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A set of data contains five terms. If the average of those terms is 12

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A set of data contains five terms. If the average of those terms is 12 [#permalink]

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New post 11 Apr 2018, 21:25
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A set of data contains five terms. If the average of those terms is 12 and the range of the set is 15, what is the greatest possible value of a term in that set?

A. 12
B. 15
C. 18
D. 21
E. 24
[Reveal] Spoiler: OA

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A set of data contains five terms. If the average of those terms is 12 [#permalink]

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New post 12 Apr 2018, 00:51
Bunuel wrote:
A set of data contains five terms. If the average of those terms is 12 and the range of the set is 15, what is the greatest possible value of a term in that set?

A. 12
B. 15
C. 18
D. 21
E. 24


If the range is 15, the minimum value is x and the maximum value is x+15

We are also given that the average of the 5 element set is 12. Since we are
asked to find the greatest possible value of the set, the other 3 elements are
equal to the minimum value
\(x+x+15+3x = 5*12 = 60\) -> \(5x + 15 = 60\) -> \(x = \frac{45}{5} = 9\)

Therefore, the greatest possible value of a term in the set is x+15 = 24(Option E)
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Re: A set of data contains five terms. If the average of those terms is 12 [#permalink]

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New post 12 Apr 2018, 09:59
Bunuel wrote:
A set of data contains five terms. If the average of those terms is 12 and the range of the set is 15, what is the greatest possible value of a term in that set?

A. 12
B. 15
C. 18
D. 21
E. 24


This question expects us to find out the greatest possible value of the term. The question also provides the average of the terms and range of terms. One of the ways of solving such questions is to assign all variables expect one with a lowest possible value 'x' for example. Now, the last variable can be called 'n'.
Since we know mean is 12, we get (x+x+x+x+n)/5 = 12 => 4x+n = 60. Now the range is given as 15 => n-x = 15.
upon solving these two linear equations, we can find out that x=9 and n=60-4*9 = 24. So greatest term in the set is 24, option D
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Re: A set of data contains five terms. If the average of those terms is 12 [#permalink]

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New post 16 Apr 2018, 16:12
Bunuel wrote:
A set of data contains five terms. If the average of those terms is 12 and the range of the set is 15, what is the greatest possible value of a term in that set?

A. 12
B. 15
C. 18
D. 21
E. 24


Using the average formula: average = sum/number, we see that the sum of the 5 terms is 60.

We can let a = the smallest term and b = the largest term. Since range = largest - smallest, we see that the range is (b - a) = 15. We want to determine the greatest possible value for b, so we should minimize the sum of the remaining terms. To do that, we let each of the remaining three terms be equal to a, Thus, we have:

a + a + a + a + b = 60

and

b - a = 15

If we subtract the second equation from the first, we have:

5a = 45

a = 9

Thus, b = 9 + 15 = 24.

Answer: E
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Re: A set of data contains five terms. If the average of those terms is 12   [#permalink] 16 Apr 2018, 16:12
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