GRE Tips & Tricks Flashcards
RTD Problems
Make a table for the information:
Rate Time Distance Car
OR
Rate Time Distance Harvey Clyde
Relative RTD Problems
Make a table to combine the information:
Rate Time Distance Harvey Clyde ------------------------------------------------------------------------ Total
Population Problems
Sometimes you need to pick a smart # to start the population and use the rate.
Ratio Labeling
Always label the ratio with units so you don’t mix up the ratio.
Ex: x dogs : x cats = 2 dogs : 3 cats
Commission-Salary Problems
Set up a chart where you can see the change in numbers:
Average # Sum Old Total: $800 n 800n This Sale: $2000 1 2000 New Total: $900 n + 1 900(n+1)
800n + 2000 = 900(n+1)
11 sales = n + the big sale = 12 sales total
Evenly Spaced Sets Trick
Median = Average, so just add the first and the last terms, then divide by two.
(First + Last)/2 = average/median
STD Question Types
1) changes in STD when a list is transformed = closer/farther from mean?
2) comparisons of the STD of two or more lists = more spread out from its mean?
Anagram Problems
Most problems involving rearranging objects can be solved by anagramming.
Anagram Problems- Uncounting
You have to “uncount” different arrangements when calculating the number of possible arrangements. Set up an Anagram Grid with unique items/people on top and repeating labels on bottom.
Ex: 7 people on shuttle, 3 seats available.
Person = 7! 7 x 6 x 5 x 4 x 3 x 2 x 1 Seat = 4! 4 x 3 x 2 x 1
7!/4! Possible Arrangements = 7 x 6 x 5 = 210
- You divide by 4! because these arrangements are irrelevant. Seats vs no seats, they are distinguishable.
Anagram Problems- CAN’T Uncount
You cannot “uncount” different arrangements when the “chosen ones” are indistinguishable from the “unchosen ones”
Ex: 7 standby passengers, 3 are selected for a flight.
- The 7 passengers are all the same! You cannot distinguish between them. Thus…
Person A B C D E F G
Seat Y Y Y N N N N
Person = 7! 7 x 6 x 5 x 4 x 3 x 2 x 1 Seat = (3! x 4!) (3 x 2 x 1) (4 x 3 x 2 x 1)
7!/(3! x 4!) Possible Arrangements = 7 x 5 = 35
Basic Quantitative Comparison Tips
3 Tips
1) Try to prove D
- Use -1, 0, and 1
- Use positive numbers greater than 1 and fractions between 0 and 1
- Use negative numbers less than -1 and fractions between 0 and -1
2) Use the Invisible Inequality
- Add or subtract to both quantities
- Multiply or divide both quantities by a positive number
- Square or square root both quantities if they are positive.
3) Use Quantity B as a Benchmark
- Use when Quantity B is a number (no variables)
- When Quantity A requires calculation, try to save time by using Quantity B
- Use Quantity B as a guide to try to prove (C)
Variable Quantitative Comparison Problems (Algebra)
4 tips
1) If a variable has a unique value (Ex: x+3 = -5) then solve for the value of the variable.
2) If a variable has a defined range (Ex: -4 ≤ w ≤ 3) then test the boundaries
3) If a variable has a relationship with another variable (Ex: 2p = r) then simplify the equation and make a direct comparison of the variables.
4) If a variable has no constraints, then try to prove (D).
5) If a variable has specific constraints (Ex: x is negative), then try to prove (D).
Quadratic Equation Quantitative Comparison Problems (Algebra)
2 tips
1) If a quadratic appears in one or both quantities:
- FOIL the quadratic
- eliminate common terms, and
- compare the quantities
2) If a quadratic appears in the common information
- factor the equation and find both solutions, and
- plug both solutions into the quantities for A and B.
*Strange Symbol Quantitative Comparison Problems (Algebra)
2 tips
1) If the question contains numbers, plug in the numbers and evaluate the formula.
2) If the question does not contain numbers, plug the give variable(s) directly into the formula.
Absolute Values Quantitative Comparison Problems
(Algebra)
2 tips
1) If the absolute value also contains a positive number, make the variable positive to maximize the absolute value.
2) If the absolute value also contains a negative number, make the variable negative to maximize the absolute value.
Inequalities Quantitative Comparison Problems
(Algebra)
2 tips
1) Focus on the common information (Ex: 0 < p < q < r)
- gives you the sign of the variable and
- gave their order from least to greatest.
2) To compare two quantities, use the invisible inequality to
- eliminate common terms, and
- try to discern a pattern if one is present.
- Don’t forget you can cross multiply when the variables are positive for comparing two fraction inequalities
Quick Elimination
Fractions Quantitative Comparison Problems
Is this fraction greater than or less than 1?
If one is greater than 1 and the other isn’t, you’re done!
Simplifying Complex Fractions
Fractions Quantitative Comparison Problems
1) Split the numerator when the denominator is one term
2) turn division into multiplication by the reciprocal (Ex; 2/(2/3) = 2 and (3/2)
Fractions with Exponents
Fractions Quantitative Comparison Problems
PLUG IN : 0 and 1
When fractions contain exponents and you have to plug in numbers for the exponents, always plug in 0 and 1 first to save time.
Percents
Fractions Quantitative Comparison Problems
When dealing with percents, always pay attention to the size of the original value. Thus, 20% of a small number is less than 20% of a larger number.
Three-Step Process for Geometry QC Problems
1) Establish what you need to know
2) Establish what you know
3) Establish what you don’t know
Diagrams
Geometry QC Problems
5 tips
When Geometry QC problems include a diagram, there are two possibilities for Quantity B:
1) Quantity B is a number, or
2) Quantity B is an unknown value.
For both situations, the process is the same: Establish what you need to know.
3) Establish what you know:
- Set up equations to solve for previously unknown lines and angles, and
- Make inferences based on the properties of shapes
4) Establish what you don’t know
- Take unknown values to extremes.
- If both quantities contain unknown values, look to gauge relative size.
5) NEVER TRUST THE PICTURE!!
Word Geometry QC Problems (w/o picture)
2 tips
1) Draw the picture
2) Ask yourself: “What changes to the picture would affect the relative size of the quantities?
Word Geometry QC Problems
(w/ specific dimensions, but doesn’t provide actual numbers)
3 tips
I the question references specific dimensions (length, width, radius) but no actual numbers, use smart numbers! To successfully pick:
1) Pick numbers that match any restrictions in the common information or statements.
2) Try to prove (D) by testing several valid cases.
3) Look for patterns that suggest the answer is (A), (B) or (C)
Greater Than/Less Than 0
Number Properties QC Problems
When the product of more than one variable is either greater than or less than 0, consider all the possible signs and test all possible scenarios.
If xy > 0, the two scenarios are:
1) x and y are both positive
2) x and y are both negative
If xy < 0, the two scenarios are:
1) x is positive and y is negative
2) x is negative and y is positive.
- TEST BOTH SCENARIOS
Positive and Negative Clues
Number Properties QC Problems
3 Major Tips
2 Reminders
Save time by figuring out whether each quantity is positive or negative.
Be on the lookout for these clues:
1) Common information states that a variable is greater than or less than 0 (Ex: x > 0, p < 0)
2) Common information states that the product of two variables is greater than or less than 0 (Ex: xy < 0)
3) An expression contains both an exponent and a negative sign (Ex: (-2)^x)
When problems contain both exponents and negative signs, try to make generalizations about the sign of each quantity:
1) A negative number raised to an odd power is negative.
2) A negative number raised to an even power is positive.
Variables with Exponents
Number Properties QC Problems
Try to prove (D) by using numbers greater than 1 and numbers between 0 and 1.
- Numbers greater than 1 get bigger as you raise them to higher powers.
- Numbers between 0 and 1 get smaller as you raise them to higher powers.
Consecutive Integers
Number Properties QC Problems
To compare the sums or products of sets of consecutive integers, eliminate overlap in order to make a direct comparison.
Ratios w/o Numbers
Word QC Problems
Remember that rations provide NO information about actual values. To try to prove (D) on a ratios problem, choose one scenario in which the actual values are the same values as the ratio and choose another scenario i which the numbers are much larger (but still pick numbers that are easy to work with).
Principal of Weighted Averages
Word QC Problems
In any question that involves two groups that have some kind of average value, use the principal of weighted averages.
Process for Solving Data Interpretation Questions
1) Scan the graph(s) (15-20 seconds)
- What type of graph is it?
- Is the data displayed in percentages or absolute quantities?
- Does the graph provide any overall total value?
2) Figure out what the question is asking. What does it ask you to do?
- Calculate a value?
- Establish how many data points meet a criterion?
3) Find the graph(s) with the needed information.
- Look for key words in the question.
Change in Total Sales
Data Interpretation
Ex: If sales of potatoes were to increase by $173 next month and sales of all other items were held constant, approximately what percentage of the total sales would be potatoes? (22% of total sales = potatoes and there is $4,441 in total sales)
[0.22(4441) +173] / (4441 + 173) = 0.249 = 25%
NOTE: you must take into account the change in total sales in both the numerator and the denominator!
Percentage Tip
Any amount is a greater percentage of a smaller number than it is of a larger number.
Charts w/ Percentages vs. Actual Quantities
Data Interpretation
You cannot assume total sales on a chart showing just percentages! Percentages are different than actual quantities!
Percentage Increase and Decrease!
KNOW THE FORMULAS
Percentage Increase:
(new - old) / old
Percentage Decrease:
(old-new) / old
