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GRE High Frequency Math Terms

Subjects : gre, math

Instructions:

Answer 50 questions in 15 minutes.
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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. What number goes on the bottom of a probability fraction?
The total # of possible outcomes.
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.
Find the total - or whole - first - and then set up a Ratio Box.
1/1

2. Convert to a percentage: 3/5
60%
(x+y)(x-y)
The total # of possible outcomes.
3:4:5 5:12:13

3. How precise do you need to be - using p on the GRE?
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
2r
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.
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

4. What'S a handy rough estimate for a circle'S perimeter - if you know it'S diameter?
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
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
The formula is a + b + c = d where a - b - c are the dimensions of the figure and d is the diagonal.
4 angles are formed. Their sum is 360 degrees

5. HIGH: How do you multiply and divide square roots?
Groups - teams - or committees.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
V=s
Find the total - or whole - first - and then set up a Ratio Box.

6. An integer is divisible by 2 if...
An integer is divisible by 2 if its units digit is divisible by 2.
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.
Not necessarily. This is a trick question - because x could be either positive or negative.
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.

7. HIGH: What is the formula for the diagonal of any square?
S
V=prh (This is just the area multiplied by the height)
S*v2
(0 -0)

8. Explain how to divide fractions.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 4/5 = 2/3 * 5/4
S*v2
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
1.4

9. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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.
2pr -or- pd

10. Does order matter for a permutation? How about for a combination?
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%.
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
An integer is divisible by 9 if the sum of its digits is divisible by 9.
Order does matter for a permutation - but does not matter for a combination.

11. How do you solve a permutation?
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.
Example: 1 < x < 10
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
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.

12. HIGH: Area of a circle
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
A=pr
40%
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

13. Probability Formula
The value that appears most often in a data set.
Favorable Outcomes/Total Possible Outcomes
360 degrees
Find a common denominator and make equivalent fractions. Then add or subtract.

14. HIGH: How do you calculate the length of an arc?
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
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.
An integer is divisible by 9 if the sum of its digits is divisible by 9.
x -2xy + y

15. How do you calculate the percentage of change?
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%.
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
This equals 7 - or 7/1 1/4 = 7/1 * 4/1 = 28/1 = 28

16. HIGH: Rough est. of v2 =
1/x^n For example - 6- = 1/6 = 1/36
1.4
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.
A radius

17. HIGH: What is the factored version of (x+y)(x-y) ?
x-y
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.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
2

18. 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) = 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.
60%
The mode is the number in a set that occurs most frequently. Example: for the set {3 -6 -3 -8 -9 -3 -11} the number 3 appears most frequently so it is the mode.

19. When 2 lines are perpendicular to each other - their intersection forms 4 angles. What degree are these 4 angles?
1/1
Add the exponents - retain the base. for example - x + x5 = x+5 = x7
A radius
90 degrees each.

20. How do you add or subtract fractions?
Find a common denominator and make equivalent fractions. Then add or subtract.
A radius
40%
Order does matter for a permutation - but does not matter for a combination.

21. What causes 80% of errors on the math section of the GRE?
Not reading the problems carefully enough!
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
1/x^n For example - 6- = 1/6 = 1/36
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

22. On the GRE - should you ever assume that diagrams are truthful?
Groups - teams - or committees.
Arrangements - orders - schedules - or lists.
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
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.

23. HIGH: How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
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
This equals 7 - or 7/1 1/4 = 7/1 * 4/1 = 28/1 = 28
6
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.

24. HIGH: What is the Pythagorean theorem?
Not necessarily. This is a trick question - because x could be either positive or negative.
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.
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.
For RIGHT triangles only: c = a + b 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')

25. Define the mode of a set of numbers.
Groups - teams - or committees.
The mode is the number in a set that occurs most frequently. Example: for the set {3 -6 -3 -8 -9 -3 -11} the number 3 appears most frequently so it is the mode.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
1. Factored: x - y Unfactored: (x+y)(x-y) 2. Factored: (x+y) Unfactored: x + 2xy + y 3. Factored: (x-y) Unfactored: x - 2xy + y

26. What is the equation for a group problem?
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.
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
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
This equals 7 - or 7/1 1/4 = 7/1 * 4/1 = 28/1 = 28

27. How is a range expressed with inequalities?
An integer is divisible by 5 if its units digit is either 0 or 5.
Invert the second fraction (reciprocal) and multiply
Multiply numerator times numerator and denominator times denominator.
Example: 1 < x < 10

28. Diameter of a circle?
V=prh (This is just the area multiplied by the height)
2r
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
This triangle is a square divided along its diagonal. Interior angles are 90:45:45 degrees. The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

29. What is the formula to determine probability?
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
(# of possible outcomes that satisfy the condition) (total # of possible outcomes)
Multiply numerator times numerator and denominator times denominator.
3:4:5 5:12:13

30. Solve this: v6 * -v6 = ?
6
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
An integer is divisible by 9 if the sum of its digits is divisible by 9.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.

31. HIGH: What is the mode?
Not reading the problems carefully enough!
The value that appears most often in a data set.
The mode is the number in a set that occurs most frequently. Example: for the set {3 -6 -3 -8 -9 -3 -11} the number 3 appears most frequently so it is the mode.
1. Factored: x - y Unfactored: (x+y)(x-y) 2. Factored: (x+y) Unfactored: x + 2xy + y 3. Factored: (x-y) Unfactored: x - 2xy + y

32. Define the range of a set of numbers.
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.
An integer is divisible by 5 if its units digit is either 0 or 5.
1. Factored: x - y Unfactored: (x+y)(x-y) 2. Factored: (x+y) Unfactored: x + 2xy + y 3. Factored: (x-y) Unfactored: x - 2xy + y
V=s

33. How many angles are formed when 2 lines intersect? and what is the sum of these angles?
4 angles are formed. Their sum is 360 degrees
The mode is the number in a set that occurs most frequently. Example: for the set {3 -6 -3 -8 -9 -3 -11} the number 3 appears most frequently so it is the mode.
25%
180 degrees.

34. v4 =
2
This triangle is a square divided along its diagonal. Interior angles are 90:45:45 degrees. The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
V=s

35. An integer is divisible by 4 if...
(x+y)(x-y)
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.
An integer is divisible by 4 if its last two digits form a number that'S divisible by 4. For example - 712 is divisible by 4 because its last two digits (12) is divisible by 4.
2pr -or- pd

36. HIGH: how do you calculate a diagonal inside a 3-dimensional rectangular box?
This triangle is a square divided along its diagonal. Interior angles are 90:45:45 degrees. The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Percentage Change = Difference/Original * 100
The formula is a + b + c = d where a - b - c are the dimensions of the figure and d is the diagonal.
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.

37. List all the prime numbers that are less than 30:
Order does matter for a permutation - but does not matter for a combination.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
This triangle is a square divided along its diagonal. Interior angles are 90:45:45 degrees. The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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

38. Explain how to calculate an average (arithmetic mean)
Order does matter for a permutation - but does not matter for a combination.
The average - mean - median - or mode.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
1. Factored: x - y Unfactored: (x+y)(x-y) 2. Factored: (x+y) Unfactored: x + 2xy + y 3. Factored: (x-y) Unfactored: x - 2xy + y

39. How do you multiply fractions?
An integer is divisible by 4 if its last two digits form a number that'S divisible by 4. For example - 712 is divisible by 4 because its last two digits (12) is divisible by 4.
4 angles are formed. Their sum is 360 degrees
60%
Multiply numerator times numerator and denominator times denominator.

40. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
Multiply numerator times numerator and denominator times denominator.
That they often have not just one answer - but two. For example - solving x -10x + 24 = 0 factors to (x-4)(x-6)=0 - which means x could equal either 4 or 6. Just accept it.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
1. Given event A: A + notA = 1.

41. HIGH: What is 'absolute value' - and how is it represented?
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
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.
1/1
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.

42. Explain how to solve for 7/
4 angles are formed. Their sum is 360 degrees
The mode is the number in a set that occurs most frequently. Example: for the set {3 -6 -3 -8 -9 -3 -11} the number 3 appears most frequently so it is the mode.
This equals 7 - or 7/1 1/4 = 7/1 * 4/1 = 28/1 = 28
(x-y)

43. HIGH: how do you calculate the surface area of a rectangular box?
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.
1. Raising a fraction (between 0 and 1) to a power greater than 1 results in a SMALLER number. For example: (1/2) = 1/4. 2. A number raised to the 0 power is 1 - no matter what the number is. For example: 1 -287 = 1.
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.
4 angles are formed. Their sum is 360 degrees

44. How many degrees does a circle contain?
25%
Example: 1 < x < 10
360 degrees
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.

45. The probability of an event happening and the probability of an event NOT happening must add up to what number?
(x+y)(x-y)
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
360 degrees
1. Given event A: A + notA = 1.

46. HIGH: What are the percentages for standard deviation?
A line is a 180-degree angle.
The formula is a + b + c = d where a - b - c are the dimensions of the figure and d is the diagonal.
This equals 7 - or 7/1 1/4 = 7/1 * 4/1 = 28/1 = 28
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |

47. What is the factored version of x -2xy + y ?
(x-y)
An integer is divisible by 4 if its last two digits form a number that'S divisible by 4. For example - 712 is divisible by 4 because its last two digits (12) is divisible by 4.
Add the exponents - retain the base. for example - x + x5 = x+5 = x7
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.

48. HIGH: What is a '30:60:90' triangle?
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.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
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'.
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

49. Define a factorial of a number - and how it is written.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Example: 1 < x < 10
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.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions

50. HIGH: List the two most common side ratios for right triangles
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
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.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
3:4:5 5:12:13

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