GRE Tips & Tricks

Question 1

RTD Problems

Answer 1

Make a table for the information:

        Rate         Time          Distance Car

OR

              Rate         Time          Distance Harvey Clyde

Question 2

Relative RTD Problems

Answer 2

Make a table to combine the information:

              Rate         Time          Distance Harvey Clyde ------------------------------------------------------------------------ Total

Question 3

Population Problems

Answer 3

Sometimes you need to pick a smart # to start the population and use the rate.

Question 4

Ratio Labeling

Answer 4

Always label the ratio with units so you don’t mix up the ratio.

Ex: x dogs : x cats = 2 dogs : 3 cats

Question 5

Commission-Salary Problems

Answer 5

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

Question 6

Evenly Spaced Sets Trick

Answer 6

Median = Average, so just add the first and the last terms, then divide by two.

(First + Last)/2 = average/median

Question 7

STD Question Types

Answer 7

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?

Question 8

Anagram Problems

Answer 8

Most problems involving rearranging objects can be solved by anagramming.

Question 9

Anagram Problems- Uncounting

Answer 9

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.

Question 10

Anagram Problems- CAN’T Uncount

Answer 10

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

Question 11

Basic Quantitative Comparison Tips

3 Tips

Answer 11

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)

Question 12

Variable Quantitative Comparison Problems (Algebra)

4 tips

Answer 12

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).

Question 13

Quadratic Equation Quantitative Comparison Problems (Algebra)

2 tips

Answer 13

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.

Question 14

*Strange Symbol Quantitative Comparison Problems (Algebra)

2 tips

Answer 14

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.

Question 15

Absolute Values Quantitative Comparison Problems
(Algebra)

2 tips

Answer 15

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.

Question 16

Inequalities Quantitative Comparison Problems
(Algebra)

2 tips

Answer 16

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

Question 17

Quick Elimination

Fractions Quantitative Comparison Problems

Answer 17

Is this fraction greater than or less than 1?

If one is greater than 1 and the other isn’t, you’re done!

Question 18

Simplifying Complex Fractions

Fractions Quantitative Comparison Problems

Answer 18

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)

Question 19

Fractions with Exponents

Fractions Quantitative Comparison Problems

Answer 19

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.

Question 20

Percents

Fractions Quantitative Comparison Problems

Answer 20

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.

Question 21

Three-Step Process for Geometry QC Problems

Answer 21

1) Establish what you need to know
2) Establish what you know
3) Establish what you don’t know

Question 22

Diagrams
Geometry QC Problems

5 tips

Answer 22

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!!

Question 23

Word Geometry QC Problems (w/o picture)

2 tips

Answer 23

1) Draw the picture

2) Ask yourself: “What changes to the picture would affect the relative size of the quantities?

Question 24

Word Geometry QC Problems
(w/ specific dimensions, but doesn’t provide actual numbers)

3 tips

Answer 24

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)

Question 25

Greater Than/Less Than 0

Number Properties QC Problems

Answer 25

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

Question 26

Positive and Negative Clues
Number Properties QC Problems

3 Major Tips
2 Reminders

Answer 26

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.

Question 27

Variables with Exponents

Number Properties QC Problems

Answer 27

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.

Question 28

Consecutive Integers

Number Properties QC Problems

Answer 28

To compare the sums or products of sets of consecutive integers, eliminate overlap in order to make a direct comparison.

Question 29

Ratios w/o Numbers

Word QC Problems

Answer 29

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).

Question 30

Principal of Weighted Averages

Word QC Problems

Answer 30

In any question that involves two groups that have some kind of average value, use the principal of weighted averages.

Question 31

Process for Solving Data Interpretation Questions

Answer 31

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.

Question 32

Change in Total Sales

Data Interpretation

Answer 32

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!

Question 33

Percentage Tip

Answer 33

Any amount is a greater percentage of a smaller number than it is of a larger number.

Question 34

Charts w/ Percentages vs. Actual Quantities

Data Interpretation

Answer 34

You cannot assume total sales on a chart showing just percentages! Percentages are different than actual quantities!

Question 35

Percentage Increase and Decrease!

Answer 35

KNOW THE FORMULAS

Percentage Increase:
(new - old) / old

Percentage Decrease:
(old-new) / old