3 e Title

Beginning Algebra
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.