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. 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
A list is ordered and can have duplicates
1/x^a
Less affected by outliers than the mean

2. (x^a)^b
1
Base * height
x^ab
Three sides congruent - two sides and included angle - two angles and included side

3. sides of isoceles right triangle
Last two digits (taken together) are divisible by 4
Less affected by outliers than the mean
N!/(n-k)!
1 - 1 - root(2)

4. divisible by 4
A + B - their intersection
Last two digits (taken together) are divisible by 4
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
Less affected by outliers than the mean

5. number of elements in set S
(1st digit + 3rd + 5th...) - (2nd + 4th + 6th...) is divisible by 11.
A + B - their intersection
|S|
101010

6. divisible by 9
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
Sum of its digits is divisible by 9
Pi * r^2
x^(a+b)

7. dividing fractions
Invert the second fraction and multiply them
2(pir^2) + 2pirh; the two bases and the side
N-2
P(E or F) = P(E) + P(F)

8. area of parallelogram
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
P(E) + P(F) - P(E and F)
Base * height
P(E and F) = P(E)P(F)

9. divisible by 8
Last three digits (taken together) are divisible by 8
The sum of the areas of the six faces: 2(lw + lh + wh)
Area of sector has the same proportion to the total area that the arc measure (angle) has to 360 degrees.
Three sides congruent - two sides and included angle - two angles and included side

10. divisible by 3
Sum of its digits is divisible by 3
2(pir^2) + 2pirh; the two bases and the side
1/x^a
x^ab

11. permutations of n different objects
A + B - their intersection
A list is ordered and can have duplicates
N(n-1)(n-2)...(2)(1) = n!
The sum of the areas of the six faces: 2(lw + lh + wh)

12. hypotenuse
Pi*r^2h
Side opposite the right angle
1/2 base * height
1098 etc

13. length of arc of circle
At least two congruent sides; the angles opposite these sides are also congruent
x^ab
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.

14. how many triangles can a polygon of n sides be divided into?
x^ab
x^(a-b) or a/x^(b-a)
At least two congruent sides; the angles opposite these sides are also congruent
N-2

15. probability of an event E
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
Number of outcomes yielding E / number of total outcomes
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.
N-2

16. isosceles triangle
At least two congruent sides; the angles opposite these sides are also congruent
A list is ordered and can have duplicates
N(n-1)(n-2)...(2)(1) = n!
x^(a+b)

17. what'S the median if there are an even number of data points?
N-2
All its interior angles are congruent
Mean of the two middle ones
A list is ordered and can have duplicates

18. chord
Mean of the two middle ones
Rules for 2 and three: even and the sum of its digits is divisible by three
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.

19. difference between normal or population standard deviation and the sample standard deviation
P(E and F) = P(E)P(F)
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides
Lwh
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

20. (x^a)(y^a)
Lwh
(x^a)/(y^a)
(xy)^a
1098 etc

21. x^0
1
Pi*r^2h
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.

22. possible combinations of three digits without allowing repeats
Sum of its digits is divisible by 9
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.
1098 etc

23. area of cylinder
x^(a+b)
Subtract the mean from each value and divide by the standard deviation
2(pir^2) + 2pirh; the two bases and the side
P(E and F) = P(E)P(F)

24. sum of measures of interior angles of a polygon with n sides
(n-2)(180 degrees)
x^(a+b)
Subtract the mean from each value and divide by the standard deviation
1 - 2 - root(3); note that this is half of an equilateral triangle

25. permutations of n objects taken k at a time (order counts)
Less affected by outliers than the mean
N!/(n-k)!
P(E or F) = P(E) + P(F)
Rules for 2 and three: even and the sum of its digits is divisible by three

26. volume of cylinder
Pi*r^2h
(x^a)/(y^a)
x^ab
(xy)^a

27. relationship between n choose k and n choose n-k
N!/(n-k)!
Always equal - i.e. 9 choose 3 = 9 choose 6
P(E) + P(F) - P(E and F)
Area of sector has the same proportion to the total area that the arc measure (angle) has to 360 degrees.

28. area of sector of circle
N(n-1)(n-2)...(2)(1) = n!
Base * height
Area of sector has the same proportion to the total area that the arc measure (angle) has to 360 degrees.
Pi * r^2

29. union of sets A and B
Base * height
1/x^a
A + B - their intersection
All its interior angles are congruent

30. sum of relative frequencies in a frequency distribution
Opposite angles formed by two intersecting lines; always congruent
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.
Less affected by outliers than the mean
1 if decimals - 100 if percents

31. independence of two events E and F
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).
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
P(E and F) = P(E)P(F)

32. sides of 30/60/90 triangle
A + B - their intersection
1 - 2 - root(3); note that this is half of an equilateral triangle
|S|
N!/(n-k)!

33. how to tell if something is prime
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.
Still bh/2 - but you can draw h as a line perpendicular to an extension of any side you take as the base.
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

34. standardization/normalization
P(E) + P(F) - P(E and F)
All its interior angles are congruent
P(E or F) = P(E) + P(F)
Subtract the mean from each value and divide by the standard deviation

35. x^-a
1/x^a
All its interior angles are congruent
P(E) + P(F) - P(E and F)
Rules for 2 and three: even and the sum of its digits is divisible by three

36. (x^a)/(x^b)
x^(a-b) or a/x^(b-a)
1 if decimals - 100 if percents
Pi*r^2h
N-2

37. volume of rectangle
Sum of its digits is divisible by 3
1
Lwh
Mean of the two middle ones

38. area of rectangle
P(E) + P(F) - P(E and F)
The sum of the areas of the six faces: 2(lw + lh + wh)
Always equal - i.e. 9 choose 3 = 9 choose 6
N-2

39. vertical angles
Opposite angles formed by two intersecting lines; always congruent
N!/(n-k)!
Rules for 2 and three: even and the sum of its digits is divisible by three
Last three digits (taken together) are divisible by 8

40. area of triangle
1/2 base * height
1 - 1 - root(2)
Any line connecting two points on a circle. The diameter is a chord
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. area of trapezoid
At least two congruent sides; the angles opposite these sides are also congruent
Sum of its digits is divisible by 3
N-2
1/2(b1 + b2)h - where b1 and b2 are the two parallel sides

42. possible combinations of three digits allowing repeats
Lwh
P(E and F) = P(E)P(F)
1
101010

43. probability that either E or F occur
|S|
P(E or F) = P(E) + P(F)
P(E) + P(F) - P(E and F)
A + B - their intersection

44. congruency of triangles
Three sides congruent - two sides and included angle - two angles and included side
Still bh/2 - but you can draw h as a line perpendicular to an extension of any side you take as the base.
Any line connecting two points on a circle. The diameter is a chord
1 if decimals - 100 if percents

45. advantage of median
Less affected by outliers than the mean
Lwh
1 - 1 - root(2)
Divide it by the prime numbers from 2 to the closest to the square root of the number (round down).

46. area of circle
A list is ordered and can have duplicates
Length of arc has the same proportion to the circumference that the arc measure (angle) has to 360 degrees.
Pi * r^2
2pi*r

47. 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
101010
Rules for 2 and three: even and the sum of its digits is divisible by three
(1st digit + 3rd + 5th...) - (2nd + 4th + 6th...) is divisible by 11.

48. differences between a set and a list
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).
A list is ordered and can have duplicates
(1st digit + 3rd + 5th...) - (2nd + 4th + 6th...) is divisible by 11.

49. (x/y)^a
P(E and F) = P(E)P(F)
Congruent angles (check this to be sure) but possibly different size. Can use proportions to get other values by cross-multiplication
(x^a)/(y^a)
Invert the second fraction and multiply them

50. regular polygon
(x^a)/(y^a)
All its interior angles are congruent
Last three digits (taken together) are divisible by 8
x^(a-b) or a/x^(b-a)