Question : Three positive numbers are in the ratio of 4 : 5 : 7, and the sum of their squares is 15,210. Find the sum of the three numbers.
Option 1: 148
Option 2: 156
Option 3: 126
Option 4: 208
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Correct Answer: 208
Solution : Let the three positive numbers be 4x, 5x, and 7x. So, (4x)2 + (5x)2 + (7x)2 = 15210 ⇒ 16x2 + 25x2 + 49x2 = 15210 ⇒ 90x2 = 15210 ⇒ x2 = 169 $\therefore$ x = 13 Sum of the three numbers = 4x + 5x + 7x = 16x = 16 × 13 = 208 Hence, the correct answer is 208.
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Question : If the square of the sum of three positive consecutive natural numbers exceeds the sum of their squares by 292, what is the largest of the three numbers?
Option 1: 5
Option 2: 6
Option 3: 3
Option 4: 8
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, then the sum of the squares of the numbers is:
Option 1: 120
Option 2: 126
Option 3: 132
Option 4: 138
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:
Question : The ratio of two positive numbers is 3 : 4. The sum of their squares is 400. What is the sum of the numbers?
Option 1: 28
Option 2: 22
Option 3: 24
Option 4: 26
Question : The sum of the squares of three positive numbers is 323. If the sum of the squares of two numbers is twice the third, their product is:
Option 1: 255
Option 2: 260
Option 3: 275
Option 4: 270
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