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The average of the eight numbers is 72. Find the least number if it is 161 of the sum of the numbers.
16
18
36
28
36
Since average is 72 and count is 8, the sum is 8×72. Divide this sum directly by 16 as requested (8×72/16 simplifies to 72/2=36).
Average of 8 numbers = 72, and the least number is 1/16 of the sum of the numbers.
Sum=Average×Count
Since average is 72 and count is 8, the sum is 8×72. Divide this sum directly by 16 as requested (8×72/16 simplifies to 72/2=36).
Many students try to find the other individual numbers, which is impossible given the information, or they mistakenly divide the average by 16 instead of the total sum.
Calculate the total sum of the eight numbers
Given the average is 72 for 8 numbers, the sum is calculated as 72×8.
Sum=72×8=576
Apply the condition for the least number
The problem states the least number is 161 of the total sum.
Least number=161×576
Perform the final division
Dividing 576 by 16 gives the value of the least number.
Least number=16576=36
C is correct because the total sum of the eight numbers is 576, and one-sixteenth of 576 is 36.
Questions involving averages and portions of sums often simplify significantly if you perform the multiplication only at the very last step to avoid large intermediate numbers.
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