Thinking Skills 1 Sections 2.2-2.5 and Problem Solving Chapter 1 Review
1. Determine if the following passages are arguments. If yes, write the argument in standard
format. If it is not an argument, determine what conclusion you could draw from the
passage.
a. The road was slippery because it had been raining. In bad weather you have to keep a safe
distance. The blue car was very close to the one in the front.
b. There’s no point in going swimming until the rain stops. I hate being cold and wet, and the
pool water isn’t heated. So we need to find something else to do this afternoon.
2. In each of the questions, the passage provided is an argument. In each passage, your task
is to say which of X, Y, and Z are reasons and which is the conclusion.
a. X: Someone has just come into the shop and paid me with four banknotes that all have the
same serial number. Y: They must be forgeries. Z: Genuine banknotes would all have
different serial numbers.
b. X: Boxing should be banned once and for all. Y: No sport should be allowed in which the
object is to injure an opponent. Z: Boxers quite deliberately set out to injure each other.
3. Given the following arguments, identify the main conclusion and the reasons using standard
format.
a. It is almost inevitable that some athletes will take drugs to improve their performance. All
too often performance-enhancing drugs make the difference between winning and losing.
The rewards for wining are so great that the risk of being caught using drugs may well seem
worth taking.
b. You won’t see as many people swimming off this beach as you will further north. Just north
of here the Gulf Stream comes in from the ocean and flows along the coast, making the
water much warmer. Besides, there is far more pollution in the sea here than there is
anywhere else.
4. Complete each problem. Each answer must include a diagram, an explicit solution, and a
well-written explanation of how you arrived at your answer.
a. Jenny’s model train is set up on a circular track. Six telephone poles are spaced evenly
around the track. The engine of Jenny’s train takes 10 seconds to go from the first pole to
the third pole. How long would it take the engine to go all the way around the track?
b. Curly used a shovel to dig his own swimming pool. He figured he needed a pool because
digging it was hard work and he could use it to cool off after working on it all day. He also
planned to build a rectangular concrete deck around the pool that would be 6 feet wide at all
points. The pool is rectangular and measures 14 feet by 40 feet. What is the area of the
deck?
c. There is a rumor that Daddy Warbucks is starting a new airline. He plans to serve six cities:
San Francisco, Los Angeles, Dallas, Chicago, New York, and Miami. There will be direct
flights between each pair of cities. How many different routes will this create?
Answers to Review
1a.
Not an argument. Could conclude that the blue car caused the crash because it was not a safe
distance away.
1b.
R1: There’s no point in going swimming until the rain stops.
R2: I hate being cold and wet
R3: The pool water isn’t heated
MC: We need to find something else to do this afternoon.
2a.
2b.
Reasons: X, Z Conclusion: Y
Reasons: Y,Z Conclusion: X
3a.
R1: All too often performance-enhancing drugs make the difference between winning and
losing
R2: The rewards for wining are so great that the risk of being caught using drugs may well
seem worth taking.
MC: It is almost inevitable that some athletes will take drugs to improve their performance.
3b.
R1: Just north of here the Gulf Stream comes in from the ocean and flows along the coast,
making the water much warmer.
R2: There is far more pollution in the sea here than there is anywhere else.
MC: You won’t see as many people swimming off this beach as you will further north.
4a.
Solution: 30 seconds
Explanation: It takes 10 seconds for the train to cover
one-third of the track, so it will take 30 seconds for the
train to cover the entire track.
4b.
Solution: 792 ft2
Explanation: If the 6’ wide deck is to surround the pool, the
dimensions of the pool and deck are 52 feet by 26 feet. The
total area can be found by multiplying 52’ x 26’= 1352 ft2.
However since we are asked for only the area of the deck,
we must subtract the area of the pool which is 14 X 40 = 560
ft2. The difference is the area of the deck: 1352 – 560 = 792
ft2.
4c.
Solution: 15 different routes
Explanation: By drawing a diagram and connecting the cities, it can
be determined that there are 15 different routes. Also, there are six
cities with five different connections for a total of 30 connections.
However, since the connections are two-way connections, it is
necessary to divide by two, thereby giving 15 connections.