Test your basic knowledge |

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. divisible by 6
Rules for 2 and three: even and the sum of its digits is divisible by three
1/x^a
P(E) + P(F) - P(E and F)
N(n-1)(n-2)...(2)(1) = n!

2. relationship between n choose k and n choose n-k
2pi*r
Always equal - i.e. 9 choose 3 = 9 choose 6
The sum of the areas of the six faces: 2(lw + lh + wh)
A list is ordered and can have duplicates

3. what'S the median if there are an even number of data points?
N!/k!(n-k)! which is also denotes as n choose k
N!/(n-k)!
Mean of the two middle ones
Always equal - i.e. 9 choose 3 = 9 choose 6

4. x^-a
1/x^a
(xy)^a
101010
1 - 1 - root(2)

5. standardization/normalization
Base * height
Subtract the mean from each value and divide by the standard deviation
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
x^(a+b)

6. union of sets A and B
Always equal - i.e. 9 choose 3 = 9 choose 6
A + B - their intersection
1/x^a
1/2 base * height

7. divisible by 3
101010
Sum of its digits is divisible by 3
2(pir^2) + 2pirh; the two bases and the side
Number of outcomes yielding E / number of total outcomes

8. circumference of circle
Pi * r^2
2pi*r
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

9. regular polygon
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.
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication
Any line connecting two points on a circle. The diameter is a chord

10. divisible by 11
2pi*r
Lwh
(1st digit + 3rd + 5th...) - (2nd + 4th + 6th...) is divisible by 11.
A list is ordered and can have duplicates

11. sum of relative frequencies in a frequency distribution
|S|
1 if decimals - 100 if percents
P(E or F) = P(E) + P(F)
The sum of the areas of the six faces: 2(lw + lh + wh)

12. similar triangles
Always equal - i.e. 9 choose 3 = 9 choose 6
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication
P(E or F) = P(E) + P(F)
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).

13. permutations of n different objects
N(n-1)(n-2)...(2)(1) = n!
Side opposite the right angle
1
x^ab

14. area of circle
Pi * r^2
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.
101010
Less affected by outliers than the mean

15. probability that either E or F occur
A list is ordered and can have duplicates
Any line connecting two points on a circle. The diameter is a chord
P(E) + P(F) - P(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.

16. sides of 30/60/90 triangle
Subtract the mean from each value and divide by the standard deviation
Last three digits (taken together) are divisible by 8
N(n-1)(n-2)...(2)(1) = n!
1 - 2 - root(3); note that this is half of an equilateral triangle

17. dividing fractions
N!/k!(n-k)! which is also denotes as n choose k
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).
(x^a)/(y^a)
Invert the second fraction and multiply them

18. volume of rectangle
|S|
Lwh
Pi*r^2h
1

19. 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
Pi*r^2h
Still bh/2 - but you can draw h as a line perpendicular to an extension of any side you take as the base.
Opposite angles formed by two intersecting lines; always congruent

20. differences between a set and a list
A list is ordered and can have duplicates
Any line connecting two points on a circle. The diameter is a chord
A + B - their intersection
1 if decimals - 100 if percents

21. permutations of n objects taken k at a time (order counts)
N!/(n-k)!
(x^a)/(y^a)
Pi*r^2h
1098 etc

22. area of cylinder
2(pir^2) + 2pirh; the two bases and the side
Side opposite the right angle
N-2
|S|

23. divisible by 9
Sum of its digits is divisible by 9
Less affected by outliers than the mean
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides

24. congruency of triangles
Three sides congruent - two sides and included angle - two angles and included side
A + B - their intersection
Lwh
x^(a+b)

25. area of a non-right triangle
Still bh/2 - but you can draw h as a line perpendicular to an extension of any side you take as the base.
Opposite angles formed by two intersecting lines; always congruent
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
Base * height

26. area of trapezoid
Area of sector has the same proportion to the total area that the arc measure (angle) has to 360 degrees.
Side opposite the right angle
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
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

27. mutually exclusive
(1st digit + 3rd + 5th...) - (2nd + 4th + 6th...) is divisible by 11.
P(E or F) = P(E) + P(F)
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.

28. sides of isoceles right triangle
(1st digit + 3rd + 5th...) - (2nd + 4th + 6th...) is divisible by 11.
N-2
1 - 1 - root(2)
At least two congruent sides; the angles opposite these sides are also congruent

29. divisible by 8
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)
Last three digits (taken together) are divisible by 8
101010

30. volume of cylinder
(1st digit + 3rd + 5th...) - (2nd + 4th + 6th...) is divisible by 11.
Pi*r^2h
Pi * r^2
Invert the second fraction and multiply them

31. (x^a)/(x^b)
x^(a-b) or a/x^(b-a)
Still bh/2 - but you can draw h as a line perpendicular to an extension of any side you take as the base.
Subtract the mean from each value and divide by the standard deviation
1098 etc

32. (x^a)(x^b)
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.
1098 etc
x^(a+b)
1 if decimals - 100 if percents

33. how many triangles can a polygon of n sides be divided into?
Lwh
N-2
Sum of its digits is divisible by 3
Mean of the two middle ones

34. length of arc of circle
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.
1
The sum of the areas of the six faces: 2(lw + lh + wh)
N!/(n-k)!

35. possible combinations of three digits without allowing repeats
1098 etc
P(E or F) = P(E) + P(F)
1
Any line connecting two points on a circle. The diameter is a chord

36. area of sector of circle
Area of sector has the same proportion to the total area that the arc measure (angle) has to 360 degrees.
N-2
P(E and F) = P(E)P(F)
x^(a+b)

37. number of elements in set S
P(E) + P(F) - P(E and F)
Sum of its digits is divisible by 9
|S|
N(n-1)(n-2)...(2)(1) = n!

38. (x/y)^a
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication
1 - 2 - root(3); note that this is half of an equilateral triangle
(x^a)/(y^a)
P(E) + P(F) - P(E and F)

39. area of rectangle
The sum of the areas of the six faces: 2(lw + lh + wh)
1098 etc
(n-2)(180 degrees)
Rules for 2 and three: even and the sum of its digits is divisible by three

40. (x^a)^b
Base * height
x^ab
Still bh/2 - but you can draw h as a line perpendicular to an extension of any side you take as the base.
|S|

41. sum of measures of interior angles of a polygon with n sides
Pi * r^2
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
(n-2)(180 degrees)
(1st digit + 3rd + 5th...) - (2nd + 4th + 6th...) is divisible by 11.

42. hypotenuse
Side opposite the right angle
Less affected by outliers than the mean
Three sides congruent - two sides and included angle - two angles and included side
All its interior angles are congruent

43. advantage of median
(n-2)(180 degrees)
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).
P(E) + P(F) - P(E and F)
Less affected by outliers than the mean

44. how to tell if something is prime
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).
Side opposite the right angle
At least two congruent sides; the angles opposite these sides are also congruent

45. combinations of n objects taken k at a time (order doesn'T count)
Invert the second fraction and multiply them
101010
N!/k!(n-k)! which is also denotes as n choose k
x^ab

46. independence of two events E and F
1 - 1 - root(2)
P(E and F) = P(E)P(F)
Rules for 2 and three: even and the sum of its digits is divisible by three
Pi * r^2

47. area of triangle
1/2 base * height
|S|
Base * height
x^(a-b) or a/x^(b-a)

48. vertical angles
1 if decimals - 100 if percents
Opposite angles formed by two intersecting lines; always congruent
P(E or F) = P(E) + P(F)
(n-2)(180 degrees)

49. (x^a)(y^a)
x^ab
Opposite angles formed by two intersecting lines; always congruent
(xy)^a
Sum of its digits is divisible by 9

50. divisible by 4
Last three digits (taken together) are divisible by 8
2(pir^2) + 2pirh; the two bases and the side
Last two digits (taken together) are divisible by 4
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides