Latest CAT Aptitude Question SOLUTION: The number of common terms in the two sequences 17, 21, 25,.............. , 417 and 16, 21, 26,............,466 is (1) 78 (2) 19 (3) 20

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(#M40019857) CAT Numerical Ability question Keep an EYE

The number of common terms in the two sequences 17, 21, 25,.............. , 417 and 16, 21, 26,............,466
is
(1) 78 (2) 19 (3) 20 (4) 77 (5) 22

Asked In CAT mandeep (10 years ago)

Unsolved Read Solution (6)

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Dipak Liladhar Patil  (10 years ago)

ans (3)20.

first series is increased by 4 and second series is increased by 5
hence LCM(4,5)=20
hence series is 21, 41, 61......
last term is 401%20=1 and not 411 because 411%20=11
d=20, first term=a= 21 last term=l= 401.
by A.P.
401=21+(n-1)20
n=20.

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pramod dusad  (10 years ago)

Common term in series is..... 21,41,61...........

The number which is last common in both series is 401.

so as we know A.P Last term is

Tn = a+(n-1)d
401 = 21+(n-1)20
380 = (n-1)20
19 = n-1
20 = n

so the ans is 20.

Is this solution Helpfull? Yes (7) | No   

Aman Agarwal  (10 years ago)

ans should be: 20
because common terms are in the sequence : 21, 41, 61, 81, 101 ....., 401
so this becomes a AP, so we get
401 = 21 + (n-1)20
n= 20

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suraj prasad  (10 years ago)

19
the numbers which can be matched are like to be 21,41,61.......
so they are in A.P having nth term close to be 417
so 21+(n-1)20=417
calculating n we can get 19 as answer

Is this solution Helpfull? Yes (2) | No (7)  

Meghal Aggarwal  (10 years ago)

for both the sequence the last term which is common is 401
so for first sequence i.e, 17,21,25,......417 the common difference is 4 and for second sequence i.e, 16,21,26,........466 the common difference is 5
now we will subtract first common term i.e, 21 from the last term twhich is 401 then we will get 380 as result
now dividing 380 by the common differences of both the series i.e, ((380/4)=95) and ((380/5)=76)
as we have to determine the common terms so...
number of common terms=95-76=19

so, the number of common terms between both the series are 19

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vanshika  (10 years ago)

as u can see series is keep on increasing and next value is bigger than previous .... through this we can eliminate all other options except 77 and 78... and in first series every num. is odd so through hit and trial method we can say that 77 is the ans

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