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. mutually exclusive
Side opposite the right angle
P(E or F) = P(E) + P(F)
Sum of its digits is divisible by 3
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.

2. standardization/normalization
Subtract the mean from each value and divide by the standard deviation
1/x^a
N(n-1)(n-2)...(2)(1) = n!
N-2

3. congruency of triangles
Rules for 2 and three: even and the sum of its digits is divisible by three
1
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
Three sides congruent - two sides and included angle - two angles and included side

4. area of rectangle
At least two congruent sides; the angles opposite these sides are also congruent
Mean of the two middle ones
The sum of the areas of the six faces: 2(lw + lh + wh)
2pi*r

5. divisible by 6
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
(xy)^a
Always equal - i.e. 9 choose 3 = 9 choose 6
Rules for 2 and three: even and the sum of its digits is divisible by three

6. (x^a)(y^a)
x^(a+b)
Last three digits (taken together) are divisible by 8
Side opposite the right angle
(xy)^a

7. combinations of n objects taken k at a time (order doesn'T count)
Less affected by outliers than the mean
1/x^a
N!/k!(n-k)! which is also denotes as n choose k
Base * height

8. what'S the median if there are an even number of data points?
A list is ordered and can have duplicates
Side opposite the right angle
Sum of its digits is divisible by 9
Mean of the two middle ones

9. x^0
1
x^ab
The sum of the areas of the six faces: 2(lw + lh + wh)
2pi*r

10. x^-a
P(E) + P(F) - P(E and F)
1/x^a
(xy)^a
Side opposite the right angle

11. area of triangle
All its interior angles are congruent
(xy)^a
(1st digit + 3rd + 5th...) - (2nd + 4th + 6th...) is divisible by 11.
1/2 base * height

12. (x^a)/(x^b)
Base * height
A + B - their intersection
x^(a-b) or a/x^(b-a)
(1st digit + 3rd + 5th...) - (2nd + 4th + 6th...) is divisible by 11.

13. number of elements in set S
|S|
P(E and F) = P(E)P(F)
1/x^a
Subtract the mean from each value and divide by the standard deviation

14. isosceles triangle
(xy)^a
At least two congruent sides; the angles opposite these sides are also congruent
1 if decimals - 100 if percents
Invert the second fraction and multiply them

15. area of trapezoid
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
101010
(n-2)(180 degrees)

16. dividing fractions
Invert the second fraction and multiply them
(x^a)/(y^a)
Three sides congruent - two sides and included angle - two angles and included side
Rules for 2 and three: even and the sum of its digits is divisible by three

17. sum of measures of interior angles of a polygon with n sides
(n-2)(180 degrees)
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
Last two digits (taken together) are divisible by 4
1098 etc

18. 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.
N-2
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.
Sum of its digits is divisible by 3

19. probability of an event E
x^(a-b) or a/x^(b-a)
Number of outcomes yielding E / number of total outcomes
x^(a+b)
At least two congruent sides; the angles opposite these sides are also congruent

20. divisible by 11
(1st digit + 3rd + 5th...) - (2nd + 4th + 6th...) is divisible by 11.
P(E) + P(F) - P(E and F)
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.

21. sum of relative frequencies in a frequency distribution
1 if decimals - 100 if percents
(n-2)(180 degrees)
Mean of the two middle ones
x^(a+b)

22. area of circle
Any line connecting two points on a circle. The diameter is a chord
Pi * r^2
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)

23. divisible by 9
Sum of its digits is divisible by 9
A list is ordered and can have duplicates
x^ab
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides

24. volume of rectangle
x^(a-b) or a/x^(b-a)
1 - 2 - root(3); note that this is half of an equilateral triangle
|S|
Lwh

25. union of sets A and B
A + B - their intersection
|S|
x^(a-b) or a/x^(b-a)
Last three digits (taken together) are divisible by 8

26. how to tell if something is prime
1
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).
A list is ordered and can have duplicates
The sum of the areas of the six faces: 2(lw + lh + wh)

27. similar triangles
Sum of its digits is divisible by 9
1 - 2 - root(3); note that this is half of an equilateral triangle
Last two digits (taken together) are divisible by 4
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication

28. permutations of n different objects
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication
N(n-1)(n-2)...(2)(1) = n!
x^(a-b) or a/x^(b-a)
Always equal - i.e. 9 choose 3 = 9 choose 6

29. permutations of n objects taken k at a time (order counts)
x^(a+b)
Base * height
Rules for 2 and three: even and the sum of its digits is divisible by three
N!/(n-k)!

30. area of parallelogram
Invert the second fraction and multiply them
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
Base * height

31. difference between normal or population standard deviation and the sample standard deviation
Last two digits (taken together) are divisible by 4
101010
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
Less affected by outliers than the mean

32. sides of 30/60/90 triangle
x^(a-b) or a/x^(b-a)
1 - 2 - root(3); note that this is half of an equilateral triangle
Any line connecting two points on a circle. The diameter is a chord
A list is ordered and can have duplicates

33. possible combinations of three digits allowing repeats
Base * height
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).
1 - 1 - root(2)
101010

34. sides of isoceles right triangle
N-2
Three sides congruent - two sides and included angle - two angles and included side
Any line connecting two points on a circle. The diameter is a chord
1 - 1 - root(2)

35. area of cylinder
2pi*r
2(pir^2) + 2pirh; the two bases and the side
1
Side opposite the right angle

36. differences between a set and a list
Pi * r^2
A list is ordered and can have duplicates
x^ab
Lwh

37. possible combinations of three digits without allowing repeats
2pi*r
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).
1098 etc
Invert the second fraction and multiply them

38. area of a non-right triangle
101010
P(E and F) = P(E)P(F)
(xy)^a
Still bh/2 - but you can draw h as a line perpendicular to an extension of any side you take as the base.

39. chord
Pi*r^2h
Any line connecting two points on a circle. The diameter is a chord
101010
N!/(n-k)!

40. (x^a)^b
Area of sector has the same proportion to the total area that the arc measure (angle) has to 360 degrees.
N(n-1)(n-2)...(2)(1) = n!
Any line connecting two points on a circle. The diameter is a chord
x^ab

41. volume of cylinder
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication
Side opposite the right angle
Pi*r^2h
1/2 base * height

42. probability that either E or F occur
Invert the second fraction and multiply them
(x^a)/(y^a)
A + B - their intersection
P(E) + P(F) - P(E and F)

43. divisible by 4
Pi*r^2h
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).
Last two digits (taken together) are divisible by 4
At least two congruent sides; the angles opposite these sides are also congruent

44. regular polygon
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.
2(pir^2) + 2pirh; the two bases and the side
All its interior angles are congruent
Invert the second fraction and multiply them

45. relationship between n choose k and n choose n-k
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
Base * height
Always equal - i.e. 9 choose 3 = 9 choose 6

46. advantage of median
Less affected by outliers than the mean
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
1 - 2 - root(3); note that this is half of an equilateral triangle
Mean of the two middle ones

47. area of sector of circle
x^(a+b)
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.
Area of sector has the same proportion to the total area that the arc measure (angle) has to 360 degrees.

48. how many triangles can a polygon of n sides be divided into?
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)!
N(n-1)(n-2)...(2)(1) = n!
N-2

49. hypotenuse
Invert the second fraction and multiply them
The sum of the areas of the six faces: 2(lw + lh + wh)
Side opposite the right angle
(xy)^a

50. divisible by 8
Base * height
Last three digits (taken together) are divisible by 8
A + B - their intersection
N!/(n-k)!