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GRE Math Rules

Subjects : gre, math

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. possible combinations of three digits without allowing repeats
Subtract the mean from each value and divide by the standard deviation
Always equal - i.e. 9 choose 3 = 9 choose 6
1098 etc
Base * height

2. congruency of triangles
Three sides congruent - two sides and included angle - two angles and included side
Area of sector has the same proportion to the total area that the arc measure (angle) has to 360 degrees.
P(E or F) = P(E) + P(F)
1098 etc

3. chord
P(E or F) = P(E) + P(F)
(xy)^a
1
Any line connecting two points on a circle. The diameter is a chord

4. mutually exclusive
Less affected by outliers than the mean
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).
Sum of its digits is divisible by 3
P(E or F) = P(E) + P(F)

5. probability of an event E
Number of outcomes yielding E / number of total outcomes
1098 etc
101010
P(E or F) = P(E) + P(F)

6. sides of isoceles right triangle
Less affected by outliers than the mean
1 - 1 - root(2)
N!/k!(n-k)! which is also denotes as n choose k
1 - 2 - root(3); note that this is half of an equilateral triangle

7. divisible by 3
Still bh/2 - but you can draw h as a line perpendicular to an extension of any side you take as the base.
1 - 2 - root(3); note that this is half of an equilateral triangle
1 - 1 - root(2)
Sum of its digits is divisible by 3

8. (x^a)(x^b)
Side opposite the right angle
The sum of the areas of the six faces: 2(lw + lh + wh)
Sum of its digits is divisible by 3
x^(a+b)

9. sides of 30/60/90 triangle
1 - 2 - root(3); note that this is half of an equilateral triangle
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
N!/k!(n-k)! which is also denotes as n choose k
x^(a-b) or a/x^(b-a)

10. area of sector of circle
Pi*r^2h
Area of sector has the same proportion to the total area that the arc measure (angle) has to 360 degrees.
Any line connecting two points on a circle. The diameter is a chord
Still bh/2 - but you can draw h as a line perpendicular to an extension of any side you take as the base.

11. area of circle
Sum of its digits is divisible by 3
Still bh/2 - but you can draw h as a line perpendicular to an extension of any side you take as the base.
Base * height
Pi * r^2

12. (x^a)/(x^b)
2(pir^2) + 2pirh; the two bases and the side
(xy)^a
x^(a-b) or a/x^(b-a)
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).

13. independence of two events E and F
P(E or F) = P(E) + P(F)
Any line connecting two points on a circle. The diameter is a chord
P(E and F) = P(E)P(F)
1098 etc

14. difference between normal or population standard deviation and the sample standard deviation
|S|
In computing the average squared difference from the mean (taking the root of this is the standard deviation) - divide by n-1 instead of n
N!/(n-k)!
At least two congruent sides; the angles opposite these sides are also congruent

15. relationship between n choose k and n choose n-k
Always equal - i.e. 9 choose 3 = 9 choose 6
1/x^a
1098 etc
1 - 1 - root(2)

16. area of rectangle
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.
N(n-1)(n-2)...(2)(1) = n!
P(E and F) = P(E)P(F)
The sum of the areas of the six faces: 2(lw + lh + wh)

17. volume of rectangle
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).
Lwh
Always equal - i.e. 9 choose 3 = 9 choose 6
Pi*r^2h

18. permutations of n objects taken k at a time (order counts)
N!/(n-k)!
101010
Subtract the mean from each value and divide by the standard deviation
N!/k!(n-k)! which is also denotes as n choose k

19. sum of measures of interior angles of a polygon with n sides
(n-2)(180 degrees)
(x^a)/(y^a)
Side opposite the right angle
Last two digits (taken together) are divisible by 4

20. standardization/normalization
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication
Lwh
Subtract the mean from each value and divide by the standard deviation
Side opposite the right angle

21. divisible by 4
Rules for 2 and three: even and the sum of its digits is divisible by three
x^(a+b)
In computing the average squared difference from the mean (taking the root of this is the standard deviation) - divide by n-1 instead of n
Last two digits (taken together) are divisible by 4

22. permutations of n different objects
Less affected by outliers than the mean
(x^a)/(y^a)
N(n-1)(n-2)...(2)(1) = n!
1/x^a

23. area of triangle
P(E and F) = P(E)P(F)
A + B - their intersection
Subtract the mean from each value and divide by the standard deviation
1/2 base * height

24. (x^a)(y^a)
(n-2)(180 degrees)
x^ab
x^(a+b)
(xy)^a

25. combinations of n objects taken k at a time (order doesn'T count)
N!/k!(n-k)! which is also denotes as n choose k
x^(a+b)
|S|
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication

26. length of arc of circle
1/x^a
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.
Pi*r^2h
1 - 2 - root(3); note that this is half of an equilateral triangle

27. divisible by 8
Last three digits (taken together) are divisible by 8
1 if decimals - 100 if percents
Sum of its digits is divisible by 9
2pi*r

28. area of trapezoid
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
1098 etc
Mean of the two middle ones
All its interior angles are congruent

29. possible combinations of three digits allowing repeats
2(pir^2) + 2pirh; the two bases and the side
(xy)^a
101010
Sum of its digits is divisible by 9

30. regular polygon
N-2
Base * height
Less affected by outliers than the mean
All its interior angles are congruent

31. area of parallelogram
1 - 1 - root(2)
A list is ordered and can have duplicates
P(E or F) = P(E) + P(F)
Base * height

32. x^0
(xy)^a
x^(a+b)
Base * height
1

33. area of a non-right triangle
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication
Still bh/2 - but you can draw h as a line perpendicular to an extension of any side you take as the base.
Pi*r^2h
x^(a-b) or a/x^(b-a)

34. dividing fractions
At least two congruent sides; the angles opposite these sides are also congruent
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).
Mean of the two middle ones
Invert the second fraction and multiply them

35. probability that either E or F occur
P(E) + P(F) - P(E and F)
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.
Rules for 2 and three: even and the sum of its digits is divisible by three
101010

36. (x/y)^a
Subtract the mean from each value and divide by the standard deviation
1 - 1 - root(2)
Rules for 2 and three: even and the sum of its digits is divisible by three
(x^a)/(y^a)

37. divisible by 9
|S|
All its interior angles are congruent
Sum of its digits is divisible by 9
Pi*r^2h

38. differences between a set and a list
x^(a-b) or a/x^(b-a)
A list is ordered and can have duplicates
P(E or F) = P(E) + P(F)
1 if decimals - 100 if percents

39. how many triangles can a polygon of n sides be divided into?
Last three digits (taken together) are divisible by 8
Area of sector has the same proportion to the total area that the arc measure (angle) has to 360 degrees.
Sum of its digits is divisible by 3
N-2

40. similar triangles
Last two digits (taken together) are divisible by 4
N!/(n-k)!
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication
(n-2)(180 degrees)

41. hypotenuse
N-2
Side opposite the right angle
Last three digits (taken together) are divisible by 8
(xy)^a

42. divisible by 11
(1st digit + 3rd + 5th...) - (2nd + 4th + 6th...) is divisible by 11.
Sum of its digits is divisible by 9
(x^a)/(y^a)
At least two congruent sides; the angles opposite these sides are also congruent

43. (x^a)^b
x^ab
1/2 base * height
Subtract the mean from each value and divide by the standard deviation
|S|

44. how to tell if something is prime
|S|
Opposite angles formed by two intersecting lines; always congruent
1 - 2 - root(3); note that this is half of an equilateral triangle
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).

45. x^-a
1/x^a
2pi*r
2(pir^2) + 2pirh; the two bases and the side
Pi*r^2h

46. circumference of circle
x^ab
2pi*r
Last two digits (taken together) are divisible by 4
Any line connecting two points on a circle. The diameter is a chord

47. volume of cylinder
Pi*r^2h
1/x^a
A + B - their intersection
Base * height

48. area of cylinder
2(pir^2) + 2pirh; the two bases and the side
(n-2)(180 degrees)
Area of sector has the same proportion to the total area that the arc measure (angle) has to 360 degrees.
Invert the second fraction and multiply them

49. what'S the median if there are an even number of data points?
1
Mean of the two middle ones
2(pir^2) + 2pirh; the two bases and the side
Any line connecting two points on a circle. The diameter is a chord

50. isosceles triangle
Less affected by outliers than the mean
Area of sector has the same proportion to the total area that the arc measure (angle) has to 360 degrees.
At least two congruent sides; the angles opposite these sides are also congruent
Side opposite the right angle