In a numerical table with $8$ rows and $10$ column... | Free GMAT Practice Question | GMAT Panda

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In a numerical table with 8 rows and 10 columns, each entry is either a 4 or a 6 . If the number of 4 s in the n th row is n + 1 for each n from 1 through 8, what is the average (arithmetic mean) of all the numbers in the table?

Explanation	Calculations	Help
$We first note that each entry is either "4" or "6", and that in the "nth row", the number of "4" s is "n+1" .$	$Number of 4s in row n = n + 1 Number of 6s in row n = 10 - (n + 1) = 9 - n$
$We then calculate the sum of the entries in the "nth row" .$	$4 (n + 1) + 6 (9 - n) = 4 n + 4 + 54 - 6 n = 58 - 2 n$
$We observe that the row sums from "n = 1" to "n = 8" form an evenly spaced list, so by Average and Median Property of Evenly Spaced Sets the average of these sums is the mean of the first and last values.$	$First row sum = 58 - 2 \times 1 = 56 Last row sum = 58 - 2 \times 8 = 42 Average row sum = \frac{56 + 42}{2} = 49 Total sum of all rows = 49 \times 8 = 392$	Theory & Tactics Method Card EVEN1-C Click to view full details
$We then find the overall average by dividing the total sum by the total number of entries.$	$Average per entry = \frac{392}{80} = 4.9$

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C

In a numerical table with 8 rows and 10 columns, each entry is either a 4 or a 6 . If the number of 4 s in the n th row is n + 1 for each n from 1 through 8, what is the average (arithmetic mean) of all the numbers in the table?

Explanation	Calculations	Help
$We first note that each entry is either "4" or "6", and that in the "nth row", the number of "4" s is "n+1" .$	$Number of 4s in row n = n + 1 Number of 6s in row n = 10 - (n + 1) = 9 - n$
$We then calculate the sum of the entries in the "nth row" .$	$4 (n + 1) + 6 (9 - n) = 4 n + 4 + 54 - 6 n = 58 - 2 n$
$We observe that the row sums from "n = 1" to "n = 8" form an evenly spaced list, so by Average and Median Property of Evenly Spaced Sets the average of these sums is the mean of the first and last values.$	$First row sum = 58 - 2 \times 1 = 56 Last row sum = 58 - 2 \times 8 = 42 Average row sum = \frac{56 + 42}{2} = 49 Total sum of all rows = 49 \times 8 = 392$	Theory & Tactics Method Card EVEN1-C Click to view full details
$We then find the overall average by dividing the total sum by the total number of entries.$	$Average per entry = \frac{392}{80} = 4.9$

Scroll horizontally to view all columns

C