Question

A tours and travel agency accepts reservations if the number of tourists in a group is a factor of $12$. Mr. Shroff and his family plan to take a break during their summer vacation. Shroff's family has a total of $5$ members. How many reservations Mr. Shroff needs to do from the travel agency in order to keep the number of bookings to a minimum?

• A. $1$
• B. $5$
• C. $6$
• D. $12$

Answer 1

The correct option is C $6$

We know,
$1\times 12=12$
$2\times 6=12$
$3\times 4=12$

$\therefore$ The factors of $12$ are $1,2,3,4,6$ and $12$.

As per the question, the tours and travel agency only accepts booking if the number of tourists in a group is a factor of $12$, i.e., for the reservation, the number of people in a group should be $1$ or $2$ or $3$ or $4$ or $6$ or $12$.

Shroff's family has $5$ members. Hence, the number of seats required to accommodate $5$ members is $5$, but which is NOT a fcator of $12$.

Hence, the minimum number of seats, which is a factor of $12$ and also comfortably accomodate $5$ members is $6$.

$\therefore$ Option (c.) is the correct one.