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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. 5/6 in percent?
(p + q)/5
83.333%
90
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150

2. Volume of a rectangular solid
(length)(width)(height)
27
3
3x - 4x - 5x

3. In a Rectangle - each angles measures
90°
(length)(width)(height)
Its divisible by 2 and by 3.
2sqrt6

4. Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
180°
The set of elements which can be found in either A or B.
2^9 / 2 = 256
The interesection of A and B.

5. What are 'Supplementary angles?'
Factors are few - multiples are many.
Infinite.
Two angles whose sum is 180.
5

6. What is the 'Solution' for a system of linear equations?
The point of intersection of the systems.
48
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
M= (Y1-Y2)/(X1-X2)

7. For similar triangles - the ratio of their corresponding sides is 2:3. What is the ratio of their areas?
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
P(E) = ø
(x+y)(x+y)
Every number

8. Probability of Event all cases
1
an angle that is less than 90°
1
Ø=P(E)=1

9. Area of a circle
16^8 64^5 = (4^3)^5 = 4^15 16^8=(4^2)^8 = 4^16
Undefined - because we can'T divide by 0.
A=pi*(r^2)
P=4s (s=side)

10. What are congruent triangles?
500
A=½bh
Triangles with same measure and same side lengths.
0

11. What are the real numbers?
41 - 43 - 47
N! / (n-k)!
All the numbers on the number line (negative - rational - irrational - decimal - integer). All the numbers on the GRE are real. (-2 - 1 - .25 - 1/2 - pi)
130pi

12. If y is directly proportional to x - what does it equal?
y/x is a constant
The sum of digits is divisible by 9.
Sum of digits is a multiple of 3 and the last digit is even.
Relationship cannot be determined (what if x is negative?)

13. factored binomial product of (x-y)²
x²-2xy+y²
A multiple of every integer
an angle that is less than 90°
16.6666%

14. What is the set of elements found in both A and B?
Lies opposite the greater angle
The interesection of A and B.
D=rt so r= d/t and t=d/r
Add them. i.e. (5^7) * (5^3) = 5^10

15. Slope
A reflection about the axis.
Positive
y2-y1/x2-x1
72

16. Circumference of a circle?
Diameter(Pi)
2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - 29
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]

17. To decrease a number by x%
(amount of decrease/original price) x 100%
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
P(E) = ø
Ø

18. 3 is the opposite of
The empty set - denoted by a circle with a diagonal through it.
M
3
1

19. Volume of a cube
Null
C = (pi)d
180
Edge³

20. What is the slope of a vertical line?

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21. Circumference of a Circle
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
C=2 x pi x r OR pi x D
360/n
3 - -3

22. Employee X is paid 19.50 per hour no matter how many a week. Employee Y earns 18 for the first 40 and 1.5 the hourly wage for every hour after that. If both earned the same amount and worked the same in one week - how many did each work?
Its divisible by 2 and by 3.
48
Two (Ø×2=Ø)
(a + b)^2

23. What is the maximum value for the function g(x) = (-2x^2) -1?
An angle which is supplementary to an interior angle.
Undefined - because we can'T divide by 0.
1
75:11

24. (a^-1)/a^5
500
1/a^6
1/x
Cd

25. What is the empty set?
The triangle is a right triangle. The triangle is isosceles (AC=BC). The ratio of the lengths of the three sides is x:x:xv2.
The set of elements found in both A and B.
A set with no members - denoted by a circle with a diagonal through it.
Smallest positive integer

26. Probability of an Event
6 : 1 : 2
Do not have slopes!
Subtract them. i.e (5^7)/(5^3)= 5^4
P(E) = number of favorable outcomes/total number of possible outcomes

27. 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.
An isosceles right triangle.
52
Ø

28. What is an exterior angle?
x²-2xy+y²
Ø
An angle which is supplementary to an interior angle.
Two (Ø×2=Ø)

29. What is the slope of a horizontal line?
0
1/a^6
1
The overlapping sections.

30. If 8 schools are in a conference - how many games are played if each team plays each other exactly once?
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 + b)^2
55%
28. n = 8 - k = 2. n! / k!(n-k)!

31. What are the rational numbers?
26
Sum of digits is a multiple of 3 and the last digit is even.
(a + b)^2
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)

32. Simplify the expression [(b^2 - c^2) / (b - c)]
2
27^(-4)
The steeper the slope.
(b + c)

33. Evaluate 4/11 + 11/12
1 & 37/132
A<-b
Even
Two (Ø×2=Ø)

34. Ø divided by 7
A reflection about the origin.
Ø
1.0843 X 10^11
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

35. How many sides does a hexagon have?
2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - 29
P= 2L + 2w
3
6

36. What is the measure of an exterior angle of a regular pentagon?
12sqrt2
The triangle is a right triangle. The hypotenuse is twice the length of the shorter leg. The ratio of the length of the three sides is x:xv3:2x
72
18

37. Legs 5 - 12. Hypotenuse?
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
x²-y²
13
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.)

38. In a Regular Polygon - the measure of each exterior angle
360/n
The shortest arc between points A and B on a circle'S diameter.
(a + b)^2
2 & 3/7

39. Legs 6 - 8. Hypotenuse?
12.5%
10
53 - 59
N! / (n-k)!

40. 1/Ø=null If a>b then
A<-b
Members or elements
The direction of the inequality is reversed.
Ab+ac

41. What does scientific notation mean?
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
3x - 4x - 5x
No - only like radicals can be added.
0

42. Volume of a rectangular box
V=Lwh
The empty set - denoted by a circle with a diagonal through it.
x^(6-3) = x^3
20.5

43. The larger the absolute value of the slope...
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
18
52
The steeper the slope.

44. What is the 'union' of A and B?
An infinite set.
The set of elements which can be found in either A or B.
A natural number greater than 1 that has no positive divisors other than 1 and itself
angle that is greater than 90° but less than 180°

45. Formula for the area of a circle?
A+c<b+c
1/2 times 7/3
Sector area = (n/360) X (pi)r^2
A = pi(r^2)

46. What are the smallest three prime numbers greater than 65?
A-b is positive
67 - 71 - 73
F(x + c)
61 - 67

47. 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
(amount of decrease/original price) x 100%
1
90pi
180

48. Ø Is
EVEN
1/2 times 7/3
27^(-4)
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.

49. What is the ratio of the sides of an isosceles right triangle?
52
Ø
F(x-c)
1:1:sqrt2

50. What is the intersection of A and B?
N! / (n-k)!
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.)
The set of elements found in both A and B.
The last 2 digits are a multiple of 4. (i.e 144 .... 44 is a multiple of 4 - so 144 must also be a multiple of 4.)