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The number of common terms in the two sequences - Quantitative Aptitude - Sequence and series

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The question below is from previous year CAT question from CAT 2019 exam comes from CAT Sequence and series: The number of common terms in the two sequences

Find out by answering this question which tests an aspirant’s Quantitative Ability Skills.

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CAT 2019 - Slot 2 - Quantitative Aptitude - Sequence and series - Question 3 - The number of common terms in the two sequences

Q. 3: The number of common terms in the two sequences: 15, 19, 23, 27, 415 and 14, 19, 24, 29, , 464 is

1. 18

2. 19

3. 21

4. 20

Common difference of first series 15, 19, 23, 27…= 4

 

Common difference of 2nd series 14, 19, 24, 29 .. =5

 

So common difference of the series formed by common terms = 4*5 = 20

 

First common term = 19

 

So series = 19, 39 , 59, … last term < 415

 

nth term = 19+20(n-1) = 20n – 1 < 415

 

so 20n < 416

 

n < 416/20 = 20.8

 

so n = 20

 

 

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