Question:-
Option (A)
78
Option (B)
19
Option (C)
20
Option (D)
77
Option (E)
22
Correct Option:
C
Question Solution:
The first sequence can be written as 17, 17 + 4, 17 + 8, ....... , 417 and second sequence can be written as 16, 16 + 5, 16 + 10, ....... , 466
The common difference for the first sequence is 4 and that for the second sequence is 5 and both the sequences have 21 as the first common term.
∴ Common terms are 21, 21 + L, 21 + 2L, .....
[Here, L = LCM of 4 and 5 = 20]
∴ Common terms are 21, 21 + 20, 21 + 40, .....
The common terms have a common difference of 20 and first term as 21.
∵ 417 − 21 = 396 and 396/20 = 19.8,
∴ 19 terms are common, other than 21.
∴ The total number of terms which are common to both the sequences = 19 + 1 = 20
Hence, option 3.