CAT 2008 | Question: 12

Question

The number of common terms in the two sequences $17, 21, 25,\dots,417$ and $16, 21 26,\dots,466$ is

• A. $78$
• B. $19$
• C. $20$
• D. $27$
• E. $22$

Answer 1

Alternate method :

difference of first series = 4, difference of second series =5 

so difference of common series will be always  LCM (4,5 )= 20 .

by seeing both series ...we can easly find first term = 21,

and last term of common series will be less than or equal to 417 ,bcoz common series will go up to common of both and first sequence is till 417 .

series like 21 ,41,61.... 401....(bcoz 401%20=1 ,) 

so 401= 21+ (n-1)20 

      380/20= (n-1)

    n= 20 hence answe is 3)

Answer 2

No of terms in first sequence be n

417=17+(n-1)4

n=101

No of terms in second seq be m

466=16+(m-1)5

m=91

First common term is 21 next is 41

Common difference=20

Now last common term will be less than or equal to 417 and not 466

Last term in common seq will be 401

401=21+(k-1)20

380/20=k-1

k=20