WBCS.LIVE practice question

The sum of two numbers is 36, and their Highest Common Factor (HCF) and Least Common Multiple (LCM) are 3 and 105 respectively. What is the sum of the reciprocals of these two numbers?

Solve this multiple-choice question and check the correct answer with its explanation below.

Answer options

  1. 2 /35
  2. 3/35
  3. 6/35
  4. 4/35

Correct answer and explanation

Correct answer: 4/35

Explanation: ✅ Correct Answer: D) 4 ÷ 35 📚 Explanation: Let the two numbers be x and y. We are given x + y = 36. A universal mathematical property states that the product of two numbers equals the product of their HCF and LCM. So, x × y = 3 × 105 = 315. The sum of their reciprocals is (1 ÷ x) + (1 ÷ y) = (x + y) ÷ (x × y). Substituting the values gives 36 ÷ 315. Dividing both by 9 perfectly simplifies the fraction to 4 ÷ 35.