Pls help to solve this and explain me

[tracyyahoo]

A total of 20 amounts are entered on a spreadsheet that has 5 rows and 4 columns; each of the 20 positions in the spreadsheet contains one amount. The average (arithmetic mean) of the amounts in row i is Ri (1 ≤ i ≤ 5). The average of the amounts in column j is Cj (1 ≤ j ≤ 4). What is the average of all 20 amounts on the spreadsheet?


(1) R1 + R2 + R3 + R4 + R5 = 550
(2) C1 + C2 + C3 + C4 = 440

I chose C because only based on these two conditions we can calculate the avg. of 20 amounts
However the OA is D, why the hell is that???? Pls explain me

[shankar.ashwin]

From (1)
Avg would be 550/5 = 110

From (2)
Avg would be 440/4 = 110

Ans would be D IMO

[tracyyahoo]

But the question is asked for What is the average of all 20 amounts?

Shouldn't be R1 + R2 + R3 + R4 + R5 = 550 + (2) C1 + C2 + C3 + C4 = 440 /20????

From (1)
Avg would be 550/5 = 110

From (2)
Avg would be 440/4 = 110

Ans would be D IMO

[GmatMathPro]

Here is another way to think of it:

Remember that the rows and the columns are describing the same numbers, so there is no need to add ALL the values together. For example, suppose the spreadsheet looks like this (ignoring the 550 and 440 values for now):

1 2 4 3
3 5 7 1
7 8 1 1
9 8 1 2
6 5 1 3

Remember that R1 is the average of row 1, not the total. In this case, the total of row 1 would be 10, but the average would be 10/4=2.5, so R1=2.5. To get the total of row 1, you would have to do 4*R1. This would be true of all 5 rows, so the total of all the rows would be 4(R1+R2+R3+R4+R5), and the average of all 20 numbers would be this sum divided by 20.

Using this idea with the actual values provided by statement 1, the sum of all the entries would be 4*550=2200. Now you can divide this by 20 to get the average value of all 20 entries, which would be 110.

The same info can be derived from statement 2, but this time we would have to multiply C1,C2,C3,C4 by 5 to get the totals since there are 5 entries per column. Again, 5*440=2200, and 2200/20=110.

[shankar.ashwin]

Summing up all rows covers all numbers and similarly summing all columns covers all number.

Here exact sum isnt given but average of rows and columns works the same way.

Just open an excel and try, would be able to understand better I guess.

But the question is asked for What is the average of all 20 amounts?

Shouldn't be R1 + R2 + R3 + R4 + R5 = 550 + (2) C1 + C2 + C3 + C4 = 440 /20????