?

Abstract Algebra

Free Version

Upgrade subject to access all content

Moderate

Using Congruence Systems

ABSALG-BENVYT

A shepherd has lost track of the size of his flock. He remembers that when he sets up drinking stations for the sheep, each station fits 5 sheep except the last station, which fits 4 sheep.

He also remembers that when he hires workers to groom the sheep, each worker grooms 7 sheep except for the last worker, who only grooms 5. Finally, he remembers owning at least 60 sheep, and that his farm is too small to hold more than 100 sheep.

How many sheep are in his flock?

A

19

B

89

C

98

D

54

E

There isn't enough information to tell.