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GRE Math (word problems)
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Terms in this set (28)
One Part Can Be Made Equal to the Other
In these type word problems, either the question will say that two values are equivalent, or it will tell you exactly how they differ.
Translation: "what percent"
always translate "what percentage" as x/100
Common WP phrases: Addition
Common WP phrases: Subtraction
Common WP phrases: Multiplication
Common WP phrases: Division
Common WP phrases: Average or Mean
Tip: write an unknown percent as a variable divided by 100
Example:
P is X percent of Q
Algebraic Translation:
P = (X/100)Q
or
P/Q = (X/100)
Tip: translate bulk discounts and similar relationships carefully
...
RTD: expressing rate
Always express rate as "distance over time"
ex: it takes an elevator 4 seconds to go up one floor.
1 floor / 4 seconds , which reduces to "0.25 floors/(per) second"
Relative Rates Problems
The defining aspect of Relative Rates problems is that two bodies are traveling at the same time.
3 possible scenarios are:
1) the bodies move towards each other
2) the bodies move away from each other
3) the bodies move in the same direction on the same path
Pro tip: you can save valuable time solving these equations by creating a third RT=D equation for the rate at which the distance between the bodies changes
"Intersection" - where two things meet
When looking for an unknown point where two variables meet (intersect), set them equal to one another.
You can stack or set equal to another and then subtract
'One Part Can Be Made Equal to the Other'
Adding the given difference to the smaller/shorter of the given variables, it would be the same amount as the larger/longer piece.
Rate to Work WP
Work - takes the place of distance. The amount of work done is often number of jobs completed or number of items produced
RATE: expresses the amount of work done in a given amount of time; R=W/T
R = W/T (Work Problems)
Be sure to express a rate as work-per-time (W/T), NOT as time-per-work (t/w)
average speed
average speed = total distance / total time
Note: in 'work problems' Work is equivalent to Distance
Unknown Multiplier technique
'Unknown Multiplier' allows you to reduce the number of variables when solving for an equation where the total is given, making hr algebra easier
Simplifying Proportions
• you can cancel fractions to simplify calculations as you go
• never cancel factors diagonally across an equals sign
Fundamental Counting Principle
Uses multiplication of the number of ways each event in an experiment can occur to find the number of possible outcomes in a sample space.
ex:
Factorials! - first 6
1! = 1
2! = 2 x 1 = 2
3! = 3 x 2 x 1 = 6
4! = 4 x 3 x 2 x 1 = 24
5! = 5 x 4 x 3 x 2 x 1 = 120
6! = 6 x 5 x 4 x 3 x 2 x 1 = 720
Factorials - identifying question types
Unlike fundamental counting principle questions looking for a Factorial calculation will as for a specific 'order' or specific 'arrangement' w/o changing
example: books on a shelf are all different and unique.
While letters in a word my have the same letter twice and is there for only counted once.
Multiple arrangements - Counting Principle + Anagram approach
When you find a question on the GRE that requires you to choose two or more sets of items from separate pools, count the arrangements separately. Then multiply the two calculates numbers of possibilities together
Probability
for events with countable outcomes, probability is defined by the following fraction:
Probability = Number of desired or successful outcomes / Total number of possible outcomes
example: rolling a die and landing on "5" is 1/6
Grouping
The goal in these types of questions is usually to maximize some quantity, such as the number of complete groups or the number of leftover items that do not fit into complete groups
overlapping sets formula
Total = Group 1 + Group 2 - Both + Neither
Total = a + b - e + f (reference image)
Ratios and Proportions - combining 2 different ratios with common variable
You can not simply combine two different ratios into a single ratio of 3 quantities bc terms/proportions will be different. However you can find a common denominator
Reminder: building equations in Word Problems
• be sure to reduce the number of unknowns when creating multi equations
• identify which variable the question is asking you to find and be sure that each answer choice allow you to solve for that variable "x"
Translating: comparison of percents
The basis (or number) or the comparison is what follows the word "than" in the problems statement
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