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The average (arithmetic mean) of 6 numbers is 8.5. When one

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The average (arithmetic mean) of 6 numbers is 8.5. When one  [#permalink]

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New post 07 Feb 2014, 05:48
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The Official Guide For GMAT® Quantitative Review, 2ND Edition

The average (arithmetic mean) of 6 numbers is 8.5. When one number is discarded, the average of the remaining numbers becomes 7.2. What is the discarded number?

(A) 7.8
(B) 9.8
(C) 10.0
(D) 12.4
(E) 15.0

Problem Solving
Question: 84
Category: Arithmetic Statistics
Page: 72
Difficulty: 600


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Re: The average (arithmetic mean) of 6 numbers is 8.5. When one  [#permalink]

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New post 07 Feb 2014, 05:48
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SOLUTION

The average (arithmetic mean) of 6 numbers is 8.5. When one number is discarded, the average of the remaining numbers becomes 7.2. What is the discarded number?

(A) 7.8
(B) 9.8
(C) 10.0
(D) 12.4
(E) 15.0

The average of 6 numbers is 8.5 --> the sum of 6 numbers = (mean)*(number of terms) = 8.5*6 = 51.

The average of 5 numbers is 7.2 --> the sum of 5 numbers = (mean)*(number of terms) = 7.2*5 = 36.

The discarded number = 51 - 36 = 15.

Answer: E.
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Re: The average (arithmetic mean) of 6 numbers is 8.5. When one  [#permalink]

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New post 07 Feb 2014, 11:10
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The average (arithmetic mean) of 6 numbers is 8.5. When one number is discarded, the average of the remaining numbers becomes 7.2 .What is the discarded number?


Sol: Since avg is given for 6 nos, we can find the sum total which is 8.5*6= 51

New average after removal of one number is 7.2 so sum total of 5 nos is 36

Discarded number is 51-36=15

Ans E

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Re: The average (arithmetic mean) of 6 numbers is 8.5. When one  [#permalink]

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New post 07 Feb 2014, 13:06
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Given that the average of 6 numbers is 8.5, then the sum of these numbers is 6*8.5= 51.

Let 'x' be the number removed, (51-x)/5 = 7.2. Solving for x, we get x = 15, so (E).
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The average (arithmetic mean) of 6 numbers is 8.5. When one  [#permalink]

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New post 21 Feb 2016, 12:48
Let's assume every number was 8.5 in the original set, now in order to reduce average to 7.2 by removing just one number, 1.3 \((8.5-7.2=1.3)\) needs to be subtracted from remaining 5 numbers \((1.3*5=6.5)\) along with removing one of the original numbers, i.e. \(6.5+8.5=15.0\)
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Re: The average (arithmetic mean) of 6 numbers is 8.5. When one  [#permalink]

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Re: The average (arithmetic mean) of 6 numbers is 8.5. When one  [#permalink]

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New post 10 Dec 2016, 01:32
Bunuel wrote:
The average (arithmetic mean) of 6 numbers is 8.5. When one number is discarded, the average of the remaining numbers becomes 7.2. What is the discarded number?

(A) 7.8
(B) 9.8
(C) 10.0
(D) 12.4
(E) 15.0


\(8.5*6 - x = 7.2*5\)

Or, \(51 - x = 36\)

Or, \(x = 15\)

Hence, answer will be (E) 15

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Re: The average (arithmetic mean) of 6 numbers is 8.5. When one  [#permalink]

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New post 10 Mar 2017, 23:41
this can be solved very easily from the following method
N-7.2/6 +7.2=8.5 so the new no. will be after solving for N=15
so the answer is E
after knowing the S.D. very precisely we gonna solve these questions within 30 sec.
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Re: The average (arithmetic mean) of 6 numbers is 8.5. When one  [#permalink]

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New post 11 Mar 2017, 00:16
Bunuel wrote:
The average (arithmetic mean) of 6 numbers is 8.5. When one number is discarded, the average of the remaining numbers becomes 7.2. What is the discarded number?

(A) 7.8
(B) 9.8
(C) 10.0
(D) 12.4
(E) 15.0


\(8.5*6 - X = 7.2*5\)

\(51 - x = 36\)

Or, \(x = 15\)

Thus, the discarded number will be (E) 15.00
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Re: The average (arithmetic mean) of 6 numbers is 8.5. When one  [#permalink]

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New post 17 Dec 2017, 10:02
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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

The average (arithmetic mean) of 6 numbers is 8.5. When one number is discarded, the average of the remaining numbers becomes 7.2. What is the discarded number?

(A) 7.8
(B) 9.8
(C) 10.0
(D) 12.4
(E) 15.0


Average of 6 numbers = (sum of all 6 numbers)/6
We get: 8.5 = (sum of all 6 numbers)/6
So, sum of the 6 numbers = (6)(8.5)
= 51

When one number is discarded, the average of the remaining numbers becomes 7.2
Sum of remaining 5 numbers = (5)(7.2)
= 36

Discarded number = (sum of original 6 numbers) - (sum of remaining 5 numbers)
= 51 - 36
= 15
= E

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