The series given below contains a missing number 'P'. Find the value of 'P' and determine which among the given three statement(s) is/are true. 74, 290, 241, 753, 672, 'P', 1551 I: The nearest perfect square number to 'P' is 1600 II: 'P' is divisible by 11 III: (P + 28) is a multiple of 50.

Explanation

4 Detailed solution: The given number series follows the pattern of alternate addition and subtraction of cubes and squares, respectively. 74 + 6³ = 290 290 – 7² = 241 241 + 8³ = 753 753 – 9² = 672 672 + 10³ = 1672 1672 – 11² = 1551 So, 'P' = 1672. For I: Nearest perfect square number of 1672, is 41² = 1681 So, statement I is false. For II: 1672 ÷ 11 = 152 So, statement II is true. For III: P + 28 = 1672 + 28 = 1700 Since, 1700 = 34 X 50 So, statement III is true.