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A total of 20 amounts are entered on a spreadsheet that has

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by VJesus12 » Sun Apr 28, 2019 10:13 am

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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?

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

[spoiler]OA=D[/spoiler]

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Source: — Data Sufficiency |

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by Ian Stewart » Mon Apr 29, 2019 3:26 am
If you have 4 values, and R is their average, then 4R is their sum, from the definition of an average (just rewrite average = sum/n so you have 'sum' on one side).

So here, 4R(1) is the sum of the four values in row 1, 4R(2) is the sum of the four values in row two, and so on, and thus 4[ R(1) + R(2) + R(3) + R(4) + R(5) ] will be the sum of all twenty values in the spreadsheet, and statement 1 is sufficient (the sum is 4*550 = 2200, and we can divide that by 20 to find the average value).

Similarly, 5C(1) will be the sum of the five values in column 1, and so on, so 5[ C(1) + C(2) + C(3) + C(4) ] is the sum of all twenty values in the spreadsheet, and Statement 2 is sufficient (the sum is 5*440 = 2200, and we can divide that by 20 to find the average value).
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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