The Process for Word Problems
Underneath the convoluted language in GMAT word problems are really just simple math concepts. It is easy to get lost in the words and fail to see the manageable math equations.
The GMAT rarely asks questions that are simple and straightforward. Expect problems that require you to convert complex written statements into variables and equations.
If you tripled Adam’s age, he would be double Frank’s age. Frank is currently 9 years old.
This translates into the equation:
3a/2 = 9
The most effective strategy for solving a word problem is to express the question as an equation or relationship where x, or some other letter, represents the quantity that you need to find.
800score Tip
Many algebra word problems contain several variables. It is helpful to track the variables by using letters that correspond to the items in the question. For example, if the question is about Adam, use the variable “a.”
The 5 Steps
1) Read the Question
Read and re-read the question until it makes sense. You might need to rephrase the question into your own words, or break the question into simpler parts. Just make sure you know exactly what the question is asking.
As you read the question, be on the lookout for tricks, traps or anything unusual.
2) Read the Answers
Look at the answers before working on a solution. The GMAT often makes questions appear more complicated than they really are, so the answers can clarify your understanding of the question. For example, reading the answers can prevent you from solving for the wrong variable. You can also see how exact your answer needs to be. Can you estimate and use rounding? Can you factor then cancel?
The GMAT often requires you to convert units, so reading the answers will help ensure you use the right units.
3) Define Variables and Relationships
Choose meaningful letters that will help you keep the variables straight.
Look for words that define relationships and actions, such as “twice as many,” “combined,” “gives,” or “greater than.” More examples of words that show relationships and actions are in the next section and throughout this chapter.
4) Choose a Technique and Apply It
Your goal when taking the GMAT is to pick the right answers on a multiple-choice exam. You are not being graded on style. It doesn’t matter if you find the answer following the usual routine. In fact, the fastest way to an answer often does not involve using a traditional method, but rather a method geared specifically to the GMAT.
Each question may have several possible approaches, so you need to develop an ability to recognize a fast and effective way to solve different question types. Once you have chosen a technique, run the numbers and follow your plan. If it is taking too long, see if you can find shortcuts on the math or change your technique. Go back to Step 1 and reread the question and answers, if necessary.
1. Plow
2. Don’t Do That Math!
3. Backsolving
4. Plug-In
5. Ballpark
6. Experiment
7. Pattern
5) Eliminate Choices
Picking the correct answer choice may not require a complete solution to the problem. Eliminating all the wrong answers is the same as finding the right answer.
If you don’t know an answer, you CANNOT skip the question and return to it later. But don’t just guess a random answer, make an educated guess.
Use the process of elimination to decrease the number of possible answers choices, even if you can’t find the exact answer. Use logic to rule out wrong answers. With every answer choice you can eliminate, you increase your odds of guessing correctly.
You have to guess aggressively on the GMAT. When a question is clearly too tough, make an educated guess and move on. Don’t get stuck on one problem. Take the time you would have wasted on that problem and use it on a question you know how to solve.
The techniques in the next section will give you tools you can use to eliminate wrong answer choices.
How to Eliminate Choices
The examples below illustrate The 5 Steps.
Solution
The question is looking for two numbers: the numbers of hardcover and paperback books.
Define the variables and write equations based on the given information. Let h be the number of hardcovers and p be the number of paperbacks.
She bought 8 books, so h + p = 8.
Since hardcover books cost $4, the total cost of h hardcovers is 4h.
Paperback books cost $2, so the cost of p paperbacks is 2p.
She spent $28, so 4h + 2p = 28.
h + p = 8
4h + 2p = 28
Method 1: Substitution
Solve for h: h = 8 − p
Substitute:
4h + 2p = 28
4(8 − p) + 2p = 28
32 − 4p + 2p = 28
-2p = -4
p = 2 paperback books
Substitute:
h + p = 8
h + 2 = 8
h = 6 hardcover books
Method 2: Addition
Multiply the first equation by 4:
4h + 4p = 32
Subtract:
4h + 4p = 32
− [4h + 2p = 28]
2p = 4
p = 2 paperback books
Substitute:
h + p = 8
h + 2 = 8
h = 6 hardcover books
Solution
Define the variables. Let w be the number of white marbles, g the number of green marbles and b the number of blue marbles.
Write an equation based on each sentence of the question.
15 = w + g + b
w = 2(g + b)
g = (1/5)(15)
g = 3
Substitute g = 3 into both of the other equations, then simplify.
15 = w + 3 + b
12 = w + b
w = 2(3 + b)
w = 6 + 2b
Substitute w = 6 + 2b into the first equation.
12 = 6 + 2b + b
6 = 3b
b = 2
Substitute g = 3 and b = 2 into the original first equation.
15 = w + 3 + 2
w = 10
There are 3 green marbles, 2 blue marbles and 10 white marbles.
Solution
Use the formula
A = 1/2 bh
15 = 1/2 (10)h
15 = 5h
h = 3
Video Quiz
Strategy
Best viewed in landscape mode
12 questions with video explanations
100 seconds per question
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https://www.youtube.com/watch?v=7RSMXSFtNqg
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https://www.youtube.com/watch?v=AIWWdCj6ZoE