CAT 2019 Slot 2 — QA Question 28
Arithmetic ProgressionEasy
The number of common terms in the two sequences: 15, 19, 23, 27, ...... , 415 and 14, 19, 24, 29, ...... , 464 is
Answer & solution
20
- B
18
- C
21
- D
19
Solution
First series - 15, 19, 23, 27, ......, 415 ⇒ Common difference = 4
Second series - 14, 19, 24, 29, ......, 464 ⇒ Common difference = 5
Common terms in both sequences = 19, 39, 59, ...., (Common difference = LCM (4,5) = 20)
Now :
19, 39, 59, ...., = (20 - 1), (40 -1), (60 -1), ...., (400-1) (There is no room for 419, as the first series ends at 415)
399 = 400 - 1 = 20 × 20 - 1
Hence, the number of common terms in the two sequences = 20
Hence, option (a).