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Math Expert V
Joined: 02 Sep 2009
Posts: 56333
The average (arithmetic mean) of 6 numbers is 8.5. When one  [#permalink]

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4 00:00

Difficulty:   5% (low)

Question Stats: 91% (01:09) correct 9% (01:34) wrong based on 758 sessions

### HideShow timer Statistics 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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Math Expert V
Joined: 02 Sep 2009
Posts: 56333
Re: The average (arithmetic mean) of 6 numbers is 8.5. When one  [#permalink]

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2
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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.

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Director  Joined: 25 Apr 2012
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Re: The average (arithmetic mean) of 6 numbers is 8.5. When one  [#permalink]

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1
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

Ans E

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

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1
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).
Manager  B
Joined: 13 Feb 2011
Posts: 81
The average (arithmetic mean) of 6 numbers is 8.5. When one  [#permalink]

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1
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. $$6.5+8.5=15.0$$
Current Student D
Joined: 12 Aug 2015
Posts: 2609
Schools: Boston U '20 (M)
GRE 1: Q169 V154 Re: The average (arithmetic mean) of 6 numbers is 8.5. When one  [#permalink]

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Here is my solution to this one-->

Sum(1)=6*8.5=>51
Sum(2)=5*7.2=>36
Hence the discarded number must be 51-36=15

Hence E

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

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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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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
after knowing the S.D. very precisely we gonna solve these questions within 30 sec.
Board of Directors P
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Re: The average (arithmetic mean) of 6 numbers is 8.5. When one  [#permalink]

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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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CEO  V
Joined: 12 Sep 2015
Posts: 3857
Re: The average (arithmetic mean) of 6 numbers is 8.5. When one  [#permalink]

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Top Contributor
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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_________________ Re: The average (arithmetic mean) of 6 numbers is 8.5. When one   [#permalink] 17 Dec 2017, 10:02
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