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

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Math Expert
Joined: 02 Sep 2009
Posts: 44655
The average (arithmetic mean) of five consecutive numbers is 48. What [#permalink]

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26 Dec 2017, 00:17
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25% (medium)

Question Stats:

77% (00:32) correct 23% (01:09) wrong based on 30 sessions

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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
[Reveal] Spoiler: OA

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Re: The average (arithmetic mean) of five consecutive numbers is 48. What [#permalink]

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26 Dec 2017, 01:28
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]

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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 $$x=230/5=46$$.

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

$$Average.Lowest=\frac{141}{3}=47$$

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Re: The average (arithmetic mean) of five consecutive numbers is 48. What [#permalink]

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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 $$\frac{46 + 47 + 48}{3} = 47$$

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Re: The average (arithmetic mean) of five consecutive numbers is 48. What   [#permalink] 27 Dec 2017, 11:21
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