Instructions:

• Answer 50 questions in 15 minutes.
• If you are not ready to take this test, you can study here.
• Match each statement with the correct term.
• Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.

1. How do you calculate the percentage of change?
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
V75 = v253 = 5v3 - and v27 = v93 = 3v3. So we have 5v3/3v3. The v3 in the top and bottom of the fraction cancel - leaving 5/3.
Percentage Change = Difference/Original * 100
(a+b)(a-b)


2. What is the sum of any 'big' angle and any 'Small' angle?
180 degrees.
1. Raising a fraction (between 0 and 1) to a power greater than 1 results in a SMALLER number. For example: (1/2)² = 1/4. 2. A number raised to the 0 power is 1 - no matter what the number is. For example: 1 -287° = 1.
Length of an Arc = (n/360)(2pr) - where 'n' equals the central angle (the angle formed by the two edge radii of the arc). For example: if n=60 - then n/360 = 1/6 - which means the arc formed by the 60-degree central angle will be 1/6 of the circle'S
Use the FOIL method: First - Outer - Inner - Last. This simply means to multiply every term in the first parentheses by every term in the second parentheses. Example: (x+4)(x+3) = First: (xx) + Outer: (x3) + Inner: (4x) + Last: (43) = (xx)+(x3)+(x4)+


3. When 2 lines are perpendicular to each other - their intersection forms 4 angles. What degree are these 4 angles?
3:4:5 5:12:13
90 degrees each.
The average - mean - median - or mode.
T = G1 + G2 - B + N Where T = Total G1 = first Group G2 = second Group B = members who are in Both groups N = members who are in Neither group


4. List two odd behaviors of exponents
1. Raising a fraction (between 0 and 1) to a power greater than 1 results in a SMALLER number. For example: (1/2)² = 1/4. 2. A number raised to the 0 power is 1 - no matter what the number is. For example: 1 -287° = 1.
V75 = v253 = 5v3 - and v27 = v93 = 3v3. So we have 5v3/3v3. The v3 in the top and bottom of the fraction cancel - leaving 5/3.
Not reading the problems carefully enough!
A=pr²


5. What should you do BEFORE you start to solve a GRE math problem?

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6. Probability Formula
That - unlike a normal chart - they are constructed to HIDE information or make it HARDER to understand. Be sure to scroll down - read everything - and look carefully for hidden information - asterisks - footnotes - small print - and funny units.
Example: 1 < x < 10
Favorable Outcomes/Total Possible Outcomes
(x+y)(x-y)


7. HIGH: Rough est. of v3 =
Order does matter for a permutation - but does not matter for a combination.
1.7
PEMDAS (Please Excuse My Dear Aunt Sally): P = Parentheses. Solve anything inside of parentheses first. E = Exponents. Solve these second. MD = Multiplication - Division. From left to right - do all multiplication and division during one step through
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.


8. HIGH: What is the unfactored version of (x-y)² ?
The length of any one side of a triangle must be less than the sum of the other two sides. It must also be greater than the difference between the other two sides. So - 'A' will always be < B+C - and > B-C or C-B.
An integer is divisible by 9 if the sum of its digits is divisible by 9.
x² -2xy + y²
T = G1 + G2 - B + N Where T = Total G1 = first Group G2 = second Group B = members who are in Both groups N = members who are in Neither group


9. How do you multiply fractions?
It will be a great advantage on test day to have your times table memorized from 1 through 15.
The range is the difference between the biggest and smallest numbers in the set. Example: for the set {2 -6 -13 -3 -15 -4 -9} the smallest number is 2 - largest is 15 - so the range is 15-2=13.
Multiply numerator times numerator and denominator times denominator.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7


10. What is the 'distributive law'?
A(b+c) = ab + ac a(b-c) = ab - ac - For example - 12(66) + 12(24) is the same as 12(66+24) - or 12(90) = 1 -080.
1.7
Absolute value is a number'S distance away from zero on the number line. It is always positive - regardless of whether the number is positive or negative. It is represented with | |. For example - |-5| = 5 - and |5| = 5.
A digit is a number that makes up other numbers. There are ten digits: 0 -1 -2 -3 -4 -5 -6 -7 -8 -9. Every 'number' is made up of one or more digits. For example - the number 528 is made up of three digits - a 5 - a 2 - and an 8.


11. If x² = 144 - does v144 = x?
80%
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Not reading the problems carefully enough!
Not necessarily. This is a trick question - because x could be either positive or negative.


12. An integer is divisible by 4 if...

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13. What is the key to dealing with ratio questions?
Find a common denominator and make equivalent fractions. Then add or subtract.
Find the total - or whole - first - and then set up a Ratio Box.
Not necessarily. This is a trick question - because x could be either positive or negative.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)


14. What is the factored version of x² -2xy + y² ?
By Plugging In an actual value for the variable(s). This will be quicker - more accurate - you'll avoid built-in traps - and you can use the calculator. When Plugging In - use simple numbers but avoid 1 and 0.
(x-y)²
1.4
A 90-degree angle.


15. HIGH: What is 'absolute value' - and how is it represented?

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16. HIGH: How much of your times table should you know - for the GRE?
360 degrees
It will be a great advantage on test day to have your times table memorized from 1 through 15.
Multiply all elements of both sides of the equation by 2 (the denominator of the fraction). This will produce 10x + 3 = 14x. Solve from there: 3 = 4x - x = 3/4.
(x-y)²


17. HIGH: How do you multiply powers with the same base?
An integer is divisible by 9 if the sum of its digits is divisible by 9.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
That - unlike a normal chart - they are constructed to HIDE information or make it HARDER to understand. Be sure to scroll down - read everything - and look carefully for hidden information - asterisks - footnotes - small print - and funny units.


18. HIGH: Define the formula for calculating slope.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
An integer is divisible by 2 if its units digit is divisible by 2.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
The range is the difference between the biggest and smallest numbers in the set. Example: for the set {2 -6 -13 -3 -15 -4 -9} the smallest number is 2 - largest is 15 - so the range is 15-2=13.


19. HIGH: What is the unfactored version of x²-y² ?
(x+y)(x-y)
1. Figure out how many slots you have (i.e. you'Re supposed to bring home 3 different types of ice cream) 2. Write down the number of possible options for each slot (i.e. 5 flavors of ice cream at the store - 5 options for the 1st slot - 4 options fo
Invert the second fraction (reciprocal) and multiply
60%


20. v4 =
2
Multiply all elements of both sides of the equation by 2 (the denominator of the fraction). This will produce 10x + 3 = 14x. Solve from there: 3 = 4x - x = 3/4.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
An integer is divisible by 9 if the sum of its digits is divisible by 9.


21. What do permutation problems often ask for?
The equation must be set equal to zero. If during the test one appears that'S not - before you can solve it you must first manipulate it so it is equal to zero.
Arrangements - orders - schedules - or lists.
Multiply numerator times numerator and denominator times denominator.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.


22. HIGH: What is the side ratio for a 30:60:90 triangle?
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
1/1
T = G1 + G2 - B + N Where T = Total G1 = first Group G2 = second Group B = members who are in Both groups N = members who are in Neither group
x²-y²


23. HIGH: Volume of a cylinder?
V=pr²h (This is just the area multiplied by the height)
First - translate into clear math: 56 = x/100(80) ('56 is x one-hundredths of 80') = 56 = 80x/100 = 56 = 4x/5 Divide both sides by 4/5 (multiply by 5/4) 70 = x - so 70%.
Groups - teams - or committees.
S*v2


24. HIGH: What is the order of math operations - and the mnemonic to remember it?
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
Example: 1 < x < 10
1. Factored: x² - y² Unfactored: (x+y)(x-y) 2. Factored: (x+y)² Unfactored: x² + 2xy + y² 3. Factored: (x-y)² Unfactored: x² - 2xy + y²
PEMDAS (Please Excuse My Dear Aunt Sally): P = Parentheses. Solve anything inside of parentheses first. E = Exponents. Solve these second. MD = Multiplication - Division. From left to right - do all multiplication and division during one step through


25. HIGH: What is the Pythagorean theorem?

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26. Explain the special properties of zero.
A=pr²
V=s³
Zero is even. It is an integer. It is neither positive nor negative. Zero multiplied by any other number = zero. You cannot divide by zero.
6


27. An integer is divisible by 8 if...

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28. HIGH: Area of a triangle?
This is an equilateral triangle that has been divided along its height. Interior angles are 30:60:90 degrees. Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse. This allows you to deduce any side - given
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
Probability A + Probability B
1. Raising a fraction (between 0 and 1) to a power greater than 1 results in a SMALLER number. For example: (1/2)² = 1/4. 2. A number raised to the 0 power is 1 - no matter what the number is. For example: 1 -287° = 1.


29. Diameter of a circle?
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
1. Raising a fraction (between 0 and 1) to a power greater than 1 results in a SMALLER number. For example: (1/2)² = 1/4. 2. A number raised to the 0 power is 1 - no matter what the number is. For example: 1 -287° = 1.
1/x^n For example - 6-² = 1/6² = 1/36
2r


30. Convert to a percentage: 4/5
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
The range is the difference between the biggest and smallest numbers in the set. Example: for the set {2 -6 -13 -3 -15 -4 -9} the smallest number is 2 - largest is 15 - so the range is 15-2=13.
80%
Calculate and add the areas of all of 6 its sides. Example: for a rectangle with dimensions 2 x 3 x 4 - there will be 2 sides each - for each combination of these dimensions. That is - 2 each of 2x3 - 2 each of 3x4 - and 2 each of 4x2.


31. What is the name of a line that extends from the center of a circle to the edge of a circle?
Not necessarily. This is a trick question - because x could be either positive or negative.
y = mx + b -- where: x -y are the coordinates of any point on the line (allows you to locate) m is the slope of the line b is the intercept (where the line crosses the y-axis) Sometimes on the GRE - 'a' is substituted for 'm' - as in 'y = ax + b'.
A radius
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.


32. Explain how to calculate an average (arithmetic mean)
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
1/1
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
80%


33. An integer is divisible by 2 if...
By Plugging In an actual value for the variable(s). This will be quicker - more accurate - you'll avoid built-in traps - and you can use the calculator. When Plugging In - use simple numbers but avoid 1 and 0.
If order matters - then you have a permutation -- do NOT divide. If order does NOT matter - then you have a combination -- divide by the factorial of the number of available slots.
An integer is divisible by 2 if its units digit is divisible by 2.
Bh


34. HIGH: What is the median?
A triangle in which one of the three interior angles is 90 degrees.
1. Figure out how many slots you have (i.e. there are 3 winning positions in a race - 1st - 2nd - and 3rd) 2. Write down the number of possible options for each slot (i.e. 5 runners in the race - so 5 options for the 1st slot - 4 options for the 2nd
The # falling in the center of an ordered data set
An integer is divisible by 5 if its units digit is either 0 or 5.


35. On the GRE - should you ever assume that diagrams are truthful?
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
x² + 2xy + y²
1


36. What'S one way to avoid mistakes on algebra questions in the GRE?

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37. HIGH: Area of a circle
A=pr²
Invert the second fraction (reciprocal) and multiply
V=s³
Probability A * Probability B


38. HIGH: What numbers does ETS hope you'll forget to consider - for quant comp questions?
The factorial of a number is that number times every positive whole number smaller than that number - down to 1. Example: 6! means the factorial of 6 - which = 65432*1 = 720.
Multiply each numerator by the other fraction'S denominator. Example: 3/7 and 7/12. Multiply 312 = 36 - and 77 = 49. If you completed the full calculation - you'd also cross-multiply the denominators - but you don'T have to in order to compare values
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
An isoceles right angle. Remember that interior angles are 90:45:45 degrees. The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.


39. An integer is divisible by 5 if...
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
(x+y)²
The length of any one side of a triangle must be less than the sum of the other two sides - and greater than the difference between the other two sides.
An integer is divisible by 5 if its units digit is either 0 or 5.


40. What number goes on the bottom of a probability fraction?
The total # of possible outcomes.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
A line is a 180-degree angle.
1. Given event A: A + notA = 1.


41. HIGH: What is a '30:60:90' triangle?
S²
First - translate into clear math: 56 = x/100(80) ('56 is x one-hundredths of 80') = 56 = 80x/100 = 56 = 4x/5 Divide both sides by 4/5 (multiply by 5/4) 70 = x - so 70%.
360 degrees
This is an equilateral triangle that has been divided along its height. Interior angles are 30:60:90 degrees. Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse. This allows you to deduce any side - given


42. What'S the most important thing to remember about charts you'll see on the GRE?
It will be a great advantage on test day to have your times table memorized from 1 through 15.
Always read the answer choices first. Try to eliminate choices by ballparking or estimating. But watch out for 'Trap' answers that look temptingly correct at first glance.
Not necessarily. This is a trick question - because x could be either positive or negative.
That - unlike a normal chart - they are constructed to HIDE information or make it HARDER to understand. Be sure to scroll down - read everything - and look carefully for hidden information - asterisks - footnotes - small print - and funny units.


43. HIGH: Rough est. of v2 =
1/x^n For example - 6-² = 1/6² = 1/36
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
An integer is divisible by 9 if the sum of its digits is divisible by 9.
1.4


44. Convert to a percentage: 3/5
60%
Not reading the problems carefully enough!
A line is a 180-degree angle.
Order does matter for a permutation - but does not matter for a combination.


45. The three exterior angles of a triangle add up to...
This is similar to an Average Pie - and can be used for some story problems. Draw a circle. Top half holds the Distance or other Amount. Bottom left holds Time. Bottom right holds Rate. Rate * Time = Amount
360 degrees
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
Not necessarily. This is a trick question - because x could be either positive or negative.


46. How many angles are formed when 2 lines intersect? and what is the sum of these angles?
60%
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Multiply all elements of both sides of the equation by 2 (the denominator of the fraction). This will produce 10x + 3 = 14x. Solve from there: 3 = 4x - x = 3/4.
4 angles are formed. Their sum is 360 degrees


47. An integer is divisible by 3 if...
An integer is divisible by 3 if the sum of its digits is divisible by 3. For example - adding the digits of the number 2 -145 (2+1+4+5) = 12 - which is divisible by 3.
1.7
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Length of an Arc = (n/360)(2pr) - where 'n' equals the central angle (the angle formed by the two edge radii of the arc). For example: if n=60 - then n/360 = 1/6 - which means the arc formed by the 60-degree central angle will be 1/6 of the circle'S


48. HIGH: Describe how to deal with 2 sets of parentheses.
2pr -or- pd
By Plugging In an actual value for the variable(s). This will be quicker - more accurate - you'll avoid built-in traps - and you can use the calculator. When Plugging In - use simple numbers but avoid 1 and 0.
(x-y)²
Use the FOIL method: First - Outer - Inner - Last. This simply means to multiply every term in the first parentheses by every term in the second parentheses. Example: (x+4)(x+3) = First: (xx) + Outer: (x3) + Inner: (4x) + Last: (43) = (xx)+(x3)+(x4)+


49. If something is certain to happen - how is the probability of this event expressed mathematically?
Length of an Arc = (n/360)(2pr) - where 'n' equals the central angle (the angle formed by the two edge radii of the arc). For example: if n=60 - then n/360 = 1/6 - which means the arc formed by the 60-degree central angle will be 1/6 of the circle'S
1/1
'Big' angles and 'Small' angles.
1.7


50. Convert to a percentage: 2/5
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
40%
Bh