Discussion
Of three numbers, the second number is twice the first and thrice the third. If the average of the three numbers is 44, the largest number is :
Answer: D
The largest number is 72.
Let the second number be the common multiple of 2 and 3, say 6k. Then the first is half of it and the third a third of it:
\[ \begin{aligned} \text{first} &= 3k,\ \text{second} = 6k,\ \text{third} = 2k \\ 3k + 6k + 2k &= 3 \times 44 = 132 \\ 11k &= 132 \Rightarrow k = 12 \end{aligned} \]
The numbers are 36, 72 and 24, and the largest is the second, 72. 36 is the first number, 22 is not one of them, and 108 would need an average of 66.
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