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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?

(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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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.

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

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07 Feb 2014, 10:10

1

This post received KUDOS

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

Posted from my mobile device _________________

“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

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

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21 Feb 2016, 11:48

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. \(6.5+8.5=15.0\) Answer: E

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

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10 Dec 2016, 00:32

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 _________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

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

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10 Mar 2017, 22:41

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.

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

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10 Mar 2017, 23:16

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 _________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

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