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What is the average of a, b and c?

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What is the average of a, b and c?

by Vincen » 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.
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by aockert » 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.
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by GMATGuruNY » 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.
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