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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. What is the set of elements found in both A and B?
The interesection of A and B.
180 degrees
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)
1

2. How many sides does a hexagon have?
x^(2(4)) =x^8 = (x^4)^2
A chord is a line segment joining two points on a circle.
6
1/x

3. 1/6 in percent?
16.6666%
P=2(l+w)
(x+y)(x+y)
41 - 43 - 47

4. Circumference of a circle?
An is positive
Diameter(Pi)
A set with a number of elements which can be counted.
(b + c)

5. Dividing by a number is the same as multiplying it by its
9 : 25
72
Reciprocal
The point of intersection of the systems.

6. 8.84 / 5.2
Two equal sides and two equal angles.
The set of output values for a function.
1.7
8

7. Ratio of ages of Anna and Emma is 3:5 and of Emma and Nicolas is 3:5. What is the ratio of Anna to Nicholas' ages?
4725
(distance)/(rate) d/r
x²+2xy+y²
9 : 25

8. 25/2³
Sum of digits is a multiple of 3 and the last digit is even.
87.5%
Members or elements
2²

9. The Perimeter of a rectangle
A 30-60-90 triangle.
55%
P=2(l+w)
(x+y)(x+y)

10. What is the coefficient of the x^2 term in the product of (x + 1)(x + 2)(x -1)?
An angle which is supplementary to an interior angle.
2
Subtract them. i.e (5^7)/(5^3)= 5^4
A set with no members - denoted by a circle with a diagonal through it.

11. What is the side length of an equilateral triangle with altitude 6?
4sqrt3. The triangle can be divided into two equal 30-60-90 triangles with side 6 as the side in which 6 = xsqrt3. So x =2sqrt3...
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
12.5%
1:sqrt3:2

12. What is the name of set with a number of elements which cannot be counted?
An infinite set.
Positive or Negative
360/n
D/t (distance)/(time)

13. What is a set with no members called?
Triangles with same measure and same side lengths.
The empty set - denoted by a circle with a diagonal through it.
13pi / 2
P(E) = ø

14. What are congruent triangles?
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
A natural number greater than 1 that has no positive divisors other than 1 and itself
1/a^6
Triangles with same measure and same side lengths.

15. 20<all primes<30
55%
23 - 29
A-b is negative
9 & 6/7

16. x^4 + x^7 =
x^(4+7) = x^11
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.
= (actual decrease/Original amount) x 100%
500

17. a<b then a - b is positive or negative?
N! / (n-k)!
87.5%
C = 2(pi)r
A-b is negative

18. What is the 'Solution' for a set of inequalities.
4.25 - 6 - 22
The overlapping sections.
Null
Positive or Negative

19. What is the empty set?
A set with no members - denoted by a circle with a diagonal through it.
Even
1/x
P=2(l+w)

20. factored binomial product of (x-y)²
x²-2xy+y²
1.0843 X 10^11
Every number
Pi(diameter)

21. What is a major arc?

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22. What is a chord of a circle?
Two equal sides and two equal angles.
x²-y²
A chord is a line segment joining two points on a circle.
Even

23. Pythagorean theorem
6 : 1 : 2
10
A²+b²=c²
The longest arc between points A and B on a circle'S diameter.

24. (x-y)(x+y)
90°
NOT A PRIME
x²-y²
360°

25. The reciprocal of any non-zero #x is
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225
zero
(rate)(time) d=rt
1/x

26. a>b then a - b is positive or negative?
(a + b)^2
Lies opposite the greater angle
A-b is positive
28

27. What is the sum of the angles of a triangle?
180 degrees
1/x
The steeper the slope.
Arc length = (n/360) x pi(2r) where n is the number of degrees.

28. If a<b - then
A+c<b+c
A set with no members - denoted by a circle with a diagonal through it.
A reflection about the origin.
3

29. If y is directly proportional to x - what does it equal?
A+c<b+c
y/x is a constant
3
A central angle is an angle formed by 2 radii.

30. What is the 'union' of A and B?
The point of intersection of the systems.
y/x is a constant
(a - b)(a + b)
The set of elements which can be found in either A or B.

31. What is the name for a grouping of the members within a set based on a shared characteristic?
A central angle is an angle formed by 2 radii.
A subset.
Even
70

32. Slope
y2-y1/x2-x1
6
1
3/2 - 5/3

33. 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))?
Two (Ø×2=Ø)
20.5
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
x²-2xy+y²

34. The sum of all angles around a point
10! / 3!(10-3)! = 120
130pi
360°
Subtract them. i.e (5^7)/(5^3)= 5^4

35. What is the surface area of a cylinder with radius 5 and height 8?
Null
Distance=rate×time or d=rt
1
130pi

36. Suppose you have a set of n objects - and you want to select k of them - but the order doesn'T matter. What formula do you use to determine the number of combinations of n objects taken k at a time?
N! / (k!)(n-k)!
2sqrt6
C=2 x pi x r OR pi x D
x^(6-3) = x^3

37. A number is divisible by 3 if ...
13
3x - 4x - 5x
V=Lwh
The sum of its digits is divisible by 3.

38. What is the graph of f(x) shifted downward c units or spaces?
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)
A=pi*(r^2)
F(x) - c
83.333%

39. Can you add sqrt 3 and sqrt 5?
F(x + c)
No - only like radicals can be added.
Arc length = (n/360) x pi(2r) where n is the number of degrees.
(x+y)(x-y)

40. First 10 prime #s
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
Its last two digits are divisible by 4.
2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - 29
The shortest arc between points A and B on a circle'S diameter.

41. binomial product of (x-y)²
V=side³
4a^2(b)
(x+y)(x-y)
A central angle is an angle formed by 2 radii.

42. The four angles around a point measure y - 2y - 35 and 55 respectively. What is the value of y?
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
90
4725
130pi

43. 1n
Triangles with same measure and same side lengths.
Two (Ø×2=Ø)
1
zero

44. What is the graph of f(x) shifted left c units or spaces?
12sqrt2
F(x + c)
Factors are few - multiples are many.
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%

45. Perfect Squares 1-15
9
Undefined - because we can'T divide by 0.
3x - 4x - 5x
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225

46. What is the third quartile of the following data set: 44 - 58 - 63 - 63 - 68 - 70 - 82
70
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225
75:11

47. Factor a^2 + 2ab + b^2
F(x) - c
(a + b)^2
90
Cd

48. How to recognize if a # is a multiple of 12
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225
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.)
$3 -500 in the 9% and $2 -500 in the 7%.
F(x-c)

49. To increase a number by x%
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
Ø
Move the decimal point to the right x places
12! / 5!7! = 792

50. If a is negative and n is even then an is (positive or negative?)
An is positive
A 30-60-90 triangle.
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
Two (Ø×2=Ø)