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The average (arithmetic mean) of the five numbers x, 91, 120, 134, and

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The average (arithmetic mean) of the five numbers x, 91, 120, 134, and  [#permalink]

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New post Updated on: 30 Jul 2018, 02:40
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The average (arithmetic mean) of the five numbers x, 91, 120, 134, and 220 is what percent of the sum of the five numbers?

(A) 20%
(B) 22%
(C) 25%
(D) 30%
(E) It cannot be determined from the information given.

Originally posted by bettatantalo on 30 Jul 2018, 02:24.
Last edited by Bunuel on 30 Jul 2018, 02:40, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
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Re: The average (arithmetic mean) of the five numbers x, 91, 120, 134, and  [#permalink]

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New post 30 Jul 2018, 02:43
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The average (arithmetic mean) of the five numbers x, 91, 120, 134, and  [#permalink]

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New post 30 Jul 2018, 22:45
bettatantalo wrote:
The average (arithmetic mean) of the five numbers x, 91, 120, 134, and 220 is what percent of the sum of the five numbers?

(A) 20%
(B) 22%
(C) 25%
(D) 30%
(E) It cannot be determined from the information given.


You can either think logically and immediately choose the choice A or do algebraically and see the same result. In both cases, the logic plays a monumental role in this problem.

Finding Average: \(\frac{x+565}{5}\)

[b]The Sum
x+565

The Sum is the total and the average is the part, so you can create an equation: \(\frac{x+565}{5}\) / x+565 = \(\frac{y%}{100%}\)
You can see that we have two variables x and y, but have only one equation. So, algebraically it's somehow impossible to find x and y. But you also can notice that you divide the numerator of the first fraction into 5, which in percent form is 100/5 yields 20%.
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The average (arithmetic mean) of the five numbers x, 91, 120, 134, and  [#permalink]

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New post 30 Jul 2018, 23:55
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Solution



Given:
    • We are given 5 numbers: x, 91, 120, 134, and 220

To find:
    • Arithmetic mean of : x, 91, 120, 134, and 220 is what percent of the sum of the five numbers

Approach and Working:

\(Average= \frac{Sum\ of\ the\ five\ numbers}{5}\)

Method:1

Hence, Average if \(\frac{1}{5}\) of sum of the five numbers.
Thus, average is 20% of sum of the five number.

Method:2

• To convert average to percentage, we can multiply by 100.
• Average= Sum of the five numbers/5 *100%= Average= 20% of Sum of the five numbers


Hence, the correct answer is option A.

Answer: A
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Re: The average (arithmetic mean) of the five numbers x, 91, 120, 134, and  [#permalink]

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New post 12 Sep 2018, 08:13
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bettatantalo wrote:
The average (arithmetic mean) of the five numbers x, 91, 120, 134, and 220 is what percent of the sum of the five numbers?

(A) 20%
(B) 22%
(C) 25%
(D) 30%
(E) It cannot be determined from the information given.


OA: A

\(Average = \frac{Sum\quad of \quad Elements}{Number \quad of \quad Elements}\)

\(\frac{Average}{Sum\quad of \quad Elements} =\frac{1}{Number \quad of \quad Elements}\)

Multiplying by 100 on both sides, we get

\(\frac{Average}{Sum\quad of \quad Elements}*100 =\frac{1}{Number \quad of \quad Elements} * 100\)

\(Number \quad of \quad Elements=5\)

\(\frac{Average}{Sum\quad of \quad Elements}*100 =\frac{1}{5}*100=20\)
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Re: The average (arithmetic mean) of the five numbers x, 91, 120, 134, and  [#permalink]

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New post 14 Sep 2018, 09:00
bettatantalo wrote:
The average (arithmetic mean) of the five numbers x, 91, 120, 134, and 220 is what percent of the sum of the five numbers?

(A) 20%
(B) 22%
(C) 25%
(D) 30%
(E) It cannot be determined from the information given.


The average of x, 91, 120, 134, and 220 is:

(x + 91 + 120 + 134 + 220)/5

The sum is:

x + 91 + 120 + 134 + 220

So the average as a percent of the sum is:

[(x + 91 + 120 + 134 + 220)/5]/(x + 91 + 120 + 134 + 220) = 1/5 = 20%

Alternate solution:

Since sum = average x quantity, the average is 1/quantity x 100 percent of the sum. Since here we have 5 numbers, the average is 1/5 x 100 = 20 percent of the sum.

Answer: A
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Re: The average (arithmetic mean) of the five numbers x, 91, 120, 134, and   [#permalink] 14 Sep 2018, 09:00
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