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The number of common terms in the two sequences: 15, 19, 23, 27, ...... , 415 and 14, 19, 24, 29, ...... , 464 is
The number of common terms in the two sequences: 15, 19, 23, 27, ...... , 415 and 14, 19, 24, 29, ...... , 464 is
- 20
- 18
- 21
- 19
CAT-2019 question
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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, observing the new series
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 x 20 -1
Hence, the number of common terms in the two sequences = 20
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