Question :
Directions : Read the data carefully and answer the following question.
Below given are two series. Series 1 contains one wrong term and series 2 contains one missing term. Both the series have different pattern.
Series 1: 56, 181, 431, 806, 1406, 1931
Series 2: A, A + 5B, 5B + 8C, A + 4C + 5D, ?, 2085
Note:
I: (M+6) and N are the wrong and correct term of series 1 respectively.
II: (M/A) and (N+7)/B are the roots of equation t2 - 121t + 2020 = 0, where A > B.
III: (B - C)/(A - D) = 12 and 3C = D + 4
What is the value of (M - C) + (N - D)?
Solution :
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
(M - C) + (N - D) = (1400 - 25) + (1306 - 71) = 1375 + 1235 = 2610
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