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GRE Math: All In One

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. (12sqrt15) / (2sqrt5) =
An isosceles right triangle.
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
x - x+1 - x+2
D/t (distance)/(time)

2. The reciprocal of any non-zero #x is
1/x
P(E) = number of favorable outcomes/total number of possible outcomes
Sum of digits is a multiple of 3 and the last digit is even.
5

3. What is a percent?
A percent is a fraction whose denominator is 100.
67 - 71 - 73
2
441000 = 1 10 10 10 21 * 21

4. 25/2³
= (actual decrease/Original amount) x100% = 20/100x100% = 20%
2²
Even
0

5. 1:1:sqrt2 is the ratio of the sides of what kind of triangle?
x²-y²
Ø=P(E)=1
An isosceles right triangle.
180

6. a^2 - 2ab + b^2
6
C=2 x pi x r OR pi x D
(a - b)^2
Two equal sides and two equal angles.

7. factored binomial product of (x+y)²
53 - 59
Cross multiplication a/b=c/d 4/6=10/15 4(15)=6(10) 60=60
x²+2xy+y²
180

8. 10^6 has how many zeroes?
A=½bh
6
D/t (distance)/(time)
360°

9. Circumference of a circle?
2(pi)r
Diameter(Pi)
an angle that is less than 90°
y = (x + 5)/2

10. What is the name of set with a number of elements which cannot be counted?
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
An infinite set.
A multiple of every integer
360/n

11. Pythagorean theorem
Straight Angle
Ø Ø=Ø
A²+b²=c²
The set of elements found in both A and B.

12. (x-y)(x+y)
1
x²-y²
Edge³
The overlapping sections.

13. If y is directly proportional to x - what does it equal?
The shortest arc between points A and B on a circle'S diameter.
3x - 4x - 5x
1
y/x is a constant

14. How to recognize a # as a multiple of 3
1/2 times 7/3
Sum of digits is a multiple of 3 and the last digit is even.
B?b?b (where b is used as a factor n times)
The sum of the digits is a multiple of 3 (i.e. 45 ... 4 + 5 = 9 so the whole thing is a multiple of 3)

15. 0^0
Undefined
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
10! / 3!(10-3)! = 120
A = length x width

16. formula for distance problems
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
Distance=rate×time or d=rt
8
9

17. How to recognize a # as a multiple of 9
The sum of the digits is a multiple of 9.
Cross multiplication a/b=c/d 4/6=10/15 4(15)=6(10) 60=60
A-b is positive
(distance)/(rate) d/r

18. Volume of a rectangular box
x^(4+7) = x^11
x²-y²
V=Lwh
P(E) = 1/1 = 1

19. A cylinder has a surface area of 22pi. If the cylinder has a height of 10 - what is the radius?
Even prime number
1
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
1:sqrt3:2

20. A triangle is inscribed in a semi circle with legs 5 and 12. What is the circumfermence of the semicircle?
Reciprocal
13pi / 2
angle that is greater than 90° but less than 180°
23 - 29

21. 200 <_ x <_ 300. How many values of x are divisible by 5 & 8?
(base*height) / 2
3
True
x²-y²

22. What is the 'Solution' for a system of linear equations?
The point of intersection of the systems.
360°
The sum of its digits is divisible by 3.
3x - 4x - 5x

23. What transformation occurs if point C is reflected over the x-axis and then the y-axis?
Ø
A reflection about the axis.
23 - 29
1

24. the measure of a straight angle
180°
1
Every number
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.

25. (6sqrt3) x (2sqrt5) =
1.7
3
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
A-b is positive

26. What is the relationship between lengths of the sides of a triangle and the measure of the angles of the triangle?
The longest side is opposite the largest (biggest) angle. The shortest side is opposite the smallest angle. Sides with the same lengths are opposite angles with the same measure.
10! / (10-3)! = 720
(x+y)(x+y)
Diameter(Pi)

27. If a pair of parallel lines is cut by a transversal that'S not perpendicular - the sum of any acute angle and any obtuse angle is
An angle which is supplementary to an interior angle.
180
A=pi*(r^2)
x^(2(4)) =x^8 = (x^4)^2

28. Pi is a ratio of what to what?

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29. How to determine percent decrease?
441000 = 1 10 10 10 21 * 21
12.5%
M= (Y1-Y2)/(X1-X2)
(amount of decrease/original price) x 100%

30. What is a chord of a circle?
An infinite set.
A chord is a line segment joining two points on a circle.
(b + c)
90

31. What number between 70 & 75 - inclusive - has the greatest number of factors?
A set with no members - denoted by a circle with a diagonal through it.
= (actual decrease/Original amount) x100% = 20/100x100% = 20%
500
72

32. 4.809 X 10^7 =
x^(6-3) = x^3
Pi is the ratio of a circle'S circumference to its diameter.
.0004809 X 10^11
3x - 4x - 5x

33. What is the third quartile of the following data set: 44 - 58 - 63 - 63 - 68 - 70 - 82
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
(rate)(time) d=rt
70
1

34. Ø²
Arc length = (n/360) x pi(2r) where n is the number of degrees.
Ø
288 (8 9 4)
All numbers multiples of 1.

35. To decrease a number by x%
N! / (k!)(n-k)!
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
Smallest positive integer
53 - 59

36. If a=-1 and b=3 - what is the value of (4(a^3)(b^2) - 12(a^2)(b^5)) / (16(a^3)(b^2))?
D=rt so r= d/t and t=d/r
Prime numbers (2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23)
10! / 3!(10-3)! = 120
20.5

37. 1/Ø=null If a>b then
11 - 13 - 17 - 19
Be Zero!
A<-b
1

38. 30< all primes<40
288 (8 9 4)
31 - 37
180°
3x - 4x - 5x

39. Vertical lines
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%
A percent is a fraction whose denominator is 100.
= (actual decrease/Original amount) x100% = 20/100x100% = 20%
Do not have slopes!

40. What is an exterior angle?
x(x - y + 1)
Ø
3
An angle which is supplementary to an interior angle.

41. If you have a set of n objects - but you only want to order k of them - what formula do you use to determine the number of permutations?
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
4096
N! / (n-k)!

42. x^6 / x^3
A-b is negative
A = length x width
The longest side is opposite the largest (biggest) angle. The shortest side is opposite the smallest angle. Sides with the same lengths are opposite angles with the same measure.
x^(6-3) = x^3

43. What is the name for a grouping of the members within a set based on a shared characteristic?
x - x+1 - x+2
13pi / 2
x^(6-3) = x^3
A subset.

44. P and r are factors of 100. What is greater - pr or 100?
Indeterminable.
87.5%
A set with a number of elements which can be counted.
1.0843 X 10^11

45. In a triangle where the two legs are 4 and 3 - what is the value of a line directly intersecting the middle coming from the meeting point of the two legs?
26
(a - b)(a + b)
180
2.4. We calculate the area (6) and then turn the triangle on its side and use x as the height to calculate again. (5x)/2=6

46. In any polygon - all external angles equal up to
360°
53 - 59
(n-2) x 180
Do not have slopes!

47. a(b-c)
0
2²
The sum of the digits it a multiple of 3 and the last two digits is a multiple of 4. (i.e 144: 1+4+4=9 which is a multiple of 3 - and 44 is a multiple of 4 - so 144 is a multiple of 12.)
Ab-ac

48. Suppose that the graph of f(x) is the result of sliding the graph of y=2x^2 down 3 units of spaces. What is the new equation?
D=rt so r= d/t and t=d/r
y = 2x^2 - 3
The sum of the digits it a multiple of 3 and the last two digits is a multiple of 4. (i.e 144: 1+4+4=9 which is a multiple of 3 - and 44 is a multiple of 4 - so 144 is a multiple of 12.)
A 30-60-90 triangle.

49. What are the rational numbers?
3/2 - 5/3
(amount of decrease/original price) x 100%
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
The sum of digits is divisible by 9.

50. If a<b - then
4096
Even prime number
A = pi(r^2)
A+c<b+c