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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. hypotenuse
At least two congruent sides; the angles opposite these sides are also congruent
1
Mean of the two middle ones
Side opposite the right angle

2. area of a non-right triangle
|S|
Still bh/2 - but you can draw h as a line perpendicular to an extension of any side you take as the base.
Rules for 2 and three: even and the sum of its digits is divisible by three
Area of sector has the same proportion to the total area that the arc measure (angle) has to 360 degrees.

3. area of parallelogram
1098 etc
Last three digits (taken together) are divisible by 8
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication
Base * height

4. dividing fractions
Still bh/2 - but you can draw h as a line perpendicular to an extension of any side you take as the base.
(n-2)(180 degrees)
Invert the second fraction and multiply them
Three sides congruent - two sides and included angle - two angles and included side

5. what'S the median if there are an even number of data points?
Mean of the two middle ones
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).
Any line connecting two points on a circle. The diameter is a chord
1/x^a

6. differences between a set and a list
A list is ordered and can have duplicates
P(E) + P(F) - P(E and F)
Side opposite the right angle
At least two congruent sides; the angles opposite these sides are also congruent

7. possible combinations of three digits allowing repeats
P(E and F) = P(E)P(F)
P(E) + P(F) - P(E and F)
101010
Number of outcomes yielding E / number of total outcomes

8. how many triangles can a polygon of n sides be divided into?
The sum of the areas of the six faces: 2(lw + lh + wh)
All its interior angles are congruent
Number of outcomes yielding E / number of total outcomes
N-2

9. (x^a)(y^a)
(1st digit + 3rd + 5th...) - (2nd + 4th + 6th...) is divisible by 11.
(xy)^a
(n-2)(180 degrees)
N!/(n-k)!

10. divisible by 11
A list is ordered and can have duplicates
1 if decimals - 100 if percents
x^(a+b)
(1st digit + 3rd + 5th...) - (2nd + 4th + 6th...) is divisible by 11.

11. mutually exclusive
Side opposite the right angle
P(E or F) = P(E) + P(F)
(xy)^a
Subtract the mean from each value and divide by the standard deviation

12. isosceles triangle
At least two congruent sides; the angles opposite these sides are also congruent
A + B - their intersection
Invert the second fraction and multiply them
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides

13. vertical angles
(x^a)/(y^a)
Opposite angles formed by two intersecting lines; always congruent
1 - 2 - root(3); note that this is half of an equilateral triangle
x^ab

14. area of trapezoid
Sum of its digits is divisible by 3
1 - 1 - root(2)
Mean of the two middle ones
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides

15. volume of cylinder
The sum of the areas of the six faces: 2(lw + lh + wh)
Always equal - i.e. 9 choose 3 = 9 choose 6
Mean of the two middle ones
Pi*r^2h

16. area of triangle
Last three digits (taken together) are divisible by 8
P(E or F) = P(E) + P(F)
Opposite angles formed by two intersecting lines; always congruent
1/2 base * height

17. x^-a
The sum of the areas of the six faces: 2(lw + lh + wh)
1/x^a
Pi * r^2
(xy)^a

18. (x^a)(x^b)
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).
N(n-1)(n-2)...(2)(1) = n!
x^(a+b)
Three sides congruent - two sides and included angle - two angles and included side

19. sides of 30/60/90 triangle
1 - 2 - root(3); note that this is half of an equilateral triangle
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.
Pi*r^2h
N!/(n-k)!

20. area of sector of circle
1/2 base * height
N!/(n-k)!
Area of sector has the same proportion to the total area that the arc measure (angle) has to 360 degrees.
All its interior angles are congruent

21. divisible by 3
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.
Number of outcomes yielding E / number of total outcomes
101010

22. regular polygon
Always equal - i.e. 9 choose 3 = 9 choose 6
(1st digit + 3rd + 5th...) - (2nd + 4th + 6th...) is divisible by 11.
Still bh/2 - but you can draw h as a line perpendicular to an extension of any side you take as the base.
All its interior angles are congruent

23. number of elements in set S
101010
|S|
A + B - their intersection
Lwh

24. divisible by 6
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
Rules for 2 and three: even and the sum of its digits is divisible by three
A list is ordered and can have duplicates
N-2

25. sides of isoceles right triangle
1 - 1 - root(2)
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.
x^(a-b) or a/x^(b-a)
P(E or F) = P(E) + P(F)

26. divisible by 4
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).
Three sides congruent - two sides and included angle - two angles and included side
1098 etc
Last two digits (taken together) are divisible by 4

27. permutations of n different objects
(1st digit + 3rd + 5th...) - (2nd + 4th + 6th...) is divisible by 11.
Three sides congruent - two sides and included angle - two angles and included side
N(n-1)(n-2)...(2)(1) = n!
Still bh/2 - but you can draw h as a line perpendicular to an extension of any side you take as the base.

28. (x^a)^b
At least two congruent sides; the angles opposite these sides are also congruent
x^ab
P(E or F) = P(E) + P(F)
Any line connecting two points on a circle. The diameter is a chord

29. congruency of triangles
The sum of the areas of the six faces: 2(lw + lh + wh)
Any line connecting two points on a circle. The diameter is a chord
Three sides congruent - two sides and included angle - two angles and included side
x^(a-b) or a/x^(b-a)

30. volume of rectangle
All its interior angles are congruent
Area of sector has the same proportion to the total area that the arc measure (angle) has to 360 degrees.
Lwh
N(n-1)(n-2)...(2)(1) = n!

31. independence of two events E and F
P(E and F) = P(E)P(F)
101010
Sum of its digits is divisible by 3
Last two digits (taken together) are divisible by 4

32. advantage of median
Mean of the two middle ones
N-2
101010
Less affected by outliers than the mean

33. sum of relative frequencies in a frequency distribution
1 if decimals - 100 if percents
N(n-1)(n-2)...(2)(1) = n!
Always equal - i.e. 9 choose 3 = 9 choose 6
N!/k!(n-k)! which is also denotes as n choose k

34. difference between normal or population standard deviation and the sample standard deviation
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)
Mean of the two middle ones
A list is ordered and can have duplicates

35. possible combinations of three digits without allowing repeats
N-2
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication
1/x^a
1098 etc

36. combinations of n objects taken k at a time (order doesn'T count)
Base * height
N!/k!(n-k)! which is also denotes as n choose k
P(E or F) = P(E) + P(F)
2pi*r

37. x^0
1
Pi * r^2
Subtract the mean from each value and divide by the standard deviation
Still bh/2 - but you can draw h as a line perpendicular to an extension of any side you take as the base.

38. relationship between n choose k and n choose n-k
2pi*r
Always equal - i.e. 9 choose 3 = 9 choose 6
(n-2)(180 degrees)
Side opposite the right angle

39. probability of an event E
(x^a)/(y^a)
Number of outcomes yielding E / number of total outcomes
P(E or F) = P(E) + P(F)
Sum of its digits is divisible by 3

40. area of cylinder
2(pir^2) + 2pirh; the two bases and the side
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
(n-2)(180 degrees)

41. how to tell if something is prime
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).
(1st digit + 3rd + 5th...) - (2nd + 4th + 6th...) is divisible by 11.
All its interior angles are congruent
Opposite angles formed by two intersecting lines; always congruent

42. divisible by 9
N!/k!(n-k)! which is also denotes as n choose k
1 - 1 - root(2)
1 - 2 - root(3); note that this is half of an equilateral triangle
Sum of its digits is divisible by 9

43. (x^a)/(x^b)
x^(a-b) or a/x^(b-a)
Any line connecting two points on a circle. The diameter is a chord
1 if decimals - 100 if percents
2(pir^2) + 2pirh; the two bases and the side

44. similar triangles
1/x^a
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication
Lwh
N-2

45. (x/y)^a
Sum of its digits is divisible by 9
(x^a)/(y^a)
(n-2)(180 degrees)
Always equal - i.e. 9 choose 3 = 9 choose 6

46. circumference of circle
(x^a)/(y^a)
1098 etc
N!/k!(n-k)! which is also denotes as n choose k
2pi*r

47. divisible by 8
(xy)^a
Less affected by outliers than the mean
Last three digits (taken together) are divisible by 8
Always equal - i.e. 9 choose 3 = 9 choose 6

48. permutations of n objects taken k at a time (order counts)
Last two digits (taken together) are divisible by 4
N!/(n-k)!
Area of sector has the same proportion to the total area that the arc measure (angle) has to 360 degrees.
A + B - their intersection

49. probability that either E or F occur
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 9
(xy)^a
P(E) + P(F) - P(E and F)

50. standardization/normalization
Side opposite the right angle
x^ab
1
Subtract the mean from each value and divide by the standard deviation