What is the number of common terms in the two sequences: 15, 19, 23, 2

Question

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

A. 18
B. 19
C. 20
D. 21
E. 22

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arvind910619 · Answer

Imo C

First common value is 19 and second common value is 39. So we see that the the common values follows an arithmetic progression where the common difference is the LCM of the common difference of both the original progression i.e LCM of 5 and 4 = 20.
So the progression is 19,39,59,79,99,119 and so on. 
We see that there are 5 values in each hundred.

5 values from 1-100 
5 values form 101-200
5 values from 201-300
5 values from 301-400
There will be no value above 400 as the value will be 419 which will not be common to both the progression.
Total common values = 20

ArunSharma12 · Answer

first sequence has a common difference 5
second sequence has a common difference 4
so If we keep adding 20 to first common term we will keep getting next common terms.
19,39,59,79,99...199,..,299..,399,419. 419 is not part of the first sequence so last common term is 399.
399 = 19 + (n-1)*20
(n-1)*20=380
(n-1)=19; n =20
Ans: C

rajatchopra1994 · Answer

Explanation:

Concept Used: A.P

15, 19, 23,....., 415 has a common difference of 4 ;
14, 19, 24,....., 465 has a common difference of 5

LCM of 5 and 4 = 5x4 = 20.

Adding 20 to the first common term i.e 19, we will get other terms, as we have to find till 415.
so progression will be 19,39,59,79,99 & last term will be 399
so,number of terms will be:
399 = 19 + (n-1)*20
380 = (n-1)*20
(n-1) = 19
n = 20

IMO-C

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What is the number of common terms in the two sequences: 15, 19, 23, 2

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What is the number of common terms in the two sequences: 15, 19, 23, 2

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