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A total of 20 amounts are entered on a spreadsheet that has [#permalink]

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02 Mar 2012, 03:54

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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 R(i) (1≤(i)≤5). The average of the amounts in column (j) is C(j) (1≤(j)≤4). What is the average of all 20 amounts on the spreadsheet?

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 R(i) (1≤(i)≤5). The average of the amounts in column (j) is C(j) (1≤(j)≤4). What is the average of all 20 amounts on the spreadsheet?

(1) R1 + R2 + R3 + R4 + R5 = 550 --> since R1 is the average of row 1, then the sum of the numbers in row 1 is R1*4, the sum of the numbers in row 2 is R2*4, and so on. Hence the sum of all 20 numbers is 4*(R1 + R2 + R3 + R4 + R5)=4*550 --> the average of all 20 numbers is (average)=(sum)/(# of terms)=(4*550)/20=110. Sufficient.

(2) C1 + C2 + C3 + C4 = 440. The same logic here: the sum of the numbers in column 1 is C1*5, the sum of the numbers in column 2 is C2*5, and so on. Hence the sum of all 20 numbers is 5*(C1 + C2 + C3 + C4 )=5*440 --> the average of all 20 numbers is (average)=(sum)/(# of terms)=(5*440)/20=110. Sufficient.

Re: A total of 20 amounts are entered on a spreadsheet that has [#permalink]

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28 Aug 2014, 11:03

Hello from the GMAT Club BumpBot!

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Re: A total of 20 amounts are entered on a spreadsheet that has [#permalink]

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06 Dec 2015, 11:40

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: A total of 20 amounts are entered on a spreadsheet that has [#permalink]

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06 Dec 2015, 12:06

Can you explain how this particular part contributes to solving this problem: The average (arithmetic mean) of the amounts in row (i) is R(i) (1≤(i)≤5). The average of the amounts in column (j) is C(j) (1≤(j)≤4).?

I don't understand how it relates to the problem as a whole, so I had trouble interpreting both statements. I couldn't reconcile the numbers because I didn't understand what exactly 550 and 440 represented. For example, I read Statement I as giving the sum total of all 5 rows (with 110 as the average sum of each row), which I realized can't be the case once I got to Statement II.

Re: A total of 20 amounts are entered on a spreadsheet that has [#permalink]

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07 Feb 2017, 13:32

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: A total of 20 amounts are entered on a spreadsheet that has [#permalink]

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19 Feb 2017, 22:01

Bunuel wrote:

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 R(i) (1≤(i)≤5). The average of the amounts in column (j) is C(j) (1≤(j)≤4). What is the average of all 20 amounts on the spreadsheet?

(1) R1 + R2 + R3 + R4 + R5 = 550 --> since R1 is the average of row 1, then the sum of the numbers in row 1 is R1*4, the sum of the numbers in row 2 is R2*4, and so on. Hence the sum of all 20 numbers is 4*(R1 + R2 + R3 + R4 + R5)=4*550 --> the average of all 20 numbers is (average)=(sum)/(# of terms)=(4*550)/20=110. Sufficient.

(2) C1 + C2 + C3 + C4 = 440. The same logic here: the sum of the numbers in column 1 is C1*5, the sum of the numbers in column 2 is C2*5, and so on. Hence the sum of all 20 numbers is 5*(C1 + C2 + C3 + C4 )=5*440 --> the average of all 20 numbers is (average)=(sum)/(# of terms)=(5*440)/20=110. Sufficient.

Answer: D.

Hope it's clear.

Can we follow the logic that the average of the averages will give us the average of all the numbers within?

Re: A total of 20 amounts are entered on a spreadsheet that has [#permalink]

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10 Apr 2017, 08:12

sfangy wrote:

Can you explain how this particular part contributes to solving this problem: The average (arithmetic mean) of the amounts in row (i) is R(i) (1≤(i)≤5). The average of the amounts in column (j) is C(j) (1≤(j)≤4).?

I don't understand how it relates to the problem as a whole, so I had trouble interpreting both statements. I couldn't reconcile the numbers because I didn't understand what exactly 550 and 440 represented. For example, I read Statement I as giving the sum total of all 5 rows (with 110 as the average sum of each row), which I realized can't be the case once I got to Statement II.

Re: A total of 20 amounts are entered on a spreadsheet that has [#permalink]

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10 Apr 2017, 09:28

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 R(i) (1≤(i)≤5). The average of the amounts in column (j) is C(j) (1≤(j)≤4). What is the average of all 20 amounts on the spreadsheet?

Re: A total of 20 amounts are entered on a spreadsheet that has [#permalink]

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10 Apr 2017, 14:45

Yeah it definetely does not feel like a sub-600 question. But apart from being a bit abstract it doesn't require any calculations, just a certain level of reasoning. Both I and II are valid since both give you the sum of either the rows or columns, which allows us to calculate the the average.

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