• Numerical Ability - Number System
Question

The number of common terms to the two sequences 17, 21, 25 …. 417 and 16, 21, 26 …. 466 is : 

  • A) 19 
  • B) 20
  • C) 21 
  • D) 84
  • E) None of these
Solution

Answer (B): 20

Explanation:

First series is incremented by 4

Second series is incremented by 5

First common term is 21

LCM(4,5)=20

Therefore, the common terms are 21, 41, 61, ... (incremented by 20)

As we can see, the common terms form an arithmetic progression with first term = 21, common difference = 20

This series is of the form 20n+1 and last common term is therefore 401 (when n=20)

Number of such terms =401−21/20 +1=20.

Answer (B): 20

Explanation:

First series is incremented by 4

Second series is incremented by 5

First common term is 21

LCM(4,5)=20

Therefore, the common terms are 21, 41, 61, ... (incremented by 20)

As we can see, the common terms form an arithmetic progression with first term = 21, common difference = 20

This series is of the form 20n+1 and last common term is therefore 401 (when n=20)

Number of such terms =401−21/20 +1=20.
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