Question : The average of five positive numbers is 56. If the first number is three-fourths of the sum of the last four numbers, then the average of the last four numbers is:
Option 1: 35
Option 2: 40
Option 3: 30
Option 4: 50
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Correct Answer: 40
Solution : Given: The average of five positive numbers is 56. The first number is three-fourths of the sum of the last four numbers. Use the formula, $\text{Average}=\frac{\text{The sum of values}}{\text{The total number of values}}$. Let the sum of the last four numbers be $4x$. ⇒ The first number = $3x$ The sum of all the values = $4x+3x=56\times 5$. ⇒ $7x=280$ ⇒ $x=40$ The average of the last four numbers = $\frac{4x}{4}=x=40$. Hence, the correct answer is 40.
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Question : The sum of three positive numbers is 18 and their product is 162. If the sum of two numbers is equal to the third number, the sum of the squares of the numbers is:
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