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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. 1:1:sqrt2 is the ratio of the sides of what kind of triangle?
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 empty set - denoted by a circle with a diagonal through it.
F(x-c)
An isosceles right triangle.

2. x^2 = 9. What is the value of x?
Every number
0
3 - -3
P= 2L + 2w

3. How many multiples does a given number have?
Infinite.
5 - 12 - 13
= (actual decrease/Original amount) x 100%
41 - 43 - 47

4. 5/8 in percent?
1
360°
62.5%
P= 2L + 2w

5. In a Rectangle - each angles measures
B?b?b (where b is used as a factor n times)
90°
(length)(width)(height)
2 & 3/7

6. formula for area of a triangle
Ø
y = (x + 5)/2
A=½bh
Factors are few - multiples are many.

7. (12sqrt15) / (2sqrt5) =
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
An isosceles right triangle.
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15

8. What are complementary angles?
Subtract them. i.e (5^7)/(5^3)= 5^4
Two angles whose sum is 90.
Reciprocal
A<-b

9. (x^2)^4
(a - b)^2
Even
.0004809 X 10^11
x^(2(4)) =x^8 = (x^4)^2

10. 1/Ø=null If a>b then
A<-b
3
61 - 67
67 - 71 - 73

11. A brick with dimensions 10. 15 and 25 weighs 1.5 kg. A second brick (same density) has dimensions 12 - 18 - and 30. What is the weight of the second brick?
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
2.592 kg
Null
A natural number greater than 1 that has no positive divisors other than 1 and itself

12. What is an arc of a circle?
360°
441000 = 1 10 10 10 21 * 21
x²+2xy+y²
An arc is a portion of a circumference of a circle.

13. 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?
The point of intersection of the systems.
Undefined
11 - 13 - 17 - 19
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

14. Consecutive integers
x - x+1 - x+2
1.0843 X 10^11
90pi
7 / 1000

15. Important properties of a 30-60-90 triangle?
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
N! / (k!)(n-k)!
Do not have slopes!
1

16. If E is certain
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
P(E) = 1/1 = 1
An infinite set.
1

17. Pi is a ratio of what to what?

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18. What is the 'Solution' for a system of linear equations?
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
(n-2) x 180
The point of intersection of the systems.
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%

19. A quadrilateral where two diagonals bisect each other
Ab+ac
288 (8 9 4)
360°
Parallelogram

20. How do you solve proportions? a/b=c/d
An angle which is supplementary to an interior angle.
C = 2(pi)r
Cross multiplication a/b=c/d 4/6=10/15 4(15)=6(10) 60=60
y = 2x^2 - 3

21. What is the 'Solution' for a set of inequalities.
75:11
The overlapping sections.
x²-y²
The point of intersection of the systems.

22. 6w^2 - w - 15 = 0
A reflection about the origin.
3/2 - 5/3
The interesection of A and B.
1:sqrt3:2

23. Formula for the area of a sector of a circle?
Sector area = (n/360) X (pi)r^2
37.5%
Relationship cannot be determined (what if x is negative?)
(a + b)^2

24. If 8 schools are in a conference - how many games are played if each team plays each other exactly once?
A 30-60-90 triangle.
2 & 3/7
28. n = 8 - k = 2. n! / k!(n-k)!
23 - 29

25. 1 is the
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
Smallest positive integer
360/n
The greatest value minus the smallest.

26. What is the graph of f(x) shifted right c units or spaces?
V=Lwh
V=side³
F(x-c)
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)

27. First 10 prime #s
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)
2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - 29
V=l×w×h
90pi

28. Which is greater? 200x^295 or 10x^294?
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
(a - b)^2
A-b is positive
Relationship cannot be determined (what if x is negative?)

29. There are 10 finalists for the school spelling bee. A first - second - and third place trophy will be awarded. How many different people can get the three prizes?
V=l×w×h
10! / 3!(10-3)! = 120
B?b?b (where b is used as a factor n times)
The interesection of A and B.

30. What is the measure of an exterior angle of a regular pentagon?
72
M
y/x is a constant
4:5

31. Suppose that the graph of f(x) is the result of stretching y=x + 5 away from the x-axis by a factor of 2. What is the new equation for the graph f(x)?
y = (x + 5)/2
A multiple of every integer
Pi is the ratio of a circle'S circumference to its diameter.
P= 2L + 2w

32. The larger the absolute value of the slope...
360°
zero
Add them. i.e. (5^7) * (5^3) = 5^10
The steeper the slope.

33. Simplify (a^2 + b)^2 - (a^2 - b)^2
3
V=l×w×h
4a^2(b)
Smallest positive integer

34. Circumference of a circle
B?b?b (where b is used as a factor n times)
2
2(pi)r
an angle that is less than 90°

35. In any polygon - all external angles equal up to
Infinite.
V=side³
3x - 4x - 5x
360°

36. Slope given 2 points
28. n = 8 - k = 2. n! / k!(n-k)!
2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - 29
52
M= (Y1-Y2)/(X1-X2)

37. Is 0 even or odd?
The sum of its digits is divisible by 3.
Even
Undefined
Cd

38. Area of a circle
4096
90
A=pi*(r^2)
10

39. Volume of a rectangular box
Indeterminable.
1.7
A=½bh
V=Lwh

40. If r - t - s & u are distinct - consecutive prime numbers - less than 31 - which of the following could be an average of them (4 - 4.25 - 6 - 9 - 24 - 22 - 24)
1
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
Two equal sides and two equal angles.
4.25 - 6 - 22

41. Can you simplify sqrt72?
3x - 4x - 5x
(p + q)/5
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
31 - 37

42. What is the relationship between lengths of the sides of a triangle and the measure of the angles of the triangle?
Lies opposite the greater angle
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
0
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.

43. 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
Even prime number
180
3 - -3
1/2 times 7/3

44. a(b+c)
The overlapping sections.
Ab+ac
4.25 - 6 - 22
Triangles with same measure and same side lengths.

45. Define a 'Term' -
Subtract them. i.e (5^7)/(5^3)= 5^4
A grouping of the members within a set based on a shared characteristic.
1.7
A term is a numerical constant or the product (or quotient) of a numerical constant and one or more variables. (3x - 4x^2 and 2a/c)

46. What is the order of operations?
(a - b)(a + b)
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
Even prime number
1 & 37/132

47. Ø Is neither
Positive or Negative
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.)
1:1:sqrt2
Cd

48. What is it called when a point is reflected to the quadrant opposite it (i.e. I to III or II to IV)?
(a - b)^2
72
Yes - like radicals can be added/subtracted.
A reflection about the origin.

49. What is the 'domain' of a function?
The set of input values for a function.
x(x - y + 1)
4a^2(b)
72

50. The consecutive angles in a parallelogram equal
180°
An arc is a portion of a circumference of a circle.
1 - P(E)
An isosceles right triangle.