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    Question

    Three distinct prime numbers 'p', 'q', and 'r' satisfy

    (p < q < r). The sum of 'p' and 'q' is 20, and the sum of 'q' and 'r' is 30. Calculate the total of the squares of all three numbers.
    A 665 Correct Answer Incorrect Answer
    B 507 Correct Answer Incorrect Answer
    C 557 Correct Answer Incorrect Answer
    D 600 Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    ATQ,

    p + q = 20 Case 1: Prime numbers whose sum is 20 are 7 and 13. It is given that q > p. So, q = 13 p = 20 - 13 = 7 Now, q + r = 30 So, r = 30 - 13 = 17 Case 2: Prime numbers whose sum is 20 are 3 and 17. It is given that q > p. So, q = 17 p = 20 - 17 = 3 Now, q + r = 30 So, r = 30 - 17 = 13, which is not valid because r must be greater than q (not true here). Hence, required sum = 7² + 13² + 17² = 49 + 169 + 289 = 507

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