < 4 and -17 > b > -21

Max(a+b ) <4+(-17)
Max(a+b ) <(-13)
Max(a+b ) = -14

Answer: Option C

Please note it is not mentioned that a and b are integers.
-14< 7a < 28 -> -2 < a < 4 implies a is between -2 & 4.
Max Value of a: 3.99
17< -b < 21 -> -17> b > -21 implies b is between -17 & -21.
Max Value of b: -17.01

a + b will give you -13. So the answer should be -13 and not -14.
Kindly let me know if there are any mistakes.

If \(-13<7a+1<29\) and \(19<2-b<23\), what is the maximum possible integer value of \(a+b\)?

A) -23
B) -18
C) -14
D) -13
E) -12

In the micro test my workings were:

\(-13 < 7a + 1 < 29\)
\(-14 < 7a < 28\)
\(-2 < a < 4\)

\(19 < 2 - b < 23\)
\(17 < -b < 21\)
\(-17 > b > -21\)

Therefore the maximum possible integer value of a+b = -18+3 = -15 (which isn't an answer choice, so I had to guess!)

I'm missing something out but can't see where I'm going wrong. Can someone shed some light on this please?

Thank you!

Merging topics. Please refer to the discussion above.

Thank you for pointing me to this post. I did search for it but nothing came up. I understand where I went wrong.

\(-13 < 7a + 1 < 29\)

\(-14<7a<28\)

\(-2<a<4\) ---------- (i)

\(19 < 2 - b < 23\)

\(17<-b<21\)

\(-17>b>-21\)

Or

\(-21<b<-17\) -------- (ii)

Adding (i) and (ii), we get;

\(-21-2<a+b<-17+4\)

\(-23<a+b<-13\)

Therefore the maximum possible integer value of \(a+b = -14\)

Answer (C)...

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Hi,
Can someone tell me why deducting the two inequalities gives the wrong answer?
-2<a<4
17<-b<21 <-after deducting 2
----------
-2-17<a-(-b)<4-21
-19<a+b<-17

When deducting 2 inequalities, we should subtract the extreme ends and not the same ends.

Therefore when doing a- (-b), we get -2 - 21 < a - (-b) < 4 - 17

-23 < a + b < -13


Hope this helps

Arun Kumar

First, let's solve the inequalities manually:

For a:
Given −13<7a+1<29,
we solve for a:
Subtracting 1 from all parts: −14<7a<28
Dividing by 7 : −2<a<4
a can take any value in the interval (−2,4), the max value of a, since it doesn't need to be an integer is something like 3.99999
For b:
Given 19<2−b<23,
we solve for b:
Subtracting 2 from all parts : 17<−b<21
Multiplying by −1(and flipping the inequalities): −21<b<−17
b can take any value in the interval (−21,-17),the max value of b, since it doesn't need to be an integer is something like -17.00000001
the maximum possible integer value of a + b= (a max) +(b max)
=(3.99999)+(-17.00000001)
=-13.00000001
Therefore, without the integers constraint, the maximum possible value of (a+b) can get infinitely close to −13 but cannot reach it and will always be slightly smaller.
Hence answer will be the next max available integer, -14.
We could also reach this conclusion by adding the 2 inequalities,(−2<a<4) and (−21<b<−17), giving us the combined range as
Add the left sides of the inequalities (−2)+(−21)=−23
Add the right sides of the inequalities :4+(−17)=−13
This gives us a combined inequality :−23<a+b<−13
Again the answer is clear as the max integer value possible for the sum is -14.­