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

It is currently 25 Sep 2018, 12:07

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

If 12a + 3b = 1 and 7b – 2a = 9, what is the average (arithmetic mean)

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49496
If 12a + 3b = 1 and 7b – 2a = 9, what is the average (arithmetic mean)  [#permalink]

Show Tags

New post 17 Aug 2018, 06:01
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

76% (01:42) correct 24% (02:17) wrong based on 29 sessions

HideShow timer Statistics

Manager
Manager
User avatar
G
Joined: 18 Jul 2018
Posts: 193
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
Premium Member
Re: If 12a + 3b = 1 and 7b – 2a = 9, what is the average (arithmetic mean)  [#permalink]

Show Tags

New post 17 Aug 2018, 06:09
Multiplying equation 2 by 6 gives 42b-12a=54.
Now adding this to eqn 1 gives 45b=55. Hence b = \(\frac{11}{9}\).
replacing this in eqn 1 gives a = \(\frac{-2}{9}\).
The average of a+b gives 0.5.
B is the answer.
Director
Director
User avatar
P
Status: Learning stage
Joined: 01 Oct 2017
Posts: 860
WE: Supply Chain Management (Energy and Utilities)
Premium Member CAT Tests
If 12a + 3b = 1 and 7b – 2a = 9, what is the average (arithmetic mean)  [#permalink]

Show Tags

New post 17 Aug 2018, 06:10
Bunuel wrote:
If 12a + 3b = 1 and 7b – 2a = 9, what is the average (arithmetic mean) of a and b ?

A) 0.1
B) 0.5
C) 1
D) 2.5
E) 5


Adding the given equations:-
12a+3b+7b-2a=10
Or, 10a+10b=10
Or, 10(a+b)=10
Or, a+b=1
So, average of a and b is 0.5.

Ans. (B)
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

BSchool Forum Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 3141
Location: India
GPA: 3.12
Premium Member CAT Tests
If 12a + 3b = 1 and 7b – 2a = 9, what is the average (arithmetic mean)  [#permalink]

Show Tags

New post 17 Aug 2018, 06:57
Bunuel wrote:
If 12a + 3b = 1 and 7b – 2a = 9, what is the average (arithmetic mean) of a and b ?

A) 0.1
B) 0.5
C) 1
D) 2.5
E) 5


In order to find the arithmetic mean, we need the value of a+b

P.S In the GMAT, most of the times, this kind of question can be done by a very straightforward
approach. You either have to add or subtract the two statements. Sometimes, you might have
to add twice the second statement to the first statement. Try these combinations before you go
ahead and find individual values for a & b.


Here, the simple addition of both the statements will lead us to the answer.

12a + 3b + 7b – 2a = 9 + 1 -> 10(a + b) = 10 -> a + b = 1

Therefore, the average of a and b is \(\frac{a+b}{2} = \frac{1}{2}\) = 0.5(Option B)
_________________

You've got what it takes, but it will take everything you've got

Manager
Manager
User avatar
S
Joined: 20 Jul 2018
Posts: 91
GPA: 2.87
Re: If 12a + 3b = 1 and 7b – 2a = 9, what is the average (arithmetic mean)  [#permalink]

Show Tags

New post 18 Aug 2018, 09:55
by adding both equations
10a + 10b = 10
a + b = 1
so arithmetic mean is 0.5
_________________

Hasnain Afzal

"When you wanna succeed as bad as you wanna breathe, then you will be successful." -Eric Thomas

GMAT Club Bot
Re: If 12a + 3b = 1 and 7b – 2a = 9, what is the average (arithmetic mean) &nbs [#permalink] 18 Aug 2018, 09:55
Display posts from previous: Sort by

If 12a + 3b = 1 and 7b – 2a = 9, what is the average (arithmetic mean)

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Events & Promotions

PREV
NEXT


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.