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

Question

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

Bunuel · Accepted Answer

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.

BrentGMATPrepNow · Answer

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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WoundedTiger · Answer

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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Abdul29 · Answer

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).

Dienekes · Answer

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

stonecold · Answer

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

Abhishek009 · Answer

8.5*6 - x = 7.2*5

Or,  51 - x = 36

Or,  x = 15 
  
Hence, answer will be (E) 15

nks2611 · Answer

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.

Abhishek009 · Answer

8.5*6 - X = 7.2*5

51 - x = 36

Or,  x = 15

Thus, the discarded number will be (E) 15.00

TheNightKing · Answer

(8.5*6)-(7.2*5)=51-36=15. Option E.

sgaaa · Answer

8.5*6= 51

7.2*5= 36

51-36=15

Answer is E.

BrushMyQuant · Answer

Theory

➡ Average = Sum of all the Values / Total Number of Values
➡ Sum of all the Values = Average * Total Number of Values

The average (arithmetic mean) of 6 numbers is 8.5

Sum of 6 numbers = Average * 6 = 8.5 * 6 = 51

When one number is discarded, the average of the remaining numbers becomes 7.2

Sum of remaining 5 numbers = Average * 5 = 7.2 * 5 = 36

Discarded number = Sum of 6 numbers - Sum of remaining 5 numbers = 51 - 36 = 15

So,  Answer will be E .
Hope it helps!

Watch the following video to Learn the Basics of Statistics

https://www.youtube.com/watch?v=Cvy_HHw4KIs

ArnauG · Answer

Let's denote the discarded number as x.

The average of 6 numbers is given as 8.5, so the sum of these 6 numbers is 6 * 8.5 = 51.

When the number x is discarded, the average of the remaining 5 numbers becomes 7.2. So, the sum of the remaining 5 numbers is 5 * 7.2 = 36.

To find the discarded number x, we can subtract the sum of the remaining 5 numbers from the sum of the original 6 numbers:

51 - 36 = 15

Therefore, the discarded number is 15.

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