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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. number of elements in set S
Sum of its digits is divisible by 3
P(E and F) = P(E)P(F)
|S|
Last two digits (taken together) are divisible by 4

2. probability of an event E
Mean of the two middle ones
Rules for 2 and three: even and the sum of its digits is divisible by three
Still bh/2 - but you can draw h as a line perpendicular to an extension of any side you take as the base.
Number of outcomes yielding E / number of total outcomes

3. possible combinations of three digits allowing repeats
N-2
Three sides congruent - two sides and included angle - two angles and included side
1 - 2 - root(3); note that this is half of an equilateral triangle
101010

4. (x^a)/(x^b)
Mean of the two middle ones
Pi*r^2h
The sum of the areas of the six faces: 2(lw + lh + wh)
x^(a-b) or a/x^(b-a)

5. area of circle
P(E or F) = P(E) + P(F)
101010
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
Pi * r^2

6. divisible by 3
Sum of its digits is divisible by 3
Invert the second fraction and multiply them
x^(a-b) or a/x^(b-a)
Area of sector has the same proportion to the total area that the arc measure (angle) has to 360 degrees.

7. sides of isoceles right triangle
1 - 1 - root(2)
(x^a)/(y^a)
Still bh/2 - but you can draw h as a line perpendicular to an extension of any side you take as the base.
The sum of the areas of the six faces: 2(lw + lh + wh)

8. (x^a)(y^a)
Base * height
Side opposite the right angle
(xy)^a
1 - 1 - root(2)

9. area of a non-right triangle
All its interior angles are congruent
Still bh/2 - but you can draw h as a line perpendicular to an extension of any side you take as the base.
x^(a+b)
Pi*r^2h

10. x^-a
The sum of the areas of the six faces: 2(lw + lh + wh)
1/x^a
Always equal - i.e. 9 choose 3 = 9 choose 6
Base * height

11. possible combinations of three digits without allowing repeats
1098 etc
Last two digits (taken together) are divisible by 4
1 - 2 - root(3); note that this is half of an equilateral triangle
At least two congruent sides; the angles opposite these sides are also congruent

12. standardization/normalization
Subtract the mean from each value and divide by the standard deviation
1098 etc
2(pir^2) + 2pirh; the two bases and the side
Less affected by outliers than the mean

13. area of cylinder
P(E and F) = P(E)P(F)
1 - 1 - root(2)
2(pir^2) + 2pirh; the two bases and the side
P(E) + P(F) - P(E and F)

14. area of rectangle
1/x^a
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.
Pi * r^2
The sum of the areas of the six faces: 2(lw + lh + wh)

15. probability that either E or F occur
Subtract the mean from each value and divide by the standard deviation
P(E) + P(F) - P(E and F)
Last three digits (taken together) are divisible by 8
A list is ordered and can have duplicates

16. divisible by 9
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 9
Rules for 2 and three: even and the sum of its digits is divisible by three
1/2 base * height

17. circumference of circle
Side opposite the right angle
2pi*r
N!/(n-k)!
1 - 2 - root(3); note that this is half of an equilateral triangle

18. how to tell if something is prime
Last three digits (taken together) are divisible by 8
All its interior angles are congruent
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).
x^(a+b)

19. divisible by 4
P(E and F) = P(E)P(F)
At least two congruent sides; the angles opposite these sides are also congruent
x^(a+b)
Last two digits (taken together) are divisible by 4

20. relationship between n choose k and n choose n-k
|S|
1 - 1 - root(2)
Always equal - i.e. 9 choose 3 = 9 choose 6
P(E and F) = P(E)P(F)

21. sum of relative frequencies in a frequency distribution
N(n-1)(n-2)...(2)(1) = n!
Pi*r^2h
Base * height
1 if decimals - 100 if percents

22. volume of cylinder
Pi*r^2h
Sum of its digits is divisible by 3
Base * height
N(n-1)(n-2)...(2)(1) = n!

23. divisible by 11
Opposite angles formed by two intersecting lines; always congruent
(1st digit + 3rd + 5th...) - (2nd + 4th + 6th...) is divisible by 11.
Mean of the two middle ones
Side opposite the right angle

24. (x^a)(x^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
x^(a+b)
Opposite angles formed by two intersecting lines; always congruent
Rules for 2 and three: even and the sum of its digits is divisible by three

25. permutations of n different objects
Three sides congruent - two sides and included angle - two angles and included side
2(pir^2) + 2pirh; the two bases and the side
Side opposite the right angle
N(n-1)(n-2)...(2)(1) = n!

26. combinations of n objects taken k at a time (order doesn'T count)
Area of sector has the same proportion to the total area that the arc measure (angle) has to 360 degrees.
N!/k!(n-k)! which is also denotes as n choose k
2pi*r
1/x^a

27. vertical angles
1 if decimals - 100 if percents
Opposite angles formed by two intersecting lines; always congruent
1 - 2 - root(3); note that this is half of an equilateral triangle
1/2 base * height

28. area of sector of circle
Still bh/2 - but you can draw h as a line perpendicular to an extension of any side you take as the base.
x^ab
101010
Area of sector has the same proportion to the total area that the arc measure (angle) has to 360 degrees.

29. length of arc of circle
(n-2)(180 degrees)
Invert the second fraction and multiply them
x^ab
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.

30. similar triangles
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication
Three sides congruent - two sides and included angle - two angles and included side
1
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

31. hypotenuse
Side opposite the right angle
Base * height
Last three digits (taken together) are divisible by 8
Sum of its digits is divisible by 3

32. sides of 30/60/90 triangle
1/2 base * height
Rules for 2 and three: even and the sum of its digits is divisible by three
1 - 2 - root(3); note that this is half of an equilateral triangle
A list is ordered and can have duplicates

33. sum of measures of interior angles of a polygon with n sides
(x^a)/(y^a)
(n-2)(180 degrees)
A + B - their intersection
The sum of the areas of the six faces: 2(lw + lh + wh)

34. isosceles triangle
(xy)^a
At least two congruent sides; the angles opposite these sides are also congruent
Lwh
Side opposite the right angle

35. dividing fractions
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.
P(E) + P(F) - P(E and F)
Invert the second fraction and multiply them
x^(a+b)

36. independence of two events E and F
Still bh/2 - but you can draw h as a line perpendicular to an extension of any side you take as the base.
Invert the second fraction and multiply them
P(E and F) = P(E)P(F)
Less affected by outliers than the mean

37. volume of rectangle
Last two digits (taken together) are divisible by 4
Lwh
Invert the second fraction and multiply them
P(E and F) = P(E)P(F)

38. union of sets A and B
A + B - their intersection
N-2
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
P(E) + P(F) - P(E and F)

39. difference between normal or population standard deviation and the sample standard deviation
x^ab
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
Sum of its digits is divisible by 3
P(E and F) = P(E)P(F)

40. area of triangle
P(E or F) = P(E) + P(F)
P(E) + P(F) - P(E and F)
1/2 base * height
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

41. differences between a set and a list
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
A list is ordered and can have duplicates
2pi*r
Opposite angles formed by two intersecting lines; always congruent

42. how many triangles can a polygon of n sides be divided into?
Invert the second fraction and multiply them
N-2
1 if decimals - 100 if percents
|S|

43. advantage of median
Last three digits (taken together) are divisible by 8
x^(a-b) or a/x^(b-a)
Less affected by outliers than the mean
P(E or F) = P(E) + P(F)

44. divisible by 6
(x^a)/(y^a)
Rules for 2 and three: even and the sum of its digits is divisible by three
1 - 1 - root(2)
Sum of its digits is divisible by 9

45. regular polygon
x^(a-b) or a/x^(b-a)
All its interior angles are congruent
2(pir^2) + 2pirh; the two bases and the side
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.

46. x^0
1/x^a
P(E) + P(F) - P(E and F)
1
x^(a+b)

47. (x/y)^a
1/2 base * height
(x^a)/(y^a)
Three sides congruent - two sides and included angle - two angles and included side
Base * height

48. mutually exclusive
1 - 1 - root(2)
Number of outcomes yielding E / number of total outcomes
P(E or F) = P(E) + P(F)
At least two congruent sides; the angles opposite these sides are also congruent

49. what'S the median if there are an even number of data points?
Mean of the two middle ones
1 if decimals - 100 if percents
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication
Pi*r^2h

50. area of parallelogram
2(pir^2) + 2pirh; the two bases and the side
x^(a+b)
Base * height
Side opposite the right angle