The sequences $3,20,37,54,71, \ldots$ and $16,27,38,49,60,71, \ldots$ each have 71 as a common term. The next term that these sequences have in common is
(A) 115
(B) 187
(C) 258
(D) 445
(E) 1006
The sequences $3,20,37,54,71, \ldots$ and $16,27,38,49,60,71, \ldots$ each have 71 as a common term. The next term that these sequences have in common is
(A) 115
(B) 187
(C) 258
(D) 445
(E) 1006

## Solution

The first sequence increases by a constant value of 17 and the second by a constant value of 11 . After 71, the next common term will be 71 plus the Lowest Common Multiple of 11 and 17. Since the L.C.M. of 11 and 17 is 187 the next term will be $71+187=258$.

ANSWER: (C)