Beginning Algebra
Answer/Discussion to Practice Problems
Tutorial 35: Reasoning Skills
Answer/Discussion
to 1a
1, 1, 3, 15, 105, ...
When you see a big jump in numbers all of the sudden  we start small
with 1, 1, 3, 15, and then all of the sudden we are at 105  a good
place to start is multiplication or exponents. It is not a 100% rule,
but it gives you a starting place. It looks like we have 1 (1),
1 (3), 3 (5),
15 (7), 105,...There is a pattern
in multiplication, we are always multiplying the next odd integer.
Final Answer:
The pattern is to multiply the next odd number. The next three
terms would have to be 945, 10395, 135135, since 105(9) = 945, 945(11) = 10395, and 10395(13) = 135135. 
Answer/Discussion
to 1b
1000, 200, 40, 8, 1.6, ...
Since the numbers are going down from term to term, chances are we are
either subtracting or dividing. In this case we are dividing.
We have 1000 divided by (5), 200 divided
by (5), 40 divided by (5),
8 divided by (5), 1.6, ....
Looks like we are always dividing by 5 to get to the next term.
Final Answer:
The pattern is dividing by 5. The next three terms are .32,
.064, and .0128 since 1.6/(5) = .32, .32/(5) = .064, .064/(5)
= .0128. 
Answer/Discussion
to 1c
5, 5, 10, 15, 25, ...
The numbers are going up again, so it is probably a sequence in addition,
multiplication and/or exponents. Since it doesn't go up high quickly,
I'm thinking it is addition. Looking at it closer, I see that we
are always adding the two previous terms to get to the next term.
This is a Fibonnaci sequence  discussed in the lesson  with starting
values of 5 and 5.
Final Answer:
The pattern is adding the two previous terms to get to the next
term.
The next three terms would be 40, 65, and 105 since 15
+ 25 = 40, 25
+ 40 = 65, 40
+ 65 = 105. 
Answer/Discussion
to 2a
It looks like several things change throughout this sequence.
It starts with one line and then one circle then it has two lines and two
circles and then three lines. So, it is alternating between lines
and circles and each time it alternates it adds one more of that figure.
So the next five figures would be:
Note that we stopped at the fifth one, if we would have continued, there
would be a total of four lines that follow the three circles. 
Answer/Discussion
to 3a
A. Suzy and John always eat lunch with the friend that plays in
the band.
B. Sally and Tom carpool with the one who likes to sew.
C. John and the friend that likes to cook visited the one who
likes to sew.
Question: Who is the friend that likes to sew?
You can use a process of elimination on this problem. Statement
A, Suzy and John always eat lunch with the friend that plays in the
band, doesn't let us definitively eliminate anyone from being the one who
likes to sew.
However, statement B, Sally and Tom carpool with the one who likes
to sew, eliminates Sally and Tom from being the one who likes to sew.
Statement C, John and the friend that likes to cook visited the
one who likes to sew, eliminates John.
The only one that could be (100%, without a doubt) the one who likes
to sew is Suzy. 
Last revised on August 6, 2011 by Kim Seward.
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