Page 289 - ABCTE Study Guide_Neat

Question

How many more faces does a cube have than a square pyramid?

A 2

B 1

C 3

D 4

Answer

The answer is B. To see how many more faces a cube has than a square pyramid, it is best to draw a
diagram of a square pyramid and a cube:

From the diagrams above, we can see that the square pyramid has five faces and the cube has six.
Therefore, the cube has one more face, so the answer is B.

Before we start having the same problem our model student in the beginning did—that is, being
overwhelmed with too much information—let's have a quick review of all the problem-solving methods
we've discussed so far:

• Sort and prioritize relevant and irrelevant information.
• Represent a problem in different ways, such as words, symbols, concrete models, and
diagrams.
• Generate and use estimations to find solutions to mathematical problems.

Mathematical Mistakes

Along with learning methods and tools for solving mathematical problems, it is important to recognize and
avoid ways to make mathematical errors. This section will review some common errors.

Circular Arguments

These involve drawing a conclusion from a premise that is itself dependent on the conclusion. In other
words, you are not actually proving anything. Circular reasoning often looks like deductive reasoning, but
a quick examination will reveal that it’s far from it. Consider the following argument:

• Premise: Only an untrustworthy man would become an insurance salesman; the fact
that insurance salesmen cannot be trusted is proof of this.
b. Conclusion: Therefore, insurance salesmen cannot be trusted.