• Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer

What is the average of a, b and c?

This topic has 2 expert replies and 0 member replies

What is the average of a, b and c?

Post Tue Dec 05, 2017 9:39 am
What is the average of a, b and c?

(1) The average of a and b is c.
(2) The average of b and c is 4.

The OA is E.

Why neither statement is sufficient? Experts, can you give me some help here? Thanks.

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

aockert Newbie | Next Rank: 10 Posts Default Avatar
Joined
17 Nov 2017
Posted:
5 messages
Post Tue Dec 05, 2017 3:54 pm
A quick way to approach this question is to plug in your own numbers.

When looking at these two statements, Statement 2 is more definite, (the average of two variables equals a constant rather than another variable) so start with that Statement.

The average of b and c is 4. Substitute 5 and 3 for b and c, respectively, since those numbers are one greater and one less than 4 (and thus average 4).
b = 5
c = 3

Now that we have numbers for b and c, we very clearly don't know what a is. So Answer B is eliminated. Now, let's see about combining this with Statement 1.

Solve for a using the b and c from before. You can set up an equation for an average, which is the sum of the numbers divided by how many there are (2).
$$\frac{a+5}{2}=3$$
$$a+5=6$$
$$a=1$$

Now that you have all 3 values, you can calculate the average for a, b, and c:

$$\frac{1+5+3}{3}=\frac{9}{3}=3$$

So at this point, the average COULD be 3. But what if you switched the values of b and c in the first place?
b=3
c=5
The average of b and c is still 4. But now solve for a

$$\frac{a+3}{2}=5$$
$$a+3=10$$
$$a=7$$

Now, the average of the 3 numbers will be:

$$\frac{7+3+5}{3}=\frac{15}{3}=5$$

Furthermore, you can have a situation where b and c are both equal to 4, making a equal to 4, and the average of a, b, and c is 4.
The issue with this problem is that the average of b and c can be equal to 4 whether b is greater than c, b is less than c, OR b is equal to c. But, each of these scenarios impacts the value of a, which then impacts the value of the average of a, b, and c.

Statement 1 is not sufficient. Statement 1 and 2, taken together, are not sufficient either. Answer E is correct.

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post Tue Dec 05, 2017 4:19 pm
Vincen wrote:
What is the average of a, b and c?

(1) The average of a and b is c.
(2) The average of b and c is 4.
Average of a, b and c = (a+b+c)/3.
To calculate the average, we need to know the value of the expression in blue.
Question stem, rephrased:
What is the value of a+b+c?

Statement 1:
(a+b)/2 = c
a+b = 2c
a = 2c-b.
No way to determine the value of a+b+c.
INSUFFICIENT.

Statement 2:
(b+c)/2 = 4
b+c = 8.
No information about a.
INSUFFICIENT.

Statements combined (b+c = 8 and a = 2c-b):
Case 1: b=0 and c=8, with the result that a = 2c-b = (2*8) - 0 = 16
In this case, a+b+c = 16+0+8 = 24.
Case 2: b=1 and c=7, with the result that a = 2c-b = (2*7) - 1 = 13
In this case, a+b+c = 13+1+7 = 21.
Since a+b+c can be different values, INSUFFICIENT.

The correct answer is E.

_________________
Mitch Hunt
GMAT Private Tutor
GMATGuruNY@gmail.com
If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.
Available for tutoring in NYC and long-distance.
For more information, please email me at GMATGuruNY@gmail.com.

  • +1 Upvote Post
  • Quote
  • Flag
Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.

Top First Responders*

1 GMATGuruNY 67 first replies
2 Rich.C@EMPOWERgma... 44 first replies
3 Brent@GMATPrepNow 40 first replies
4 Jay@ManhattanReview 25 first replies
5 Terry@ThePrinceto... 10 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description GMATGuruNY

The Princeton Review Teacher

132 posts
2 image description Rich.C@EMPOWERgma...

EMPOWERgmat

112 posts
3 image description Jeff@TargetTestPrep

Target Test Prep

95 posts
4 image description Scott@TargetTestPrep

Target Test Prep

92 posts
5 image description Max@Math Revolution

Math Revolution

91 posts
See More Top Beat The GMAT Experts