Triggers and Glossary of Math Terms - Math Workout for the GRE

Math Workout for the GRE, 3rd Edition (2013)

Chapter 13. Triggers and Glossary of Math Terms

TRIGGER, RESPONSE

You may have noticed that the hardest part of any math question is simply getting started. Once you know what to do, the actual math is simply about writing down numbers and occasionally using the calculator. But when a question appears on the screen, most people’s first impulse is to keep rereading the question, and then stare off into the distance and think about what to do.

Remember that the math section of the GRE is not about thinking. The more time you spend staring at a problem without actually writing anything down on your scratch paper, the more time you are wasting. Triggers are simple things to look for in GRE math problems: Once you see a certain trigger, you should always have the same response. That way, rather than trying a problem several different ways before realizing that you could have simply Plugged In, you get used to seeing the problem, noticing variables in the answers (Trigger) and knowing to Plug In (Response). Math problems on the GRE test the same concepts, over and over again, generally in the same couple of ways. When you’re ready for the GRE’s repetitive questions, the slight variations between questions won’t throw you for a loop.

The best way to practice Triggers is to simply open up to a page of GRE math questions, perhaps from this book, from Cracking the GRE, or from The Official Guide to the revised GRE, and look for Triggers in each question. You don’t even have to solve any questions (although it couldn’t hurt), just spend a couple minutes per page looking through the questions, telling yourself what the first couple of steps for each question would be.

These Triggers are listed in the order in which they appear in the book. If you are unfamiliar with the question types that use a particular Trigger, go back to that chapter to see questions of that type, how we solved them, and what clues we found that told us how to solve them.

Chapter 3: The Nuts and Bolts

Trigger: Problem contains percentages.

Response: Translate, Convert percentages to fractions, use Proportions, or use Tip Calculation.

Trigger: Question asks for “percent change,” “percent increase,” or “percent decrease.”

Response: Write the percentage change formula: Percent change = × 100

Trigger: Exponent problems with large numbers.

Response: Factor the base to compare exponents. Use MADSPM.

Chapter 4: Algebra, and How to Get Rid of It

Trigger: Variables in the answer choices.

Response: Plug In.

Trigger: Variables in the answer; Problem says “must be”

Response: Plug In a simple number, then use FROZEN numbers.

Trigger: Quant Comp with variables.

Response: Set up your scratch paper and plug in using FROZEN

Trigger: “How much,” “How many,” “What is the value,” numbers in the answer choices.

Response: Plug In the Answers (PITA)

Chapter 5: Math in the Real World

Trigger: The word “average.”

Response: Draw an Average Pie for every time the word average appears in the question.

Trigger: The word “median” appears in the problem.

Response: Put the list of numbers in order and find the middle number.

Trigger: The word “ratio” appears in the problem.

Response: Draw a Ratio Box on your scratch paper.

Chapter 6: Geometry

Trigger: Two parallel lines cut by a transversal.

Response: Label all acute (small) angles as equal, and all obtuse (large) angles as equal.

Trigger: Need to know the side of a right triangle.

Response: Write down a2 + b2 = c2 and plug in the two sides you know.

Trigger: Triangle question contains the word “area.”

Response: Write down A = bh and plug in what you know. The height will always be perpendicular to the base.

Trigger: Problem with parallelogram, rectangle, or square contains the word “area.”

Response: Write down the area formula and plug in information.

Trigger: Problem mentions “perimeter.”

Response: Find the length of each side and add up all sides.

Trigger: Circle problem contains the word “circumference.”

Response: Write C = 2πr or C = πd on your scratch paper.

Trigger: Circle problem contains the word “area.”

Response: Write A = πr2 on your scratch paper.

Chapter 7: The Rest of the Story

Trigger: Factorials with division.

Response: Expand factorial and reduce.

Trigger: Factorials with addition or subtraction.

Response: Factor out common factorials.

Trigger: The word “probability” appears in the problem.

Response: For each event, find the number of outcomes you want, and divide by the total number of outcomes.

Trigger: Probability question asks “at least.”

Response: Find the probability event won’t happen, and subtract from 1.

Trigger: Group problem with overlap.

Response: Write down group formula: Total = [Group 1] + [Group 2] − [Both] + [Neither]

Trigger: Group question with no “Both Group A and B” elements.

Response: Draw Group Table:

Trigger: Question contains the words “normal distribution” or “standard deviation.”

Response: Draw a bell curve and label the mean and the 34-14-2 points for each standard deviation.

Trigger: The phrases “arrangements,” “combinations,” “different ways,” “many ways,” or “different groups” appear in the problem.

Response: Draw a horizontal line for each choice we have to make.

Trigger: The words “team,” “groups,” “combinations,” or order doesn’t matter.

Response: At the end of the problem, divide answer by the factorial of the number of slots.