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# For the 3 numbers in a list, the average

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For the 3 numbers in a list, the average [#permalink]  03 Feb 2017, 01:59
Expert's post
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Question Stats:

83% (00:46) correct 16% (01:21) wrong based on 18 sessions

For the 3 numbers in a list, the average (arithmetic mean) and the median are equal to 8. If the greatest number in the list is 10 greater than the least number, what is the greatest number in the list?

[Reveal] Spoiler: OA
13

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Re: For the 3 numbers in a list, the average [#permalink]  12 Feb 2017, 16:27
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Explanation

If the median of the three numbers is 8, we know that 8 is the second term. The first and third term can be x and (x + 10):
$$x, 8, (x + 10)$$

We know the average = 8, so use the average formula to find x:

$$\frac{sum}{number_of_terms}= Average$$ or

$$\frac{x+8 +(x+10)}{3}=8$$.

or $$x + 8 + (x + 10) = 24$$ or $$x=3$$.

The question asks for the greatest number (x + 10), not the least number (x). The correct answer is 13.
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Re: For the 3 numbers in a list, the average [#permalink]  24 Mar 2017, 15:52
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Carcass wrote:

For the 3 numbers in a list, the average (arithmetic mean) and the median are equal to 8. If the greatest number in the list is 10 greater than the least number, what is the greatest number in the list?

[Reveal] Spoiler: OA
15

Let the 3 numbers (when arranged in ascending order) be x, y, and z.
This means x < y < z

Average = 8
So, (x + y + z)/3 = 8, which means x + y + z = 24

Median = 8
So, y = 8
Plug this value into x + y + z = 24 to get: x + 8 + z = 24
Rewrite as: x + z = 16

The greatest number in the list is 10 greater than the least number
In other words, z is 10 greater than x
We can write: z = x + 10

We now have two equations:
x + z = 16
z = x + 10

Take x + z = 16 and replace z with x + 10
We get: x + (x + 10) = 16
Simplify: 2x + 10 = 16
Solve, x = 3

Now that we know that x = 3, we can use the fact that z = x + 10, to conclude that z = 13

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Re: For the 3 numbers in a list, the average   [#permalink] 24 Mar 2017, 15:52
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