Foundations of Mathematics 11
Reasoning To Solve Problems
Name ______________________ Day ___
1. Ann, Bob, Cathy and Derek each work as a doctor, lawyer, teacher or farmer. Use the clues to
find who has which job.
Ann




Cathy is not a teacher or a farmer
Ann is either a teacher or a doctor
Derek is not a doctor or a farmer
The lawyer is a woman
Bob
Cathy
Derek
Doctor
Lawyer
Teacher
Farmer
Conclusions:
Doctor
Lawyer
Teacher
Farmer
2. The sixth grade has a different special class for each day of the school week. Using only three
clues, try to figure out which class is held each day.
M
 Art is two days after Music
 Spanish is earlier in the week than art,
but it follows PE
 Computer class is on Thursday
Conclusions:
Art
Music
Computers
PE
Spanish
Art
Music
Computers
PE
Spanish
Tu
W
Th
F
3. Two friends, Matt and Pat, have just traveled hundreds of miles to finally have a taste of Hank’s
famous treats. Use the clues, the menu, and the chart to determine what kind of hot dogs each
bought, and what toppings each ordered, what side dish each purchased, and how much each
friend spent in all.
Menu
Basic “No Frills” Hot Dog - $1.20
Hot Dog with ketchup and mustard $1.35
Chili Dog with ketchup and mustard - $1.90
Extra Topping: Cheese $.25
Lettuce, Pickles, Onions, Peppers - $.10 each







Side Dishes:
Onion Rings - $.95
Small Fries - $.75
Large Fries - $.95
Applesauce - $.55
Each friend ordered one “dog” and one side dish
Pat paid for her lunch with a $5 bill and received less than $2 in change
Matt does not like ketchup, but he did get four other toppings
Pat does not like onions and is allergic to all dairy products
Neither of them likes peppers
Pat received two fewer toppings than Matt did
Matt chose the lowest-priced side dish
Sandwich
Matt
Pat
Toppings
Side Dish
Price
4. Towards high water in a tidal estuary a line of vessels can usually be seen making its way towards
an inland port. From the clues given below, can you name each of the ships lettered A to D, work
out its port of registration and say what cargo it is bringing into the country?
 The Triton is somewhere behind the ship registered in Antwerp,
which is importing a cargo of textiles
 The name of ship C is the Stella
 The iron ore is in the holds of the Memphis, which is not vessel B
 The home port of the Athena is Rotterdam
 Vessel D, which is not the oil tanker, is not registered in Hamburg
Ships: Athena
Ports: Antwerp
Cargoes Grain
:
Memphis
Hamburg
Iron ore
Stella
Lisbon
Oil
Triton
Rotterdam
Textiles
Port
A
B
Tide
C
D
5. The delivery driver is to deliver packages to each of the eight businesses shown below, but they
are not necessarily meant to visit them in a logical order. Instead, the driver is to follow the
instructions listed here. Help the confused driver plan their route. Number the businesses in the
order in which they should be visited. Write the number of packages to be delivered to each
business in the blank under each shop.
 The second delivery is directly north of the first delivery and has one fewer
package than the first
 Melody’s Music needs all five packages delivered before 11:00 AM
 By the time the paperwork is completed, the packages verified and greetings
exchanged between the driver and the recipient, each deliver takes 15 minutes
 The bank is never the last delivery. It always receives four packages
 Troy’s Toys has the most packages of all. His delivery will contain as many
packages as all other combined
 Pete’s deliveries are live animals which need to be unloaded first when the
store opens at 9:30 AM
 The fourth delivery is directly east of the first delivery and contains twice
the number of packages
 The travel agency and the pet store combined are to receive the same number
of packages as the music store
 The fifth delivery contains three boxes
 The third deliver is two stores west of the second
 The tire store, the grocer, and the pet store will all receive the same number
of packages. They are the only ones to receive this exact amount.