Identify the logic of the below given series and given answer.

Series I :: 1840, 1719, (P), 1694, 1890, 1665, 1921

Series II :: 175, 481, 753, 993, (Q), 1385

Which of the following statements is/are true?

(i) The value of Q is a prime number.

(ii) P = (2Q-543)

(iii) (P/6) + (Q/2) = 912

Solution

Series I 1840-11 ² = 1840-121 = 1719 1719+12 ² = 1719+144 = 1863 (P) 1863-13 ² = 1863-169 = 1694 1694+14 ² = 1694+196 = 1890 1890-15 ² = 1890-225 = 1665 1665+16 ² = 1665+256 = 1921 So here P = 1863 Series II 175+18x17 = 175+306 = 481 481+17x16 = 481+272 = 753 753+16x15 = 753+240 = 993 993+15x14 = 993+210 = 1203 (Q) 1203+14x13 = 1203+182 = 1385 So here Q = 1203 (i) The value of Q is a prime number. The above given statement is not true. Because the value of ‘Q’ is not a prime number. (ii) P = (2Q-543) 1863 = (2x1203-543) 1863 = (2406-543) 1863 = 1863 The above given statement is true. Because this equation is satisfied. (iii) (P/6) + (Q/2) = 912 (1863/6) + (1203/2) = 912 310.5 + 601.5 = 912 912 = 912 The above given statement is true. Because this equation is satisfied.