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      Question

      Two positive integers multiply to 5070, with their

      highest common factor being 13 and their sum amounting to 143. What is the difference between these two integers?
      A 26 Correct Answer Incorrect Answer
      B 39 Correct Answer Incorrect Answer
      C 52 Correct Answer Incorrect Answer
      D 13 Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      Let the two numbers be ‘13a’ and ‘13b’ ATQ; 13a × 13b = 5070 So, (a × b) = 30 ……………………. (1) Also, 13a + 13b = 143 So, a + b = 11 Or, a = (11 – b) …………………... (2) Putting value of ‘a’ in equation (1), we have (11 – b) × b = 30 Or, 11b – b2 = 30 Or, b2 – 11b + 30 = 0 Or, b2 – 6b – 5b + 30 = 0 Or, b(b – 6) – 5(b – 6) = 0 Or, (b – 6)(b – 5) = 0 So, b = 6 or b = 5 So, the two numbers are = 13 × 5 = 65 and 13 × 6 = 78 Required difference = 78 - 65 = 13 

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