Mathematical Reasoning Question Types and Solving Strategies
IN THIS CHAPTER
Checking out the different Math test question types and strategies
Getting familiar with the calculator and formula sheet
Doing a little math to help manage your time on the test
The Mathematical Reasoning (Math) test is 115 minutes long. The first five questions are designed to be done without a calculator and must be attempted before you can continue; for the rest of the items, you may or may not need a calculator to complete them. If you see the calculator icon on the screen, you can use the onscreen calculator (or your own if you’ve brought one) to solve the problem. Getting a basic understanding of these question formats helps you avoid any surprises when you sit down to the take the test. The Math test presents you with questions from every area of Math. It ranges from arithmetic calculations, which you have to do without a calculator, to basic algebra, and more. In this chapter, we explain the four formats of questions you encounter on this test and offer advice on how to solve them with ease.
Perfecting Your Approach with Sample Problems
New tests usually require new ways of approaching the questions in them. Although the Mathematical Reasoning test has a new format and is given on a computer, it’s still about math — the same old math that has been around for several thousand years. Be careful of the format and pay particular attention to the math. The basic operations are still addition, subtraction, multiplication, and division, but you have to know how to use them to solve problems. Practice doesn’t make perfect but will increase your chances of getting the correct answer to the question.
Because you’re not penalized for guessing, if you don’t know the answer to a question, go ahead and guess. Although you can’t get a point for a blank answer, you can get a point for eliminating all but the most possible answer and marking it (if you get it right, of course).
Making the most of multiple-choice questions
Most of the questions on the Math test are a form of multiple-choice. You’re given four possible answers, and all you have to do is choose the one best answer.
Answering basic multiple-choice questions
The multiple-choice questions on the Math test are pretty straightforward. You’re given some information or a figure and asked to solve the problem based on that info. Here are a couple examples.
Milton wanted to be taller than his father, who was 2 yards tall. Milton was 5 feet 10 inches tall even when he stretched. How much taller would Milton have to grow to be taller than his father by at least an inch?
(A) 1 inch
(B) 2 inches
(C) 3 inches
(D) 4 inches
The first thing you have to do with questions like this one is make sure all measurements are in the same format. Two yards equals 6 feet (1 yard = 3 feet). So Milton is 2 inches shorter than his father. The question asks how much he would have to grow to be at least 1 inch taller than his father. If he were to grow 3 inches, he would have reached that goal. Choice (C) is correct.
Samantha was a super salesperson and by far the best salesperson at Industrial Chemicals Ltd. She was so good that she knew that she had to work for only three months not only to beat the sales records of her fellow salespeople but also to boost the total sales for the company substantially. The following chart appeared in the company’s annual report. In which quarter do you think Samantha made all her sales?
The graph shows that the majority of sales were made in the first quarter, and if Samantha’s boasts were correct, she would have made the majority of those sales. In the other nine months of the year, without her sales, the sales slipped considerably. In a graph such as this one, the area of the segment of the circle represents the data.
Extracting the info you need
Some of the questions on the Math test may have extra information that you don’t need; in those cases, just ignore it. Of course, you have to make sure that the information you think is extra really is. For example, if the last question in the previous section said that Irving was the poorest salesperson the company had ever employed, that information really is extra and makes no difference to the rest of the question.
The people who write the test questions include extra information for a reason — extra information can make guessing more difficult and separate the test-takers who are paying attention from those who aren’t. Sometimes, extra information is put in to make the question a bit more realistic. You don’t want to disregard anything essential to solving the problem.
While reading the following question, try to visualize the situation and consider where the plot takes an extreme turn. This is usually the place where the information turns from important to irrelevant or vice versa.
Kenny, Dharma, and Sophie went out for a snack after school. The wall of their favorite burger place has the following menu:
Item
Calories (kcal)
Fat (g)
Cost ($)
Hamburger
780
44
4.09
Bacon Cheeseburger
793
56
4.09
Chicken Wrap
450
25
1.69
French Fries
360
17
1.59
Chocolate Muffin
450
15
2.10
Chocolate Chip Cookies
160
7
1.00
Soda
220
0
1.49
Their total bill came to $24.31, and after a long discussion, they decided to tip the server 15%. What was the server’s tip?
(A) $2.92
(B) $3.00
(C) $3.65
(D) $4.86
The first part of this item may be interesting, but it’s irrelevant. The relevant information is the part that asks about the server’s tip. The only important information becomes the amount of the bill and the percentage of the tip. So you multiply the total bill by 15% to get a tip of , rounded to the nearest penny.
Deciding what to do when you don’t have enough info
Some questions may not give you enough information to solve the problem. For example, a question may ask for a conclusion that you can’t make from the information given. Even if you know some information that would help you solve the problem, don’t use it.
You bring with you to the test the knowledge of what the basic operations are and how to use them. You aren’t expected to know the dimensions of some fictional character’s room or how well a character does on her reading scores. You’re expected to know how to solve problems and to leave the specifics of the problems to the GED test-makers.
Not every question on the GED Math test is solvable. If you come across a question that doesn’t include enough information to solve the problem or it can’t be answered with the information given, don’t panic! Reread the question to make sure it can’t be answered and then choose the appropriate answer choice, which is usually “not enough information given” or some variation.
Don’t assume that when a question includes the answer choice “not enough information given,” it’s a clue to mean that you don’t have enough information, because some questions that can be solved include this answer choice to make you think. Use this clue only when you’ve already determined that the question can’t be solved.
Carmen bought a new Thunderbolt 8 as a gift to himself. He was impressed with its shiny aluminum wheels, its all-electronic dashboard, and its ventilated leather seats. The acceleration made him feel like a race car driver. He opted for rustproofing and a deluxe GPS and sound system. He negotiated with the salesperson for several hours to get a monthly payment he could barely afford. What were his annual insurance premiums if he was under 25?
(A) $4,159
(B) $4,638
(C) $5,200
(D) not enough information given
This question includes a lot of information; unfortunately, none of it pertains to the question, and Choice (D) is the only answer possible.
Providing the answer in fill-in-the-blank items
Fill-in-the-blank items require that you fill in the answer without the benefit of four answer choices to choose from. Often, they involve some calculation, using the information provided in the item. We walk you through answering two fill-in-the-blank questions in this section.
Demitri wanted to buy a new television set. His old one had a diagonal measurement of 32 inches, but he wanted to buy a 50-inch diagonal set. The new television set would be inches wider, measured diagonally.
To answer this question, you have to find the difference between the two TV sets. The new set would be inches wider, measured diagonally.
Carol found a part-time job to augment her scholarship. She was paid $13.45 an hour and was promised a 15% raise after three months. Business had been very poor during that period, and the owner of the business called Carol in to explain that he could afford only an 11% raise but would reassess the raise in the next quarter depending on how business was. With this raise, Carol’s new hourly rate would be .
Carol’s new salary would be calculated at the rate of $13.45 times 11%, or (to the nearest penny). If you want to calculate the amount of an 11% raise, you can multiply by 111% (, or 1.11 expressed as a decimal).
Using the Mathematical Reasoning Test’s Special Features
During the Mathematical Reasoning test, you can use the built-in (or your own) calculator for all but the first five questions. Before you start celebrating, remember that the calculator is an instrument that makes calculations easier. It doesn’t solve problems or perform other miracles. You still have to solve the problems, using the computer between your ears.
The test also has a formula sheet. This feature also isn’t a miracle to work out problems for you. It’s just a memory aid if you don’t remember the formulas. And as a special treat, the Math test also provides symbols for you to use in the fill-in-the blank items as needed. We explore all these features in the following sections.
Solving questions with and without a calculator
For all but the first five items in the Math test, you can use a calculator. You have to finish the first five items before you go on to questions that use the calculator. To pull up the calculator on the computerized GED Math test, click on the calculator icon. A calculator — a Texas Instruments TI-30XS calculator to be exact — appears on-screen.
It’s a good idea to get familiar with the calculator before taking the GED test. You can either use the one on the GED Testing Service website for practice or find an identical hand-held one. The computer version of the calculator operates just like the hand-held device. Then make sure you know how to solve the various types of mathematical problems and depend on the calculator only to do mechanical operations quicker and easier.
Often, solving a problem without a calculator is easier, especially with multiple-choice questions where you have four answer choices to choose from. And the more questions you practice in your head, the easier it will be. Here are some ways to practice solving problems in your head (without a calculator):
When you go shopping, add up the items as you put them in the cart.
Calculate discounts off items you see or buy when you shop.
Be the first at your table in a restaurant to figure out the tip. And for bonus practice, figure out different tip percentages on your bill, such as 10, 15, 18, and 20 percent tips.
For multiple-choice questions, sometimes estimating the answer to a question is easier and faster. For example, is almost , which equals 36. If you see only one answer choice that’s close to 36, that answer is probably correct. If you see that all the answer choices are close to 36, however, you need to spend time calculating the exact answer. Although you may be able to solve problems in your head, always work them out to verify you have the correct answer.
Refreshing your memory with the formula sheet
The GED Math test includes a formula sheet with a list of formulas you may need for the test. You simply click on the formula icon to make the page of formulas appear. Unfortunately, no genie will appear to tell you which formula to use. Figuring out which formula you need is your job.
To get familiar with the formulas you may need on the GED test, study the formulas in this book (you can find a list of formulas in the practice tests in Chapters 23 and 31), and make sure you know their purpose. Then make sure you understand what kind of problem you can use each formula for. For example, if you have a formula for the volume of a rectangular cube and the question asks you how many cubic feet of water a swimming pool contains, you know this formula will let you work out the answer. If the question asks you how many tiles it’d take to go around the rim of the pool, you need another formula.
Inserting special symbols
When answering fill-in-the-blank items, you sometimes need special symbols. Fortunately, the Math test provides such symbols on the screen behind the special icon. These formulas are mainly math operators, such as add or subtract, greater than or less than, and so on. You have to know what they mean and how to use them. To make a symbol appear in the fill-in-the-blank box on the test, click on the symbols icon, and then click on the symbol you want to include in the box.
Managing Your Time for the Math Test
Try not to be intimidated by the word math or the subject as a whole. A math teacher once said that mathematicians are lazy people — they always use the easiest way to find the right answer. We don’t want to insult or irritate any mathematicians by calling them lazy, but finding the easiest way to solve a problem is usually the right way. If your way is too long and complicated, it’s probably not right.
The Mathematical Reasoning test allows you 115 minutes to complete 50 questions. You must answer the first five items without using the calculator, and then the rest follow after you have answered these five questions. The rest of your time is yours to divide any way you see fit. Just remember that you have to answer a question to get the points.
On the computerized GED test, each question is given a specific number of points depending on how difficult it is. That means that each version of the test may have a different number of questions, but each test has the same number of points. Don’t worry if you find out after you leave that you had fewer or more items than a friend. It will all work out.
To help you manage your time for the Math test, check out the following suggestions (refer to Chapters 3 for some general time-management tips):
Stay on schedule. Being able to manage your time is the most important indicator of success on the Math test. If you can keep to your schedule of less than 1½ minutes per question, you’ll have enough time to go over your answers and make any changes necessary after you finish solving all the questions.
With such a tight schedule for taking the Math test, you have no time to panic. Aside from the fact that panicking distracts you from your overall goal, it also takes time — and you have very little time to spare. So relax and just do your best — save the panicking for another day.
Know when to move ahead. If you don’t see what’s being asked by a question within a few seconds, reread the question and try again. If it still isn’t clear, go on to the next question. Spending all your time trying to solve one problem at the expense of the others isn’t a good idea. If you have time left at the end, you can always go back.
Keep an eye on the time. The timer on the computer screen is your only time-management tool. You’re not allowed to bring any electronics into the testing area.
Checking out the different Math test question types and strategies
Because you’re not penalized for guessing, if you don’t know the answer to a question, go ahead and guess. Although you can’t get a point for a blank answer, you can get a point for eliminating all but the most possible answer and marking it (if you get it right, of course).
Milton wanted to be taller than his father, who was 2 yards tall. Milton was 5 feet 10 inches tall even when he stretched. How much taller would Milton have to grow to be taller than his father by at least an inch?
, rounded to the nearest penny. 
Not every question on the GED Math test is solvable. If you come across a question that doesn’t include enough information to solve the problem or it can’t be answered with the information given, don’t panic! Reread the question to make sure it can’t be answered and then choose the appropriate answer choice, which is usually “not enough information given” or some variation.
Don’t assume that when a question includes the answer choice “not enough information given,” it’s a clue to mean that you don’t have enough information, because some questions that can be solved include this answer choice to make you think. Use this clue only when you’ve already determined that the question can’t be solved.
inches wider, measured diagonally.
inches wider, measured diagonally.
(to the nearest penny). If you want to calculate the amount of an 11% raise, you can multiply by 111% (
, or 1.11 expressed as a decimal).
is almost 
, which equals 36. If you see only one answer choice that’s close to 36, that answer is probably correct. If you see that all the answer choices are close to 36, however, you need to spend time calculating the exact answer. Although you may be able to solve problems in your head, always work them out to verify you have the correct answer.