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

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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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16 Mar 2014, 18:42
4
9
00:00

Difficulty:

95% (hard)

Question Stats:

49% (02:12) correct 51% (02:15) wrong based on 316 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
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Re: If -13 < 7a + 1 < 29 and 19 < 2 - b < 23, what is the  [#permalink]

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16 Mar 2014, 21:22
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

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

-23 < a + b < -13
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Director
Joined: 23 Jan 2013
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16 Mar 2014, 21:24
-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!
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Re: If -13 < 7a + 1 < 29 and 19 < 2 - b < 23, what is the  [#permalink]

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19 Feb 2015, 09:35
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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26 Sep 2015, 06:52
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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Re: If -13 < 7a+1 < 29 and 19 < 2 - b < 23 what is the maximum possible in  [#permalink]

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26 Sep 2015, 06:55
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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If -13 < 7a + 1 < 29 and 19 < 2 - b < 23, what is the  [#permalink]

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26 Sep 2015, 06:58
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.
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Re: If -13 < 7a + 1 < 29 and 19 < 2 - b < 23, what is the  [#permalink]

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26 Sep 2015, 07:04
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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Posts: 51285
If -13 < 7a + 1 < 29 and 19 < 2 - b < 23, what is the maximum possible  [#permalink]

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16 Oct 2016, 05:52
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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Joined: 28 Jun 2016
Posts: 207
Concentration: Operations, Entrepreneurship
Re: If -13 < 7a + 1 < 29 and 19 < 2 - b < 23, what is the maximum possible  [#permalink]

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16 Oct 2016, 06:46
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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Re: If -13 < 7a + 1 < 29 and 19 < 2 - b < 23, what is the maximum possible  [#permalink]

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16 Oct 2016, 07:59
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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25 Dec 2016, 23:19
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
Joined: 20 Apr 2017
Posts: 6

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05 Jul 2017, 05:38
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
Joined: 02 Sep 2009
Posts: 51285
Re: If -13 < 7a + 1 < 29 and 19 < 2 - b < 23, what is the  [#permalink]

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05 Jul 2017, 06:00
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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Posts: 6
Re: If -13 < 7a + 1 < 29 and 19 < 2 - b < 23, what is the  [#permalink]

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05 Jul 2017, 07:26
Thank you for pointing me to this post. I did search for it but nothing came up. I understand where I went wrong.
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Re: If -13 < 7a + 1 < 29 and 19 < 2 - b < 23, what is the  [#permalink]

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09 Jul 2017, 04:42
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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Re: If -13 < 7a + 1 < 29 and 19 < 2 - b < 23, what is the  [#permalink]

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09 Aug 2018, 07:43
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Re: If -13 < 7a + 1 < 29 and 19 < 2 - b < 23, what is the &nbs [#permalink] 09 Aug 2018, 07:43
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