Source: Official Guide for GMAT Review 2016 Problem Solving; #15

2

# If the average (arithmetic mean) of the four

If the average (arithmetic mean) of the four numbers 3, 15, 32, and (N + 1) is 18, then N =

### 2 Explanations

1

John Robertson

Following this, https://magoosh.com/gmat/2012/gmat-averages-and-sums-formulas/
if you see an question involving averages, set up the sum = (mean)(# of items) formula and go from there

-> sum = (mean)(# items)
-> 3+15+32+(N+1)=18(4)
-> 51+N = 72
->72-51=71-50= 21, C (the magoosh subtracting mental math thing)
ANS: 21, C

Jan 15, 2017 • Comment

Cydney Seigerman, Magoosh Tutor

Thanks for sharing your work, John! You've done a great job breaking down the solution step by step to clearly show how to arrive at the final answer of N = 21

:D

Jan 16, 2017 • Reply

Maria Gonzalez

i don´t really understad this , can you give us a another solution?

Jan 29, 2018 • Reply

David Recine, Magoosh Tutor

Hi Maria,

I'll be happy to help break down John's explanation a little further. :)

Basically, this is about knowing how averages and parentheses work and then using algebra to solve for N.

The problem says that the average of four given numbers is 18. The values of those four numbers are:

3, 15, 32, and (N+1).

We can know that N+1 is just one number, because it's contained in parentheses and stated as a single value in the math problem.

We can also know that if you take the sum of 3+15+32+(N+1), and divide that sum by 4, you'll get 18. This is because a the sum of the set of values, divided by the number of values in the set, will get you the average for the set. So for example, the average of 2+4 is (2+4)/4, the average of 1,3,5,7, and 9 is (1+3+5+7+9)/5.

So here we have four values: 3, 15, 32, (N+1). We know that these 4 values, when combined and divided by 4, have an average of 18. What we don't know is the value of N within (N+1). That's what we need to solve for.

From here, we start with the equation:

[3+15+32+(N+1)]/4 = 18

Next, we simplify things. The first thing to do is remove the parenthesis around N+1. We can do this because the order of numbers and operations doesn't matter if you're just adding:

(3+15+32+N+1)/4 = 18

Actually, though, it's better to group all the numbers together, so we can add those up and separate them from N:

(N+ 3+15+32++1)/4 = 18

And from here, we just solve for N step-by-step, algebraically:

(N+ 3+15+32++1)/4 = 18

(N + 51)/4 = 18 (combine all the numbers in the parentheses on the right)

[(N+ 51)/4]*(4) = 18*(4) (multiply both sides by 4 to get rid of the 4 in the numerator on the rightand side of the equation.

N+51 = 72

N + 51 - 51 = 72 -51 (subtract 51 form both sides to eliminate 51 on the righthand side of the equation, so that N is alone)

N = 72 -51

N = 21

So N has a value of 21. If you want to test this, you can plug it into the original 4 values and divide by 4 to make sure you get 18:

3+15+32+(N+1) =
3+15+32+(21+1) =
3+15+32+22 =
72

72/4 = 21

Hopefully this more detailed breakdown helps. But let me know if you still have questions. :)

Jan 30, 2018 • Reply

1

Zubin Baisiwala

3+ 15+ 32 + (N+1)= 51 +N
Arithmetic Mean= 18
So, (51+N)/ 4= 18
51+ N= 18 X 4
N = 72-51= 21
If we solve for N, we get N = 21

Nov 2, 2016 • Comment

Sam Kinsman

That's right, great job Zubin! :D

Nov 2, 2016 • Reply

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