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.
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
In case you didn’t notice, we recently held the 1st ever GMAT game show and it was awesome! See who won a full GMAT course, and register to the next one.
Re: What is the average of a, b and c?
[#permalink]
Show Tags
01 Aug 2014, 06:30
2
What is the average of a, b and c?
The average of a, b and c is (a + b + c)/3. So, basically to answer the question we need to know the value of a + b + c.
(1) The average of a and b is c --> (a + b)/2 = c --> a + b = 2c. Not sufficient.
(2) The average of b and c is 4 --> (b + c)/2 = 4 --> c = 8 - b. Not sufficient.
(1)+(2) We have that a + b = 2c and c = 8 - b, thus a + b + c = 2c + c = 3c = 3(8 - b). Without knowing the value of c or b we cannot get this value. For example, consider a = 1, b = 5, c = 3 or a = 4, b = 4 and c = 4. Not sufficient.
Re: What is the average of a, b and c?
[#permalink]
Show Tags
18 Sep 2016, 05:31
Top Contributor
suk1234 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.
Target question:What is the average of a, b, and c? NOTE: since the average = (a+b+c)/3, our goal here is to find the SUM a + b + c
So, we can REPHRASE the target question.... REPHRASED target question:What is the value of a + b + c?
Statement 1: The average of a and b is c This means that (a + b)/2 = c Multiply both sides by 2 to get: a + b = 2c There are several values of a, b, and c that satisfy statement 1. Here are two: Case a: a = 1, b = 1 and c = 2, in which case a + b + c = 1 + 2 + 2 = 5 Case b: a = 1, b = 2 and c = 3, in which case a + b + c = 1 + 2 + 3 = 6 Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: The average of b and c is 4 Since there's no information about a, there's no way to find the value of a + b + c Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined Statement 1 tells us that a + b = 2c Statement 2 tells us that (b + c)/2 = 4, which means b + c = 8
So, we have the following system: b + c = 8 a + b = 2c
IMPORTANT: Many students will look at this system and incorrectly conclude that, since we have 2 equations and 3 variables, there's no way to answer the target question. This is not necessarily the case, because the target question does NOT ask us to find the individual values of a, b and c. The target question asks us to find the SUM of a, b, and c. So, for example, if the two equations happened to be a + b + 2c = 5 and 2a + 2b + c = 19, then we could ADD the equations to get 3a + 3b + 3c = 24, and upon dividing both sides by 3, we'd see that a + b + c = 8, in which case we COULD answer the target question despite only having 2 equations with 3 variables. So, we can't just automatically assume that we don't have sufficient information.
So, let's TEST some values of a, b and c that satisfy BOTH equations.
NOTE: since the equation b + c = 8 doesn't have the variable a, let's use it to first find some values of c and b, then we'll use the other equation, a + b = 2c, to find the corresponding a value.
Case a: b = 1 and c = 7 satisfies the equation b + c = 8 . Now plug these values into the other equation (a + b = 2c) to get: a + 1 = 2(7). Solve to get: a = 13. So, the values are a = 13, b = 1 and c = 7, which means a + b + c = 13 + 1 + 7 = 21 Case b: b = 0 and c = 8 satisfies the equation b + c = 8 . Now plug these values into the other equation (a + b = 2c) to get: a + 0 = 2(8). Solve to get: a = 16. So, the values are a = 16, b = 0 and c = 8, which means a + b + c = 16 + 0 + 8 = 24 Since we cannot answer the REPHRASED target question with certainty, the combined statements are NOT SUFFICIENT
close
69% (01:42) correct 
