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# The average (arithmetic mean) of five numbers is 25. After o

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The average (arithmetic mean) of five numbers is 25. After o [#permalink]  13 May 2018, 10:32
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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.
[Reveal] Spoiler: OA

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Re: The average (arithmetic mean) of five numbers is 25. After o [#permalink]  04 Jul 2018, 08:00
Carcass 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.

Here,

We know $$Arithmetic mean = \frac{Sum of numbers}{number of terms}$$

i.e. $$\frac{Sum of numbers}{5} = 25$$

or $$Sum of numbers = 125$$

Now if 1 number is removed then Arithmetic mean = 31

i.e. $$\frac{Sum of numbers}{4} = 31$$

or $$Sum of numbers = 124$$

Therefore $$the number removed = 125 - 124 = 1$$
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Re: The average (arithmetic mean) of five numbers is 25. After o [#permalink]  13 Jun 2019, 05:34
Expert's post
Carcass 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.

Let the 5 numbers be a, b, c, d, and e

The average (arithmetic mean) of five numbers is 25

We can write: $$\frac{a+b+c+d+e}{5}=25$$

Multiply both sides by 5 to get: $$a+b+c+d+e=125$$

After one of the numbers is removed, the average (arithmetic mean) of the remaining numbers is 31
Let's say we remove the number e

We can now write: $$\frac{a+b+c+d}{4}=31$$

Multiply both sides by 4 to get: $$a+b+c+d=124$$

What number has been removed?
In other words, what is the value of e?

Take:
$$a+b+c+d+e=125$$
$$a+b+c+d=124$$

Subtract the bottom equation from the top equation to get: $$e = 1$$

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Re: The average (arithmetic mean) of five numbers is 25. After o   [#permalink] 13 Jun 2019, 05:34
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