If -13

Question

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

MacFauz · Accepted Answer

Really nice question and plays with a classic GMAT trap. We arrive at the final equation that a + b < -13. So the maximum integer values of a + b should be LESSER THAN -13 and that can only be -14. Answer is C.

-13 < 7a + 1 < 29

Subtracting 1 from the equation

-14 < 7a < 28

Dividing by 7

-2 < a < 4 ........... (1)

19 < 2 - b < 23

Multiplying by -1

-23 < b - 2 < -19

Adding 2 to the equation

-21 < b < -17 ........... (2)

Adding 1 and 2

-23 < a + b < -13

Temurkhon · Answer

-13<7a+1<29 -13-1<7a<29-1 -14<7a<28 -2b>-21, max=-17,9999 so -17,9999+3,9999=-14 or -17,1111+3,1111=-14 Problem does bot say A and B integers but say that A+B integer. Any difference in digitals of A and B can give more but does not give integer. Answer is C, but very tricky!

GSBae · Answer

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.

reto · Answer

Because the question does not state that a and b are integers it follows: -2b>-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.

ENGRTOMBA2018 · Answer

reto , it should be -14, C and NOT D. -13<7a+1<29 ---> -14<7a<28---> -2 17<-b<21 ---> -21 the greatest INTEGER value is -14. C is the correct answer.

ENGRTOMBA2018 · 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.

reto · Answer

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

acegmat123 · Answer

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

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GMATinsight · Answer

-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

dnalost · Answer

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.

tommh · Answer

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!

sashiim20 · Answer

-13 < 7a + 1 < 29 -14<7a<28 -2b>-21 Or -21

rencsee · Answer

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

CrackverbalGMAT · Answer

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

RohitHande · Answer

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.

bumpbot · Answer

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

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