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      Question

      There are four prime numbers A, B, C and D (A < B < C

      D). Only A and B are consecutive prime numbers. Sum of A and B is not divisible by 2. LCM of B, C and D is 357. Sum of all the numbers is less than 30. Which of the following are true: I. The sum of A and B is 20.83% (approx.) of the sum of C and D. II. LCM of B and C is 20 more than the HCF of all the numbers. III. (A+B)/C × 7D = {2(B × C)} + (D+26)
      A Only I Correct Answer Incorrect Answer
      B Only III Correct Answer Incorrect Answer
      C Both I and II Only Correct Answer Incorrect Answer
      D Both I and III Only Correct Answer Incorrect Answer
      E All the three Correct Answer Incorrect Answer

      Solution

      ATQ, ATQ, Sum of A and B is not divisible by 2 and both are prime numbers, so one of them is 2. A < B, so A = 2 A and B are consecutive prime numbers, so B = 3 LCM of B, C and D = 357 LCM of C and D = 357/3 = 119 Product of C and D = 119 = 7 × 17 Sum of all numbers < 30 and only A and B are consecutive prime numbers, so C = 7, D = 17 I => A+B = 20.83% (approx.) of (C+D) 5 = 20.83% of 24 = 4.999 (CORRECT) II => LCM of B and C = LCM(3,7) = 21 HCF of all numbers = 1 Difference = 21 – 1 = 20 (CORRECT) III => (A+B)/C × 7D = {2(B × C)} + (D+26) 5/7 × 7 × 17 = 2 × (3 × 7) + (17+26) 85 = 42 + 43 85 = 85 (CORRECT) Hence, all three are true.

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