1. In series II, if ‘x’ is the right term, then find which of the following statement(s) are true.

I. x/124 is a factor 6 and 8.

II. x + 1069 is a perfect cube.

III. x/961 is a perfect square.

Solution

Series I: 18 17 32 93 374 1835 (18-1) x 1 = 17 (17 - 1) x 2 = 32 (32 - 1) x 3 = 93 (93 - 1) x 4 = 368 (368 - 1) x 4 = 1835 Therefore, 368 will come instead of 374. Series II:The pattern is: 202 × 19 = 7600 192 × 18 = 6498 182 × 17 = 5508 172 × 16 = 4624 162 × 15 = 3840 152 × 14 = 3150 So, 3844 will be replaced by 3840. so, 374 will be replaced by 368. Alternate Method: 203-20 = 7600 193-19 = 6498 183-18 = 5508 173-17 = 4624 163-16 = 3840 153-15 = 3150 So, 3844 will be replaced by 3840. Now from second series, x = 3844 From statement I, X/124 is a factor 6 and 8 => 3840/124 = 31 statement I not follows From statement II: X + 1069 is a perfect cube. => 3844 + 1069 = 4913, is a perfect cube of 17 Hence, statement II follows From statement III: x/961 is a perfect square => 3844/961 = 4, is a perfect square. Hence, statement II and III follows.