L Stands for Live
Living the problem means pretending you’re actually
in the situation described in the word problem. To do
this effectively, make up details concerning the events
and the people in the problem as if you were part of
the picture. This process can be done as you are read-
ing the problem and should take only a few seconds.
V Stands for View
View the problem with different numbers while keep-
ing the relationships between the numbers the same.
Use the simplest numbers you can think of. If a prob-
lem asked how long it would take a rocket to go
1,300,000 miles at 650 MPH, change the numbers to
300 miles at 30 MPH. Solve the simple problem, and
then solve the problem with the larger numbers the
same way.
E Stands for Eliminate
Eliminate answers you know are wrong. You may also
spend a short time checking your answer if there is
time.
Sample Question
Solve this problem using the SOLVE steps described
above.
1. There are 651 children in a school. The ratio of
boys to girls is 4:3. How many boys are there in
the school?
a. 40
b. 325
c. 372
d. 400
e. 468

Answer
1. Subject Experience: You know that 4 and 3 are
only one apart and 4 is more. You can conclude
from this that boys are a little over half the school
population. Following up on that, you can cut 651
in half and eliminate any answers that are under
half. Furthermore, since there are three numbers
in the problem and two are paired in a ratio, you
can conclude that this is a ratio problem. Then
you can think about what methods you used for
ratio problems in the past.
2. Organize: The clue word total means to add. In
the context in which it is used, it must mean girls
plus boys equals 651. Also, since boys is written
before girls, the ratio should be written Boys:Girls.
3. Live: Picture a group of three girls and four boys.
Now picture more of these groups, so many that
the total would equal 651.
4. View: If there were only 4 boys and 3 girls in the
school, there would still be a ratio of 4 to 3. Think
of other numbers that have a ratio of 4:3, like 40
and 30. If there were 40 boys and 30 girls, there
would be 70 students in total, so the answer has to
be more than 40 boys. Move on to 400 boys and
300 girls—700 total students. Since the total in the
problem is 651, 700 is too large, but it is close, so
HOT TIP
Don’t try to keep a formula in your head as you solve the
problem. Although writing does take time and effort, jot-
ting down a formula is well worth it for three reasons: 1) A

formula on paper will clear your head to work with the
numbers; 2) You will have a visual image of the formula
you can refer to and plug numbers into; 3) The formula will
help you see exactly what operations you will need to per-
form to solve the problem.
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the answer has to be less than 400. This would
narrow your choices to two.
5. Eliminate: Since you know from the step above
that the number of students has to be less than
400, you can eliminate d and e. Since you know
that the number of boys is more than half the
school population, you can eliminate a and b. Yo u
are left with c, the correct answer.
Quick Tips and Tricks
Below is a miscellaneous list of quick tips to help you
solve word problems.
Work From the Answers
On some problems, you can plug in given answers to
see which one works in a problem. Start with choice c.
Then if you need a larger number, go down, and if you
need a smaller answer, go up. That way, you don’t have
to try them all. Consider the following problem:
1. One-fifth of what number is 30?
a. 6
b. 20
c. 50
d. 120
e. 150

Tr y c:
ᎏ
1
5
ᎏ
of 50 is 10. A larger answer is needed.
Tr y d:
ᎏ
1
5
ᎏ
of 120 is 24. Not yet, but getting closer.
Tr y e:
ᎏ
1
5
ᎏ
of 150 is 30—Bingo!
Problems with Multiple Variables
If there are so many variables in a problem that your
head is spinning, put in your own numbers. Make a
chart of the numbers that go with each variable so
there is less chance for you to get mixed up. Then write
your answer next to the given answer choices. Work
the answers using the numbers in your chart until one
works out to match your original answer. In doing this,
avoid the numbers 1 and 2 and using the same num-
bers twice. There may appear to be two or more right
answers if you do.
Sample Multi-Variable Question

2. A man drove y miles every hour for z hours. If he
gets w miles to the gallon of gas, how many gal-
lons will he need?
a. yzw
b.
ᎏ
y
w
z
ᎏ
c.
ᎏ
y
w
z
ᎏ
d.
ᎏ
w
z
y
ᎏ
e.
ᎏ
z
y
w
ᎏ
Answer
Picture yourself in the situation. If you drove 4 (y)

miles every hour for 5 (z) hours, you would have
driven 20 miles. If your car gets 10 (w) miles to the gal-
lon, you would need 2 gallons. Since 2 is your answer,
plug the numbers you came up with into the answer
choices and see which one is correct. Choice b equals
2 and is therefore correct.
a. yzw 4 × 5 × 10 ≠ 2
b.
ᎏ
y
w
z
ᎏ
ᎏ
4
1
×
0
5
ᎏ
= 2
c.
ᎏ
y
w
z
ᎏ
ᎏ
4
1

×
0
5
ᎏ
≠
2
d.
ᎏ
w
z
y
ᎏ
ᎏ
10
5
× 4
ᎏ
≠
2
e.
ᎏ
z
y
w
ᎏ
ᎏ
5 ×
4
10
ᎏ

≠
2
Let the Answers Do the Math
When there is a lot of multiplication or division to do,
you can use the answers to help you. Suppose you are
asked to divide 9,765 by 31. The given answers are as
follows:
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a. 324
b. 316
c. 315
d. 314
e. 312
You know then that the answer will be a three-
digit number and that the hundreds place will be 3.
The tens place will either be 1 or 2, and more likely 1
because most of the answers have 1 in the tens place.
Your division problem is practically worked out for
you.
Problems with Too Much or Too Little
When you come across a problem that you think you
know how to answer, but there seems to be a number
left over that you just don’t need in your equation,
don’t despair. It could very well be that the test writers
threw in an extra number to throw you off. The key to
not falling prey to this trick is to know your equations
and check to make sure the answer you came up with
makes sense.
When you come across a problem that doesn’t

seem to give enough information to calculate an
answer, don’t skip it. Read carefully, because some-
times a question asks you to set up an equation using
variables, and doesn’t ask you to solve the problem at
all. If you are expected to actually solve a problem with
what seems like too little information, experiment to
discover how the information works together to lead to
the answer. Try the CA tips.
More than One Way to Solve a Problem
Some questions ask you to find the only wrong way to
solve a problem. Sometimes these are lengthy ques-
tions about children in a classroom who get the right
answer the wrong way and the wrong answer the right
way. In this type of question, do the computation
yourself, and work from the answers. The choice that
gives an answer different from the others has to be the
wrong answer. Consider these choices:
a. 5% of 60
b.
ᎏ
1
5
00
ᎏ
× 60
c. 0.05 × 60
d. 5 × 60 ÷ 100
e. 5 × 60
All of the answers compute to 3 except choice e,
which turns out to be 300. Therefore, e must be the

correct answer.

Math 11: Logic and
Venn Diagrams
You deserve a break after all your hard work on math
problems. This lesson is shorter than the others; unless
logic problems give you a lot of trouble, you can prob-
ably spend less than half an hour on this lesson.
If Problems
If problems are among the easiest problems on the test
if you know how to work them. A genuine if problem
begins with the word if and then gives some kind of
rule. Generally, these problems mention no numbers.
In order for the problem to be valid, the rule has to be
true for any numbers you put in.
Sample If Question
The following is a typical if problem. Experiment with
this problem to see how the answer is always the same
no matter what measurements you choose to use.
One Success Step for If Problems
Pick some numbers and try it out!
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1. If the length and width of a rectangle are
doubled, the area is
a. doubled
b. halved
c. multiplied by 3
d. multiplied by 4
e. divided by 4

Answer
First of all, choose a length and width for your rectan-
gle, like 2′ by 3′. The area is 2 × 3, or 6. Now double the
length and the width and find the area: 4 × 6 = 24. 24
is 4 times 6, so d must be the answer. Try a few differ-
ent numbers for the original length and width to see
how easy these types of questions can be.
Practice
Try another one:
2. If a coat was reduced 20% and then further
reduced 20%, what is the total percent of dis-
count off the original price?
a. 28%
b. 36%
c. 40%
d. 44%
e. 50%
Answer
Since this question concerns percents, make the coat’s
beginning price $100. A 20% discount will reduce the
cost to $80. The second time 20% is taken off, it is
taken off $80, not $100. Twenty percent of 80 is 16.
That brings the cost down to $64 (80 – 16 = 64). The
original price of the coat, 100, minus 64 is 36. One
hundred down to 64 is a 36% reduction. So two suc-
cessive discounts of 20% equal not a 40%, but a 36%
total reduction.
Venn Diagrams
Venn diagrams provide a way to think about groups in
relationship to each other. Words such as some, all, and

none commonly appear in these types of questions.
In Venn diagram problems, you are given two or
more categories of objects. First, draw a circle repre-
senting one of the categories. Second, draw another
circle representing the other category. Draw the second
circle according to these rules:
1. If the question says that ALL of a category is the
second category, place the second circle around
the second category.
Example: All pigs (p) are animals (a).
2. If the question says that SOME of a category is
the second category, place the second circle so
that it cuts through the first circle.
Example: Some parrots (p) are talking birds (t).
3. If the question says NO, meaning that none of
the first category is in the second category, make
the second circle completely separate from the
first.
Example: No cats (c) are fish (f).
HOT TIP
When choosing numbers for if problems, choose small
numbers. When working with percents, start with 100.
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Sample Venn Diagram Question
3. All bipeds (B.) are two headed (T.H.). Which
diagram shows the relationship between bipeds
and two-headed?
a.
b.

c.
d.
e.
Answer
The question says ALL, so the two-headed shape, in
this case, a square, is around the triangle denoting
bipeds. The answer is d.
More than Two Categories
Should there be more than two categories, proceed in
the same way.
Example: Some candy bars (c) are sweet (s), but no
bananas (b) are candy bars.
The sweet circle will cut through the candy bar
circle. Since the problem did not specify where
bananas and sweet intersect, bananas can have several
positions. The banana circle can be outside both circles
completely:
The banana circle can intersect the sweet circle:
Or the banana circle can be completely inside the
sweet circle but not touching the candy bar shape:
HOT TIP
Even when there are no pictures of Venn diagrams in the
answers, you can often solve this type of problem by
drawing the diagram one way and visualizing all the
possible positions of the circles given the facts in the
problem.
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
Writing 1: Outlining the Essay

You will be required to write two essays during your
test time. One essay may be a persuasive essay, and the
other a narrative or story essay. The persuasive essay
question will ask your opinion, usually on a current or
well-known issue. You will need to convince the reader
of your side of the issue. The story essay question will
often concern a person or event in your life that has
influenced you in some way. You will need to commu-
nicate your experience to the reader in such a way that
the reader will be able to understand and appreciate
your experience. The evaluators are not concerned
about whether or not the facts are correct—they are
solely judging your writing ability.
Unlike math, writing is flexible. There are many
different ways to convey the same meaning. You can
pass the test with any logical arrangement of para-
graphs and ideas that are “clearly communicated.”
Most CBEST and English instructors recommend a
five-paragraph essay, which is an easy and acceptable
formula. The five-paragraph essay assures that your
ideas are logically and effectively arranged, and gives
you a chance to develop three complete ideas. The
longer and richer your essay, the better rating it will
receive.
The first step in achieving such an essay is to
come up with a plan or outline. You should spend the
first four or five of the 30 minutes allowed in organiz-
ing your essay. This first writing lesson will show you
how. The rest of the writing lessons will show you
where to go from there.

Outlining the Persuasive Essay
Below are some tips on how to use your first four or
five minutes in planning a persuasive essay, based on
an essay topic similar to the one found in the diagnos-
tic exam in Chapter 3.
Sample Persuasive Essay Question
1. In your opinion, should public schools require
student uniforms?
Minute 1
During the first minute, read the question carefully
and choose your side of the issue. If there is a side of
the issue you are passionate about, the choice will be
easy. If you know very little about a subject and do not
have an opinion, just quickly choose a side. The test
scorers don’t care which side you take.
Minutes 2 and 3
Quickly answer as many of the following questions as
apply to your topic. These questions can be adapted to
either side of the argument. Jot down your ideas in a
place on your test booklet that will be easily accessible
as you write. Examples of how you might do this for
the topic of school uniforms are provided here.
1. Do you know anyone who might feel strongly
about the subject?
Parents of school-age children, children, uni-
form companies, local children’s clothing
shops.
2. What reasons might they give for feeling the way
they do?
Pro: Parents will not have to worry about

what school clothing to buy for their children.
Children will not feel peer pressure to dress a
certain way. Poorer children will not feel that
their clothing is shabbier or less fashionable
than that of the more affluent children. Uni-
form companies and fabric shops will receive
business for the fine work they are doing.
Con: Parents will not be able to dress their
children creatively for school. Children will
not have the opportunity to learn to dress and
match their clothes very often. They will not
be able to show off or talk about their new
clothes. Clothing shops will lose money,
–CBEST MINI-COURSE–
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