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The average (arithmetic mean) of five consecutive numbers is 48. What

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Bunuel
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The average (arithmetic mean) of five consecutive numbers is 48. What [#permalink] New post   26 Dec 2017, 00:17
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The average (arithmetic mean) of five consecutive numbers is 48. What is the average of the three smallest of these numbers?

A. 45
B. 45.5
C. 46
D. 46.5
E. 47
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E
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DavidTutorexamPAL
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Re: The average (arithmetic mean) of five consecutive numbers is 48. What [#permalink] New post   26 Dec 2017, 01:28
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Bunuel wrote:
The average (arithmetic mean) of five consecutive numbers is 48. What is the average of the three smallest of these numbers?

A. 45
B. 45.5
C. 46
D. 46.5
E. 47


Anytime we're give a question involving consecutive integers, we'll look for a solution involving number properties.
This is a Logical approach.

In any sequence containing an odd number of consecutive integers, the average equals the middle number.
Therefore our middle number is 48 so our sequence is 46,47,48,49,50.
Then the average of the 3 smallest numbers is 47 - option (E).
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Re: The average (arithmetic mean) of five consecutive numbers is 48. What [#permalink] New post   27 Dec 2017, 04:30
Bunuel wrote:
The average (arithmetic mean) of five consecutive numbers is 48. What is the average of the three smallest of these numbers?

A. 45
B. 45.5
C. 46
D. 46.5
E. 47


\(Average=\frac{Sum}{Quantity}\), so \(48=\frac{Sum}{5}\), \(Sum=240\).

\(Sum=(x)+(x+1)+(x+2)+(x+3)+(x+4)=5x+10=240\), so \(x=230/5=46\).

\(Sum.Lowest=(x)+(x+1)+(x+2)=3x+3=3(46)+3=141\)

\(Average.Lowest=\frac{141}{3}=47\)

(E) is the answer.
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Re: The average (arithmetic mean) of five consecutive numbers is 48. What [#permalink] New post   27 Dec 2017, 11:21
Bunuel wrote:
The average (arithmetic mean) of five consecutive numbers is 48. What is the average of the three smallest of these numbers?

A. 45
B. 45.5
C. 46
D. 46.5
E. 47
\(n + (n+1) + (n+2) + (n+3) + (n+4) = 240\)

Or, \(5n + 10 = 240\)

So, \(5n = 230\)

Or, \(n = 46\)

Thus, average of the three smallest of these numbers is \(\frac{46 + 47 + 48}{3} = 47\)

Answer will be (E) 47
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Re: The average (arithmetic mean) of five consecutive numbers is 48. What [#permalink] New post   09 Sep 2019, 17:25
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Bunuel wrote:
The average (arithmetic mean) of five consecutive numbers is 48. What is the average of the three smallest of these numbers?

A. 45
B. 45.5
C. 46
D. 46.5
E. 47


In any evenly-spaced set, such as this one, the average (arithmetic mean) and the median are always equal. Since the average of the 5 consecutive numbers is 48, the median, which is the 3rd number, is also 48.

Thus, the first 3 numbers must be 46, 47, and 48, so the average of those numbers, which is equal to the middle number, is 47.

Answer: E
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Re: The average (arithmetic mean) of five consecutive numbers is 48. What [#permalink]
09 Sep 2019, 17:25
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