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CAT 2019 Slot 2 QA Question & Solution

AlgebraMedium

Question

The number of common terms in the two sequences: 15, 19, 23, 27, . . . . , 415 and 14, 19, 24, 29, . . . , 464 is

Options

21
20
18
19

Solution

A: $15, 19, 23, 27, \ldots, 415$

B: $14, 19, 24, 29, \ldots, 464$

Here the first common term = $19$

Common difference = $LCM(5, 4) = 20$

$19 + (n-1)20 \le 415$

$(n-1)20 \le 396$

$(n-1) \le 19.8$

$n=20$