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Intern  Joined: 16 Mar 2014
Posts: 3
If -13 < 7a + 1 < 29 and 19 < 2 - b < 23, what is the  [#permalink]

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Difficulty:   95% (hard)

Question Stats: 48% (02:14) correct 52% (02:13) wrong based on 287 sessions

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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
VP  Joined: 02 Jul 2012
Posts: 1105
Location: India
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Re: If -13 < 7a + 1 < 29 and 19 < 2 - b < 23, what is the  [#permalink]

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9
1
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
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Director  G
Joined: 23 Jan 2013
Posts: 525
Schools: Cambridge'16
Re: Min/Max Problem  [#permalink]

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-13<7a+1<29
-13-1<7a<29-1
-14<7a<28
-2<a<4, max=3,9999

19<2-b<23
19-2<-b<23-1
17<-b<21
-17>b>-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!
Current Student B
Joined: 23 May 2013
Posts: 183
Location: United States
Concentration: Technology, Healthcare
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Re: If -13 < 7a + 1 < 29 and 19 < 2 - b < 23, what is the  [#permalink]

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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.

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Re: If -13 < 7a+1 < 29 and 19 < 2 - b < 23 what is the maximum possible in  [#permalink]

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1
reto wrote:
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

Is it D?

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.
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Joined: 20 Mar 2014
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Re: If -13 < 7a+1 < 29 and 19 < 2 - b < 23 what is the maximum possible in  [#permalink]

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1
1
reto wrote:
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

Is it D?

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.
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Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
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If -13 < 7a + 1 < 29 and 19 < 2 - b < 23, what is the  [#permalink]

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reto wrote:
reto wrote:
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

Is it D?

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.

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.
Retired Moderator Joined: 29 Apr 2015
Posts: 822
Location: Switzerland
Concentration: Economics, Finance
Schools: LBS MIF '19
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Re: If -13 < 7a + 1 < 29 and 19 < 2 - b < 23, what is the  [#permalink]

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Engr2012 wrote:
reto wrote:
reto wrote:
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

Is it D?

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.

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.
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Math Expert V
Joined: 02 Sep 2009
Posts: 58445
If -13 < 7a + 1 < 29 and 19 < 2 - b < 23, what is the maximum possible  [#permalink]

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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
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Manager  B
Joined: 28 Jun 2016
Posts: 214
Concentration: Operations, Entrepreneurship
Re: If -13 < 7a + 1 < 29 and 19 < 2 - b < 23, what is the maximum possible  [#permalink]

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Solving the question stem gives

-2 < a < 4

-21< b < -17

-23 < a+b < -13

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

C

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CEO  D
Status: GMATINSIGHT Tutor
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Re: If -13 < 7a + 1 < 29 and 19 < 2 - b < 23, what is the maximum possible  [#permalink]

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Bunuel wrote:
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

-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

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Re: If -13 < 7a + 1 < 29 and 19 < 2 - b < 23, what is the  [#permalink]

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Bunuel wrote:
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

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.
Intern  B
Joined: 20 Apr 2017
Posts: 10
Location: United Kingdom
GMAT 1: 660 Q48 V32 GPA: 3.5
If -13<7a+1<29 and 19<2-b<23  [#permalink]

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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!
Math Expert V
Joined: 02 Sep 2009
Posts: 58445
Re: If -13 < 7a + 1 < 29 and 19 < 2 - b < 23, what is the  [#permalink]

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tommh wrote:
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.
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Intern  B
Joined: 20 Apr 2017
Posts: 10
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GMAT 1: 660 Q48 V32 GPA: 3.5
Re: If -13 < 7a + 1 < 29 and 19 < 2 - b < 23, what is the  [#permalink]

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Thank you for pointing me to this post. I did search for it but nothing came up. I understand where I went wrong. Director  V
Joined: 04 Dec 2015
Posts: 743
Location: India
Concentration: Technology, Strategy
WE: Information Technology (Consulting)
Re: If -13 < 7a + 1 < 29 and 19 < 2 - b < 23, what is the  [#permalink]

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derek123 wrote:
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

$$-13 < 7a + 1 < 29$$

$$-14<7a<28$$

$$-2<a<4$$ ---------- (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 $$a+b = -14$$

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

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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 If -13 < 7a + 1 < 29 and 19 < 2 - b < 23, what is the   [#permalink] 05 May 2019, 11:56
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