CliffsNotes CBEST - BTPS TESTING Ph.D., Jerry Bobrow Ph.D. & 8 more 2021

Word problems
Math reasoning problems

Proficiency with numbers is not just about finding the correct solution to an equation. It is the ability to see how numbers relate to one another when applied to real-world problems. On the CBEST, these types of problems appear as short word problems. To solve word problems, you must be able to translate English words that describe a situation or scenario into a math equation. The goal is to find a mathematical way to organize the problem so that you can work toward a solution.

Words That Signal Math Operations

Use the following list of math operation words to help you decipher word problems.

Strategies to Solve Word Problems

As you practice working problems to prepare for the CBEST, you are encouraged to pace yourself as you become familiar with how to translate math words into a math equation. Consider these steps when approaching word problem questions.

· Watch for key math words in the question to provide you with facts about what is being asked, and write down these words to better understand what the question is asking. For example, look for words or symbols that require an operation (add, subtract, multiply, divide); look for words that signal the unit of measurement (length or width); and look at all labels in the context of the question. For example, “How much time does it take to get to a concert hall that is 50 miles away?” or “What is the cost of two cell phones at $124.75 each, plus one adapter at $36.55?”

· Organize the math words and operations. Organizing information helps you form visual representations of the written material. If you can, set up the equation with math symbols or draw a diagram to help point you to what is being asked in the question.

· Clarify what is being asked. Some word problems are difficult to understand, but the answer to every question is always stated directly within the word problem. If there is a word, concept, or math symbol that you don’t necessarily understand, write a quick note to yourself to seek further clarification. Your written notes will often trigger your memory to remember how to solve the problem.

· Use the elimination strategy whenever possible to eliminate one or more answer choices. Read all of the answer choices carefully and try to eliminate obvious wrong answers as soon as you recognize them. The elimination approach is described on p. 5 of the Introduction.

· Restate your answer in a sentence to verify that it makes sense and that it is reasonable.

Examples:

1.   Maria purchased a new backpack that sells for $39.99. If the sales tax on the purchase was 8.5%, what was the total cost of the backpack?

2.   A history class has 24 female students enrolled and 16 male students enrolled. What is the ratio of male students to the total number of students in the class?

A ratio of means that there are 2 male students for every 5 students in the class.

TEST TIP: It is important to note that in a ratio, the first number mentioned is always the numerator unless the directions say “What is the ratio of. . . .”

3.   Mr. Cervantes has 80 students in his class. One-fifth of them are averaging 65% on tests, 30% of them are averaging 75% on tests, and the remaining students are averaging 85% on tests. What is the class percent average?

A.  75%

B.  76%

C.  7%

D.  78%

E.  79%

The class percent average is found by finding the class total percentage and dividing that by the number of students in the class. The class has 80 students with one-fifth of them averaging 65%. One-fifth of 80 is 16, so the total percentage for the 16 students is 16 × 65%. Similarly, 30% of 80 is 24, so 24 × 75% is their percentage total.

Since 16 + 24 = 40, 40 of the 80 students are accounted for, leaving 40 students who averaged 85% for a total percentage of 40 × 85%. The class percent average is:

One method to speed up this arithmetic is to do the following. Notice that the 16, 24, and 40 in the numerator and the 80 in the denominator are each divisible by 8. Divide each by 8 before doing any multiplying.

The correct answer is choice D.

4.   Economic indicators predict 12% inflation over the next 12 months. If that’s true, how much must a $20,000 salary be increased to keep up with inflation?

First, circle what you must find: how much must a . . . salary be increased. Now, using the information given in the problem, you could simply multiply: 0.12 × $20,000 = $2,400. Or, if you want to plug into the standard equation:

5.   Katie wants to buy a block of tickets for a theater play. She can spend $3,500 for the tickets. Tickets for orchestra seats cost $17.50 each, and tickets for balcony seats cost $12.50 each. How many more tickets can Katie buy if she chooses to buy tickets for balcony seats instead of buying tickets for orchestra seats?

A.  65

B.  70

C.  75

D.  80

E.  85

Divide $3,500 by both $17.50 and $12.50 to determine how many of each type of ticket can be purchased with the $3,500. Then, subtract the two quantities. Katie could buy 200 orchestra seat tickets or 280 balcony seat tickets. Thus, the difference is 80. The correct answer is choice D.

6.   Adam’s lunch bill was as follows:

7.   What was the cost of Adam’s soft drink?

A.  $1.75

B.  $1.25

C.  $1.00

D.  $0.95

E.  $0.75

To answer this question, simply add the cost of the salad and the sandwich and then subtract that total from the subtotal to find the cost of the soft drink.

Now subtract that total from the subtotal of $8.65:

The correct answer is choice E.