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The average (arithmetic mean) of five numbers is 25. After one of the

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Joined: 02 Sep 2009
Posts: 51072
The average (arithmetic mean) of five numbers is 25. After one of the  [#permalink]

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02 Jul 2018, 23:18
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The average (arithmetic mean) of five numbers is 25. After one of the numbers is removed, the average (arithmetic mean) of the remaining numbers is 31. What number has been removed?

(A) 1

(B) 6

(C) 11

(D) 24

(E) It cannot be determined from the information given.

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The average (arithmetic mean) of five numbers is 25. After one of the  [#permalink]

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02 Jul 2018, 23:33
Bunuel wrote:
The average (arithmetic mean) of five numbers is 25. After one of the numbers is removed, the average (arithmetic mean) of the remaining numbers is 31. What number has been removed?

(A) 1

(B) 6

(C) 11

(D) 24

(E) It cannot be determined from the information given.

We'll translate our question into equations so we understand what we need to do.
This is a Precise approach.

If we treat the sum of the 4 remaining elements as one variable, S, and the 5th variable as x, then:
S/4 = 31 --> S = 124
(S+x)/5 = 25 --> 124 + x = 125
x = 1

(A) is our answer.
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Re: The average (arithmetic mean) of five numbers is 25. After one of the  [#permalink]

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03 Jul 2018, 01:22
[quote="Bunuel"]The average (arithmetic mean) of five numbers is 25. After one of the numbers is removed, the average (arithmetic mean) of the remaining numbers is 31. What number has been removed?

(A) 1

(B) 6

(C) 11

(D) 24

(E) It cannot be determined from the information given.[/quote

Sum of the 5 numbers = 5*25 = 125

Sum of the 4 numbers = 4 * 31 = 124

So the number that is removed = 125 - 124 = 1

The best answer is A.
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Re: The average (arithmetic mean) of five numbers is 25. After one of the  [#permalink]

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03 Jul 2018, 08:10
Bunuel wrote:
The average (arithmetic mean) of five numbers is 25. After one of the numbers is removed, the average (arithmetic mean) of the remaining numbers is 31. What number has been removed?

(A) 1

(B) 6

(C) 11

(D) 24

(E) It cannot be determined from the information given.

Sum of the five numbers is 125

Given, $$\frac{125 - x}{4} = 31$$

So, $$125 - x = 124$$

Or, x = 1 , Answer must be (A) 1
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Re: The average (arithmetic mean) of five numbers is 25. After one of the &nbs [#permalink] 03 Jul 2018, 08:10
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