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

A) 19
B) 20
C) 21
D) 22
E) 29

If the average of the four numbers is 18, then we know that [3 + 15 + 32 + (N+1)]/4 = 18
Multiply both sides by 4 to get: 3 + 15 + 32 + (N+1) = 72
Simplify: 51 + N = 72
Solve: N = 21
Answer: C


Related Resource
The following video covers the concepts/strategies that are useful for answering this question:
- Mean, median and mode: https://www.gmatprepnow.com/module/gmat ... /video/800

Cheers,
Brent

Hi All,

We're told that If the average (arithmetic mean) of the four numbers 3, 15, 32, and (N + 1) is 18. We're asked for the value of N.

In these types of straight-forward 'Average' questions, the fastest approach is almost always to set up the Average Formula and just do the necessary math steps. That having been said, on tougher Average questions, alternative ways to get to the correct answer can be a lot faster (and easier to implement) IF you know what those alternatives are. Here is an alternative to the the Average Formula:

Here, we have 4 numbers (3, 15, 32 and N+1). Since the average of the group is 18, each of these 4 numbers is a certain 'distance' from the average - and all of those 'distances' have to 'cancel out' for the average to be 18.

For example, if we had just two numbers: 17 and 19, then the average would be 18. The number 17 is "one BELOW" and the number 19 is "one ABOVE" That "-1" and "+1" cancel out and we have the average.

The number 3 is "15 below" 18
The number 15 is "3 below" 18
The number 32 is "14 above" 18
So far, we have "-15", "-3" and "+14" --> "-4 total"

We need the last term to cancel out that "-4", so it has to be "+4"....
(N+1) is "4 above" 18
N+1 = 22
N = 21

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

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

A) 19
B) 20
C) 21
D) 22
E) 29

C

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

51 + N = 72

N = 21

Answer: C