A certain roller coaster ride has more than 29 people waiting in line to board. If riders are let on only in groups of 5 there will be 2 riders that do not get on. If the riders are let on only in groups of 6 all riders will be able to get on the roller coaster. If less than 112 people are in the line, which of the following is the largest possible value of number of people in the line?
Choose the most appropriate option:  A) 112  B) 108  C) 106  D) 102  E) 96
No which leaves 2 as remainder when divided by 5 = ( 7, 12, 17, .....)   No which leaves 0 remainder when divided by 6 = (6, 12, 18...)   Common no in two sets = 12   So the numbers which satisfy this condition will be of the form 30x + 12.   Now we know that the no is greater than 29 and has to be less than 112...so option which satisfies is 102   ANSWER:102
<result>D</result>
A certain roller coaster ride has more than 29 people waiting in line to board. If riders are let on only in groups of 5 there will be 2 riders that do not get on. If the riders are let on only in groups of 6 all riders will be able to get on the roller coaster. If less than 112 people are in the line, which of the following is the largest possible value of number of people in the line?