GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 Oct 2019, 03:20

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# If 5a – 3b = –9 and 3a + b = 31, then a + b =

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58450
If 5a – 3b = –9 and 3a + b = 31, then a + b =  [#permalink]

### Show Tags

03 Jun 2018, 11:53
00:00

Difficulty:

(N/A)

Question Stats:

88% (01:52) correct 12% (02:29) wrong based on 49 sessions

### HideShow timer Statistics

If 5a – 3b = –9 and 3a + b = 31, then a + b =

A) –7

B) –3

C) 6

D) 13

E) 19

_________________
VP
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1013
WE: Supply Chain Management (Energy and Utilities)
Re: If 5a – 3b = –9 and 3a + b = 31, then a + b =  [#permalink]

### Show Tags

03 Jun 2018, 12:48
1
Bunuel wrote:
If 5a – 3b = –9 and 3a + b = 31, then a + b =

A) –7

B) –3

C) 6

D) 13

E) 19

Elimination method:-
Multiply equation (1) with 3 and equation (2) with 5, then subtracting (2) from (1), we have
3*(5a – 3b = –9) --------(1)
5*(3a + b = 31) --------(2)
(-) (-) (-)
.......................................................
-14b = -182
or, b=$$\frac{-182}{-14}$$=13

from (2) we have, 3a=31-b
or, a=$$\frac{(31-b)}{3}$$
Now substituting the value of b, we have
a=$$\frac{(31-13)}{3}$$=$$\frac{18}{3}$$=6

So, we have a+b=6+13=19.

Hence, Option (E) is the answer.
_________________
Regards,

PKN

Rise above the storm, you will find the sunshine
Senior SC Moderator
Joined: 22 May 2016
Posts: 3558
If 5a – 3b = –9 and 3a + b = 31, then a + b =  [#permalink]

### Show Tags

03 Jun 2018, 20:01
Bunuel wrote:
If 5a – 3b = –9 and 3a + b = 31, then a + b =

A) –7

B) –3

C) 6

D) 13

E) 19

Given:
5a – 3b = –9 ...(P)
3a + b = 31 ....(Q)

Multiply (Q) by 3 to get (R), then add (P) and (R)

5a – 3b = –9 ...(P)
9a + 3b = 93 ...(R)
-------------------
14a = 84
a = 6

Find b

From (Q): 3a + b = 31

(3)(6) + b = 31
b = (31-18) = 13

(a + b) = (6 + 13) = 19

_________________
SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here.

Instructions for living a life. Pay attention. Be astonished. Tell about it. -- Mary Oliver
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3333
Location: India
GPA: 3.12
Re: If 5a – 3b = –9 and 3a + b = 31, then a + b =  [#permalink]

### Show Tags

04 Jun 2018, 00:26
Bunuel wrote:
If 5a – 3b = –9 and 3a + b = 31, then a + b =

A) –7

B) –3

C) 6

D) 13

E) 19

Given: 5a – 3b = –9 and 3a + b = 31

Rearranging the second equation we get b = 31 - 3a

Substituting this value of b in the first equation.
5a - 3(31 - 3a) = -9 -> 14a - 93 = -9 -> 14a = 84 -> a = 6 | b = 31 - 18 = 13

Therefore, a+b = 6+13 = 19(Option E)
_________________
You've got what it takes, but it will take everything you've got
NUS School Moderator
Joined: 18 Jul 2018
Posts: 1020
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
If 5a − 3b = −9 and 3a + b = 31, then a + b =  [#permalink]

### Show Tags

Updated on: 28 Feb 2019, 11:07
5a-3b = -9.............(1)
3a+b = 31.............(2)

Multiply (1) by 3 and (2) by 5, then

15a-9b = -27
15a+5b = 155
subtract (1) from (2); 14b = 182, b = 13,
a = 6
a+b = 19
_________________
Press +1 Kudos If my post helps!

Originally posted by Chethan92 on 28 Feb 2019, 10:55.
Last edited by Chethan92 on 28 Feb 2019, 11:07, edited 1 time in total.
Math Expert
Joined: 02 Sep 2009
Posts: 58450
Re: If 5a − 3b = −9 and 3a + b = 31, then a + b =  [#permalink]

### Show Tags

28 Feb 2019, 11:03
Afc0892 wrote:
5a-3b = -9.............(1)
3a+b = 31.............(2)

Multiply (1) by 3 and (2) by 5, then

15a-9b = -27
15a+5b = 155
add both, -4b = 128, b = -32,
a = 21
a+b = -11

Bunuel sir, can you check the options?

If you add you'd get 30a -4b = 128. You should subtract.
_________________
NUS School Moderator
Joined: 18 Jul 2018
Posts: 1020
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
Re: If 5a − 3b = −9 and 3a + b = 31, then a + b =  [#permalink]

### Show Tags

28 Feb 2019, 11:05
Bunuel wrote:
Afc0892 wrote:
5a-3b = -9.............(1)
3a+b = 31.............(2)

Multiply (1) by 3 and (2) by 5, then

15a-9b = -27
15a+5b = 155
add both, -4b = 128, b = -32,
a = 21
a+b = -11

Bunuel sir, can you check the options?

If you add you'd get 30a -4b = 128. You should subtract.

oh yes. silly mistake
_________________
Press +1 Kudos If my post helps!
VP
Joined: 31 Oct 2013
Posts: 1465
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Re: If 5a − 3b = −9 and 3a + b = 31, then a + b =  [#permalink]

### Show Tags

28 Feb 2019, 11:51
Bunuel wrote:
If 5a − 3b = −9 and 3a + b = 31, then a + b =

A. −7
B. −3
C. 6
D. 13
E. 19

Given,

3a + b = 31

b = 31 - 3a.

again

5a - 3b = -9

5a - 3(31 - 3a) = -9

5a - 93 + 9a = -9

14a = 84.

a = 6.

we know,

3a + b = 31

3*6 + b = 31

18 + b = 31

b = 31 - 18

b = 13.

Now we have ,

a = 6

b = 13.

a + b = 6 +13 = 19.

Intern
Joined: 02 Jan 2019
Posts: 2
Re: If 5a − 3b = −9 and 3a + b = 31, then a + b =  [#permalink]

### Show Tags

28 Feb 2019, 12:19
Is there a shorter solution?
My solution:
5a - 3b + 3a + b = 31 - 9
8a - 2b = 22
4a - b = 11 => b = 4a - 11

2) find a and b by plugging b into any of them
5a - 12a + 33 = - 9
7a = 42
a = 6 => b = 31-18 = 13

Answer: a+b = 13+6 = 19. Choice E
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5020
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: If 5a − 3b = −9 and 3a + b = 31, then a + b =  [#permalink]

### Show Tags

01 Mar 2019, 04:01
Bunuel wrote:
If 5a − 3b = −9 and 3a + b = 31, then a + b =

A. −7
B. −3
C. 6
D. 13
E. 19

solve for two given eqns

5a − 3b = −9 and 3a + b = 31
we get a = 6
and b = 13
a+b=19
IMO E
Re: If 5a − 3b = −9 and 3a + b = 31, then a + b =   [#permalink] 01 Mar 2019, 04:01
Display posts from previous: Sort by