Question
Given below are three numbers series I, II and II where
each series contains a wrong (odd one out) term. The wrong number in series I, II and III are 'P', 'Q' and 'R', respectively. Find the values of 'P', 'Q' and 'R' and answer the questions that follow. I: 137, 112, 334, 279, 791, 710 II: 56, 90, 132, 180, 240, 306, 380 III: 226, 220, 244, 124, 884, -4192 If the first term of a number series is 54 and the series follows the same pattern as series III, then the 5th term of the series will be 'T'. The number that should actually come in place of 'Q' in series II is 'S'. Which among the following statement(s) is/are true regarding (T - S)? I: (T - S) is a multiple of a perfect square II: The H.C.F of 'P' and (T - S) is 21 III: The smallest perfect cube that is greater than (T - S) is 512.Solution
For series I: 137 - 52 = 112 112 + 63 = 328 328 - 72 = 279 279 + 83 = 791 791 - 92 = 710 Therefore, 328 should come in place of 334. So, P = 334 For series II: 7 x 8 = 56 9 x 10 = 90 11 x 12 = 132 13 x 14 = 182 15 x 16 = 240 17 x 18 = 306 19 x 20 = 380 Therefore, 182 should come in place of 180. So, Q = 180 For series III: 226 - 3! = 220 220 + 4! = 244 244 - 5! = 124 124 + 6! = 844 844 - 7! = - 4196 Therefore, -4196 should come in place of - 4192. So, R = - 4192 Completing the series that begins with 54. 54 - 3! = 48 48 + 4! = 72 72 - 5! = -48 -48 + 6! = 672 So, 5th term of the series will be 672 So, T = 672 Since, S = 182 So, (T - S) = 672 - 182 = 490 Statement I: 490 = 49 x 10 = 72 x 10 So, statement I is true Statement II: P = 334 So, H.C.F of 334 and 490 = 2 So, statement II is not true. Statement III: 73 = 343 83 = 512 Since, 512 is larger than 490. So, statement III is true.
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