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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. (x-y)(x+y)
0
The two xes after factoring.
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
x²-y²

2. What are 'Supplementary angles?'
27
Two angles whose sum is 180.
Ø
(x+y)(x+y)

3. What is the graph of f(x) shifted left c units or spaces?
9
(x+y)(x-y)
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%
F(x + c)

4. Area of a circle
The set of elements found in both A and B.
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
3/2 - 5/3
(pi)r²

5. 5/6 in percent?
The sum of digits is divisible by 9.
P(E) = ø
x(x - y + 1)
83.333%

6. What is the set of elements which can be found in either A or B?
The union of A and B.
(length)(width)(height)
180 degrees
10! / 3!(10-3)! = 120

7. 2 is the only
12sqrt2
90pi
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
Even prime number

8. (x^2)^4
x^(2(4)) =x^8 = (x^4)^2
The sum of digits is divisible by 9.
(a - b)(a + b)
(a - b)^2

9. What is the 'domain' of a function?
A multiple of every integer
M= (Y1-Y2)/(X1-X2)
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
The set of input values for a function.

10. Formula to find a circle'S circumference from its diameter?
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
Every number
x²-y²
C = (pi)d

11. Which is greater? 200x^295 or 10x^294?
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225
The interesection of A and B.
F(x) - c
Relationship cannot be determined (what if x is negative?)

12. a/Ø
D/t (distance)/(time)
A set with no members - denoted by a circle with a diagonal through it.
3/2 - 5/3
Null

13. How to recognize a # as a multiple of 4
A reflection about the origin.
x²-2xy+y²
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.)
4096

14. How to determine percent decrease?
Its last two digits are divisible by 4.
1
1
(amount of decrease/original price) x 100%

15. If Event is impossible
Positive or Negative
P(E) = ø
= (actual decrease/Original amount) x100% = 20/100x100% = 20%
70

16. How many 3-digit positive integers are even and do not contain the digit 4?
Distance=rate×time or d=rt
288 (8 9 4)
Smallest positive integer
90°

17. What is the side length of an equilateral triangle with altitude 6?
72
P(E) = 1/1 = 1
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...
F(x) + c

18. Ø is a multiple of
Straight Angle
Two (Ø×2=Ø)
$11 -448
(rate)(time) d=rt

19. When multiplying exponential #s with the same base - you do this to the exponents...
Add them. i.e. (5^7) * (5^3) = 5^10
x²-2xy+y²
Diameter(Pi)
Infinite.

20. Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
M
= (actual decrease/Original amount) x 100%
x^(4+7) = x^11
2^9 / 2 = 256

21. What is the sum of the angles of a triangle?
180 degrees
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
.0004809 X 10^11
Infinite.

22. a<b then a - b is positive or negative?
11 - 13 - 17 - 19
A-b is negative
A = pi(r^2)
0

23. What is the measure of an exterior angle of a regular pentagon?
(rate)(time) d=rt
Triangles with same measure and same side lengths.
Every number
72

24. The Perimeter of a rectangle
All numbers multiples of 1.
Sum of digits is a multiple of 3 and the last digit is even.
P=2(l+w)
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.)

25. Can you add sqrt 3 and sqrt 5?
The longest arc between points A and B on a circle'S diameter.
F(x) + c
No - only like radicals can be added.
Distance=rate×time or d=rt

26. To multiply a number by 10^x
Move the decimal point to the right x places
360°
2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - 29
13pi / 2

27. 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?
P=2(l+w)
A natural number greater than 1 that has no positive divisors other than 1 and itself
N! / (n-k)!
F(x) + c

28. The perimeter of a square is 48 inches. The length of its diagonal is:
A natural number greater than 1 that has no positive divisors other than 1 and itself
12sqrt2
A central angle is an angle formed by 2 radii.
An infinite set.

29. A number is divisible by 4 is...
10! / 3!(10-3)! = 120
360/n
Its last two digits are divisible by 4.
Negative

30. What are the real numbers?
Right
31 - 37
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)
3 - 4 - 5

31. How to recognize a # as a multiple of 3
x²+2xy+y²
Arc length = (n/360) x pi(2r) where n is the number of degrees.
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
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)

32. 1 is the
0
F(x) + c
C = 2(pi)r
Smallest positive integer

33. Perimeter of a rectangle
P= 2L + 2w
(x+y)(x-y)
x²+2xy+y²
ODD number

34. What is the graph of f(x) shifted downward c units or spaces?
F(x) - c
The two xes after factoring.
Subtract them. i.e (5^7)/(5^3)= 5^4
P(E) = ø

35. Define a 'monomial'
An expression with just one term (-6x - 2a^2)
0
Even prime number
Every number

36. a^0 =
1
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.)
A=pi*(r^2)
Two equal sides and two equal angles.

37. If a is positive - an is
1/xn i.e. 5^-3 = 1/(5^3) = 1/ 125 = .008
Positive
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

38. What is the slope of a vertical line?

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39. The important properties of a 45-45-90 triangle?
4096
1.7
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.
Do not have slopes!

40. What is the empty set?
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.
Two angles whose sum is 180.
A set with no members - denoted by a circle with a diagonal through it.
9 & 6/7

41. 30 60 90
An is positive
A-b is negative
V=Lwh
3x - 4x - 5x

42. What is a finite set?
360°
A set with a number of elements which can be counted.
The objects within a set.
The sum of its digits is divisible by 3.

43. (x-y)²
The set of elements which can be found in either A or B.
Ø
x²-2xy+y²
The overlapping sections.

44. 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
1
180
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...
D/t (distance)/(time)

45. binomial product of (x-y)²
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
The sum of the digits is a multiple of 9.
(x+y)(x-y)
M

46. Circumference of a Circle
(a - b)(a + b)
C=2 x pi x r OR pi x D
3
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.

47. What is the relationship between lengths of the sides of a triangle and the measure of the angles of the triangle?
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.)
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.
16^8 64^5 = (4^3)^5 = 4^15 16^8=(4^2)^8 = 4^16
x²-y²

48. Factor x^2 - xy + x.
x(x - y + 1)
90°
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)
Its last two digits are divisible by 4.

49. How to recognize if a # is a multiple of 12
A tangent is a line that only touches one point on the circumference of a circle.
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.)
16^8 64^5 = (4^3)^5 = 4^15 16^8=(4^2)^8 = 4^16
1/x

50. 200 <_ x <_ 300. How many values of x are divisible by 5 & 8?
(amount of decrease/original price) x 100%
Sector area = (n/360) X (pi)r^2
(a - b)^2
3