Sample CBEST Questions Worked Through, and Tips on Solving Them
We are going to go through 9 common CBEST type questions. Each one will be explained and solved in detail using simple techniques. All of these problems can be solved with some adult logic and basic math skills. If you are iffy on your adding, subtracting, multiplying, and dividing, numbers from 1 to 12, you need to practice that on your own. Also, you should have somewhat of a working knowledge of the techniques and tips in previous sections. There are a few basic rules to live by:
1) It is sometimes easier to spot wrong answers than it is to spot correct
ones.
2) Do preliminary step arithmetic twice. If you get 2 different answers,
do it again. Do not look at how you did it the first time. If you get the
same answer twice, rest assured you did it correctly. Trust me. This in
my opinion is the #1 reason people fail.
3) Double check to make sure you have solved for what you were asked.
4) Don't jump on an answer right away. Read and solve the problem carefully.
Seemingly correct answers are there to fool you. And many people are fooled.
This is my #2 reason why people fail.
5) Work through test using this strategy: The first time through the
test, do all problems you can do quickly first. Put a check mark by the
ones you think you can do, but need more time to solve it. Put an X by
the ones you have no idea how to do. The second time through, do the ones
with a check mark by them. Some of these may turn into X ones. The third
time through, attempt the ones with an X. Guess at all of these you cannot
do. My #3 reason why people fail is they try and do all problems in order.
Forget that. If you concentrate on the ones you CAN do, you have a higher
chance at passing.
6) Use the whole test book, except for the writing pages if you are
taking the writing, as scratch paper.
7) Double check that you are marking the answer for the correct problem.
Circle the answer in your test book first. Then find the problem on your
answer sheet. Put your finger on the answer in the book and bubble it in
the test sheet. All the while glancing back and forth making sure you are
marking the correct answer. You will almost never be able to go back and
check at the end. And who wants to?
8) Be flexible. If you have failed the test before, try looking at
the test in a new way as I show you. Forget about your past math troubles
and how you were taught to always to math problems.
9) Last, but not least, MAKE A PLAN if you can) and WRITE IT DOWN.
More on this as we solve the problems.
So, let's get started!
#1 Mr. Finch is using ribbon in his art class of 34 students. For the
project, each student will need 4 feet 5 inches of ribbon. How much total
ribbon does Mr. Finch need to order?
A. 136 ft
B. 120 ft 2 in
C. 165 ft 8 in
D. 150 ft 2 in
E. 155 ft 3 in
First we write a plan if we can. What do we know we need to do? Write
it down something like this:
1) Multiply 4 feet 5 inches X 34
There is no second step, we just have one.
We do not need to change feet to inches, etc. We will split the problem
up. First, we will multiply 4 x 34 = 136. This tells us that we need at
least 136 feet. But we have not added on the extra inches, so we
know it will be more. That eliminates answers A and B. Next we will do
the inches, 5 x 34 = 170. We do need to change that into feet. But that's
easier than it would have been if we had done it first. And get this: We
do not care about the remainder. The remainder represents the left over
inches. But all answers are so different, it doesn't matter. To change
170 inches into feet, we know we need to divide by 12. That should be easy
for everyone. It goes 14 times. That means we have at most, 14 more feet
to add on to our 136 feet. That means we need 150 feet and some irrelevant
inches. The answer is D. Oh yeah. You do need to know there are 12 inches
in a foot, and perhaps 3 feet to a yard for some problems.
#2 John can staple 5 tests together in about 15 minutes. If he keeps
at this rate, how long would he take to staple 32 tests together?
A. 1 hr 36 min
B. 2 hr 16 min
C. 56 min
D. 3 hr 5 min
E. 1 hr 12 min
This is classic if-then problem. They can all be done similar. We need
to go from 5 tests to 32 tests. Since the rule is 5 tests in 15 minutes,
that will be our starting point. We just keep adding 5 tests and 15 minutes
each time, stopping to check the answers. We will stop as soon as we get
to our goal or we go over.
5 tests in 15 minutes
10 tests in 30 minutes
15 tests in 45 minutes
20 tests in 60 minutes ( Now we know answer C is wrong. )
25 tests in 75 minutes
30 tests in 90 minutes (Now we know answer E is wrong.)
We know we only need 2 more tests and we have gone 1 hr 30 min. Going
once more will give us:
35 tests in 105 minutes (1 hr 45 min) But that is too many tests. Our
answer lies between 30 and 35 tests, or between 1 hr 30 min and 1 hr 45
min. There is only one answer. A. Notice how we used no algebra and no
complicated calculations. Oh yeah. You do need to know there are 60 minutes
to an hour.
#3 Last week, John used 6 3/4 gallons of gasoline. This week he used
a total of 14 5/6 gallons. What is the difference between the gallons he
used this week and the gallons he used last week?
A. 8 gallons
B. 9 1/2 gallons
C. 20 2/3 gallons
D. 8 1/6 gallons
E. 8 1/12 gallons
Remember, make a plan! We know we have one step:
1) 14 5/6 - 6 3/4
This is subtracting fractions, I hope you remember how to do it the
easy way. First, subtract 1 from the first whole number and then subtract
the other whole number. 14 is the first, 6 is the second, so we will do
13 - 6 = 7. Set this aside. Now we have the problem looking like:
1 5/6 - 3/4
Remember to just do 1 - 3/4. I hope you practiced these. The answer
is 1/4. Now we simply add 1/4 + 5/6. 4 x 6 = 24, our new denominator. (1
x 6) + (5 x 4) = 6 + 20 = 26, our new numerator. We now have 26/24. That
reduces to 1 2/24, which further reduces to 1 1/12. We now add that to
our 7 that we set side and get 8 1/12 for the answer. However, we could
have even noticed that only ONE fraction in the answers has a 1/12. That
had to of been the answer!
#4 Karen works 37 hours each week and earns $8.25 per hour. She receives a raise and now makes $337.80 before taxes each week. What was the increase in her weekly pay?
A. $305.25
B. $35.40
C. $32.55
D. $42.30
E. $40.75
First, come up with a plan and write it down. On problems like this,
I urge you to do just that. Something like:
1) Do 37 x 8.25
2) Subtract that from 337.80
37 x 8.25 is something you should do twice, making sure you get the
same answer each time. If not, you have done something wrong and can catch
it now. I would suggest you just plod through it. 37 x 8.25 = 305.25. We
now need to subtract that from 337.80. Setting it up the old-fashioned
way,
337.80
-305.25
But, I hope you can tell what the answer is by looking at the answers.
337 - 305 is 32. That you can do in your head and gives a rough estimate.
We also know it will end with a 55, because 80 - 25 = 55. In fact, there
is only one answer that ends with a 55. We could have done that and got
the answer right away.
#5 Joan has three boxes of cookies. The first box has 46 cookies, the second one has 38, and 78 are in the third. If her class of 27 students are going to divide these equally, how many cookies will each student get?
A. 4
B. 5
C. 6
D. 162
E. 12
Write down what you need to do.
1) Do 46 + 38 + 78
2) Divide that answer by 27
Again, add up the numbers twice. If you are going to make a mistake,
here is where you will do it. The total is 162. Now we divide 27 into 162.
If this is something you don't want to do, relax. We can work backwards.
Change it to a multiplication problem and try the answers. The answer times
27 will equal 162. Obviously, D is too high. We can just start with A and
work our way down. Eventually we will find that 6 x 27 = 162, so the answer
is C. However, thinking like a math person, we could have chosen C quickly
because 27 ends in a 7 and 6 x 7 = 42. That is the only answer when multiplied
by 7 has a 2 on the end.
4 x 27 ends in 8 because 4 x 7 = 28
5 x 27 ends in a 6 because 5 x 7 = 35
6 x 27 ends in a 2 because 6 x 7 = 42
162 is logically too high
12 x 7 ends in a 4 because 2 x 7 = 14
#6 John spent the day planting shrubs. He planted 24 more in the morning than he did in the afternoon. If he planted a total of 56 flowers, how many did he plant in the afternoon?
A. 16
B. 32
C. 40
D. 78
E. 102
Quite a few people will want to take 56 - 24 = 32 and mark it. Wrong.
This is a classic problem where you are finding two numbers that follow
certain rules and total to a certain amount. Each problem of this type,
including age problems, can be done similarly. First we will write a general
equation with 2 blank spaces.
_____ + ______ = 56
What do the two blanks represent? AM and PM and we will mark them as
such
______+______=56
AM PM
Now we will look at the problem and decide which blank we are looking
for. We need to find the number for afternoon, so we will put a star by
that.
______+______=56
AM PM*
Let's look at the answers and try to eliminate some. Since only 56
flowers were planted, we can eliminate D and E.
Now, we will work backwards, trying all answers in the SECOND slot
because that is what we are looking for. But we need to go back and NOW
look at the rule. This will help us even further. Since he planted 24 MORE
in the morning, that means the LARGEST number will be in the first blank.
We will start by trying 32. Why? Because it is in the middle of the
answers left. If it is too high, then answer A is correct. If it is too
small, answer C must be correct. Putting 32 in the second slot we get:
______+ ___32_=56
AM
PM*
This forces the first number to be 24 because 24 + 32 = 56. But this
is a contradiction. The first number must be larger. Therefore, 32 is too
high. The answer MUST be A.
But you did not need to even know this. You could have tried each answer
and seen which one followed the given rule. The first number is 24 more
than the second and we are looking for the second. But this is a great
problem to show logic that can be used on most CBEST questions.
#7 Bob wants to increase his coin collection by 6%. Currently he has 150 coins. How many coins would be in his collection if he attains his increase?
A. 151
B. 153
C. 155
D. 159
E. 240
Here is another problem to make a plan.
1) Find 6% of 150
2) Add it to 150.
If you are comfortable doing .06 x 150, go ahead. But do it twice.
To do it my proposed way, we know that moving the decimal will give
us 10% and 1%.
10% of 150 is 15
1% of 150 is 1.5
We also can find 5% by cutting 10% in half. Half of 15 is 7.5
6% = 5% + 1% = 1.5 + 7.5 = 9. Most of this you can do in your head.
Adding 9 to 150 we get 159. D.
We could have stopped after 5% because 7.5 + 150 = 157.5. We know the
answer will be only slightly more. And 240 is way too big.
#8 The value of x is between 0.0037 and 0.029. Which of the following could be x ?
A. 0.25
B. 0.036
C. 0.0018
D. 0.001
E. 0.015
We will do this the no-brainer way. If you have trouble doing these
problems, take notes.
The first thing we will do is notice what the maximum number of spaces
to the right of the decimal is in every number in this problem.
0.0037 and answer C have the most. There are 4 places to the right
of the decimal. What we will do is add enough zeroes to the end of all
the rest to make 4 spaces in each number.
0.029 becomes 0.0290
So we are looking for a number between 0.037 and 0.0290.
Changing the answers looks like the following:
A. 0.25 = 0.2500
B. 0.036 = 0.0360
C. 0.0018 stays the same
D. 0.001 becomes 0.0010
E. 0.015 becomes 0.0150
Remember, adding zeroes to the end does not change the value. We now
have all numbers in the same units.
Now comes the important part. We will eliminate all zeroes that occur
in front (the left side.)
If there was a number like 0.0203, we would change it to 203. We are
only eliminating zeroes in front, not the middle.
0.037 becomes 37, 0.0290 becomes 290.
We are now looking for a number between 37 and 290. We change the answers
as follows.
A. 2500
B. 360
C. 18
D. 10
E. 150
It is now very easy to see that the only number between 37 and 290 is
E, 150.
If you are one of those who has trouble doing these problems, read
this solution carefully and learn the technique.
#9 Which fraction would fit in the blank space to make the following
a true statement?
8/12 < _____ < 12/16
A. 1/3
B. 11/12
C. 4/5
D. 1/4
E. 3/4
We are looking for a fraction that is between 8/12 and 12/16. That is, larger than 8/12, but smaller than 12/16. The first thing we should do is decide if these fractions can be reduced. They can. 8/12 = 2/3 and 15/18 = 5/6. You should not be asked to compare any more difficult fractions thn this. Now we can find one that is between 2/3 and 5/6. Remember the part on being familiar with fractions? No difficult math is needed here. Look at the smallest value, 2/3. We know that 1/3 has to be smaller than this, so answer A is out. B, we don't know yet, so we will try C. You should know that 3/5 = .6 and 2/3 = .66, so C is out for being too small. D is also too small. 1/4 is smaller than 1/3, so it is obviuosly smaller than 2 of them, or 2/3. This leaves a choice between B and E. We will try the easiest one. If that works, that is the answer. If it does not, the other MUST be the answer. 3/4 is equal to .75 and 2/3 = .66, so .75 fits at least for being larger than 2/3. We need to make sure it is less than 5/6. We can do that by comparing fractions. 3/4 is less than 5/6 because 3 x 6 is less than 4 x 5. So, E is the answer by fitting both conditions. We don't even have to try B.
Another tip: By adding 1 to the denominator and numerator, you will
always get a larger fraction.
Example, 3/4 is smaller than 4/5, which is smaller than 5/6, which
is smaller than 6/7, etc. So using this logic, 3/4 is known right away
to be less than 5/6.