Question
Given below are two numbers series 'I' and 'II' and
each series has a wrong (odd one out) number. The number that should come in place of the wrong number in series 'I' and 'II' are 'P' and 'Q', respectively. First find the values of 'P' and 'Q' and then find which among the given statement(s) is/are true. I: 68, 82, 92, 103, 107, 118, 122 II: 3840, 1920, 1480, 1200, 1050, 945 Statement I: One of the factors of 'P' is a double digit prime number. Statement II: 22.5% of 'Q' is a perfect square number. Statement III: The H.C.F of 'P' and 'Q' is 8.Solution
For series I: The series follows the pattern as: Number + sum of digits of the number. 68 + (6 + 8) = 82 82 + (8 + 2) = 92 92 + (9 + 2) = 103 103 + (1 + 3) = 107 107 + (1 + 7) = 115 115 + (1 + 1 + 5) = 122 Therefore, 115 should come in place of 118. So, P = 115 For series II: 3840 X (1/2) = 1920 1920 X (3/4) = 1440 1440 X (5/6) = 1200 1200 X (7/8) = 1050 1050 X (9/10) = 945 Therefore, 1440 should come in place of 1480. So, Q = 1440 Statement I: Since, P = 115 = 5 X 23 And, 23 is a prime number. So, statement I is true. Statement II: 22.5% of 'Q' = 1440 X (22.5/100) = 324 Since, √324 = 18 So, statement II is true. Statement III: H.C.F of 115 and 1440 = 5 ≠8 So, statement III is not true.
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