Solve this multiple-choice question and choose the correct option.

Problem restatementLet the numbers be a and b with ab = 120 and a2 + b2 = 289. Find a + b. Concept/ApproachUse the identity (a + b)2 = a2 + b2 + 2ab. Step-by-step calculation (a + b)2 = 289 + 2×120 = 289 + 240 = 529 a + b = √529 = 23 Verification/Alternative529 is 232. The sum could be −23 algebraically, but the context typically takes the positive sum. Final Answer23

Curioustab

The product of two numbers is 120 and the sum of their squares is 289. What is the sum of the numbers?

Aptitude Problems on Numbers Difficulty: Easy

Choose an option

A

23
B

21
C

25
D

17

Answer

Correct Answer: 23

Explanation

Problem restatementLet the numbers be a and b with ab = 120 and a² + b² = 289. Find a + b.

Concept/ApproachUse the identity (a + b)² = a² + b² + 2ab.

Step-by-step calculation (a + b)² = 289 + 2×120 = 289 + 240 = 529 a + b = √529 = 23

Verification/Alternative529 is 23². The sum could be −23 algebraically, but the context typically takes the positive sum.

Final Answer23

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