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

Problem restatementGiven S = x + y = 25 and D = x − y = 13, find xy. Concept/ApproachUse the identity S2 − D2 = 4xy. Step-by-Step calculationxy = (S2 − D2) ÷ 4 = (252 − 132) ÷ 4= (625 − 169) ÷ 4 = 456 ÷ 4 = 114 Verification/AlternativeExplicit solution: x = (S + D)÷2 = 19, y = (S − D)÷2 = 6 ⇒ xy = 114. Common pitfallsComputing (S − D)2 instead of S2 − D2, or dividing by 2 instead of 4. Final Answer114

Curioustab

The sum of two numbers is 25 and their difference is 13. What is their product?

Aptitude Problems on Numbers Difficulty: Easy

Choose an option

A

114
B

156
C

192
D

104

Answer

Correct Answer: 114

Explanation

Problem restatementGiven S = x + y = 25 and D = x − y = 13, find xy.

Concept/ApproachUse the identity S² − D² = 4xy.

Step-by-Step calculationxy = (S² − D²) ÷ 4 = (25² − 13²) ÷ 4= (625 − 169) ÷ 4 = 456 ÷ 4 = 114

Verification/AlternativeExplicit solution: x = (S + D)÷2 = 19, y = (S − D)÷2 = 6 ⇒ xy = 114.

Common pitfallsComputing (S − D)² instead of S² − D², or dividing by 2 instead of 4.

Final Answer114

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