Problem Solving

Brent@GMATPrepNow wrote:

[email protected] wrote:There is a set of 160 numbers, beginning at 6, with each subsequent term increasing
by an increment of 3. What is the average of this set of numbers?

I am not able to understand how to calculate the last digit?to calculate the average.

There's an important rule that says, "If the numbers in a set are equally spaced, then the mean and median of that set are equal"

So, for example, the mean and median of this set {1, 4, 7, 10, 13, 16} are equal since the numbers are evenly/equally spaced.

In this question, we have 160 numbers. They look like this: {6, 9, 12, 15, . . . }
We can find either the mean or the median, since they'll be equal here.

Let's find the median.
Since there's an even number of integers in the set, we'll need to find the mean of the two middle numbers. In other words, we'll need to find the mean of the 80th value and the 81st value in the set.

But what are the 80th and 81st values in the set?

To find out, let's rewrite the numbers in the set {6, 9, 12, 15, ..}

1st value = 6 = 3 + 3
2nd value = 9 = 3 + 2(3)
3rd value = 12 = 3 + 3(3)
4th value = 15 = 3 + 4(3)
5th value = 18 = 3 + 5(3)
.
.
.

From this we can see a pattern.
80th value = 3 + 80(3) = 243
81st value = 3 + 81(3) = 246

The median (aka the mean) of all 160 terms will equal the mean of 243 and 246.

Median = (243 + 246)/2 = 244.5

So the mean and median are both 244.5

Cheers,
Brent