Previous Year Questions

Series 1:

56 + 125 = 181

181 + 250 = 431

431 + 375 = 806

806 + 500 = 1306 (not 1406)

1306 + 625 = 1931

M + 6 = 1406 => M = 1400

N = 1306

t² - 121t + 2020 = 0

t² - 20t - 101t + 2020 = 0

(t - 20)(t - 101) = 0

t = 20, 101

When M/A = 20 => A = 1400/20 = 70

(N+7)/B = 101 => B = (1306+7)/101 = 13

When M/A = 101 => A = 1400/101 = 13.86

(N+7)/B = 20 => B = (1306+7)/20 = 65.65

So, A = 70, B = 13

(B - C)/(A - D) = 12

(13 - C)/(70 - D) = 12

C = 12D - 827 ----(1)

and 3C = D + 4 ----(2)

From eqn (1) and (2) -

C = 25 and D = 71

Series 2:

A, A + 5B, 5B + 8C, A + 4C + 5D, ?, 2085

70, 135, 265, 525, ?, 2085

70*2 - 5 = 135

135*2 - 5 = 265

265*2 - 5 = 525

525*2 - 5 = 1045

1045*2 - 5 = 2085

Missing term = 1045

From I:

A + C = 70 + 25 = 95

B + D = 13 + 71 = 84

A + C ≥ B + D

Statement I is correct.

From II:

Difference between 4^th terms of both series = 806 - 525 = 281

Product of B and C = 13*25 = 325

Difference between 4^th terms of both series < product of B and C.

Statement II is not correct.

From III:

M = 1400

D - 1 = 71 - 1 = 70

HCF of 1400 and 70 = 70 = A

Statement III is correct.