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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. T or F? Given d -e &f =/ 0 - [(d^3)e(f^5)] / 2d(e^3) / [3(d^2)(e^3)(f^7)] / [6(e^5)(f^2)]?
Pi(diameter)
True
Add them. i.e. (5^7) * (5^3) = 5^10
Undefined - because we can'T divide by 0.

2. 30 60 90
1
A set with a number of elements which can be counted.
Infinite.
3 - 4 - 5

3. 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.
C = (pi)d
4725
The direction of the inequality is reversed.

4. 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))?
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
20.5
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
The interesection of A and B.

5. What is the 'domain' of a function?
(base*height) / 2
The objects within a set.
The set of input values for a function.
441000 = 1 10 10 10 21 * 21

6. 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?
9 : 25
F(x-c)
180°
6

7. 200 <_ x <_ 300. How many values of x are divisible by 5 & 8?
10! / (10-3)! = 720
3
9 & 6/7
Null

8. the slope of a line in y=mx+b
Two angles whose sum is 90.
3 - -3
The sum of its digits is divisible by 3.
M

9. 4.809 X 10^7 =
Ab-ac
.0004809 X 10^11
Positive or Negative
7 / 1000

10. Legs: 3 - 4. Hypotenuse?
The direction of the inequality is reversed.
18
3 - -3
5

11. x^6 / x^3
x^(6-3) = x^3
Two (Ø×2=Ø)
90
(x+y)(x+y)

12. What is the graph of f(x) shifted downward c units or spaces?
F(x) - c
Undefined
x²-2xy+y²
Positive

13. x^2 = 9. What is the value of x?
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
41 - 43 - 47
Its last two digits are divisible by 4.
3 - -3

14. Write 10 -843 X 10^7 in scientific notation
N! / (k!)(n-k)!
x²+2xy+y²
1.0843 X 10^11
1

15. If a<b - then
x - x(SR3) - 2x
Move the decimal point to the right x places
75:11
A+c<b+c

16. What are complementary angles?
Two angles whose sum is 90.
4096
Its last two digits are divisible by 4.
27^(-4)

17. A number is divisible by 6 if...
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
Infinite.
41 - 43 - 47
Its divisible by 2 and by 3.

18. A number is divisible by 3 if ...
The sum of its digits is divisible by 3.
1:1:sqrt2
90°
360°

19. a^2 - b^2 =
(a - b)(a + b)
A=pi*(r^2)
1 - P(E)
3 - 4 - 5

20. When does a function automatically have a restricted domain (2)?
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
27
288 (8 9 4)
A+c<b+c

21. What is the intersection of A and B?
D/t (distance)/(time)
The set of elements found in both A and B.
P=2(l+w)
Every number

22. What number between 70 & 75 - inclusive - has the greatest number of factors?
72
P= 2L + 2w
441000 = 1 10 10 10 21 * 21
A set with a number of elements which can be counted.

23. If a is inversely porportional to b - what does it equal?
Cd
The greatest value minus the smallest.
Ab=k (k is a constant)
(base*height) / 2

24. Area of a rectangle
18
A = length x width
(x+y)(x-y)
y/x is a constant

25. a>b then a - b is positive or negative?
A subset.
A-b is positive
Two angles whose sum is 90.
The greatest value minus the smallest.

26. What is the graph of f(x) shifted upward c units or spaces?
y = 2x^2 - 3
The shortest arc between points A and B on a circle'S diameter.
F(x) + c
360°

27. P and r are factors of 100. What is greater - pr or 100?
Add them. i.e. (5^7) * (5^3) = 5^10
72
Indeterminable.
C = (pi)d

28. Can you add sqrt 3 and sqrt 5?
Do not have slopes!
Every number
1.0843 X 10^11
No - only like radicals can be added.

29. A company places a 6-symbol code on each product. The code consists of the letter T - followed by 3 numerical digits - and then 2 consonants (Y is a conson). How many codes are possible?
A= (1/2) b*h
2sqrt6
x^(6-3) = x^3
441000 = 1 10 10 10 21 * 21

30. What is a finite set?
A set with a number of elements which can be counted.
D=rt so r= d/t and t=d/r
Ø Ø=Ø
180°

31. What is the name of set with a number of elements which cannot be counted?
An infinite set.
A central angle is an angle formed by 2 radii.
Its divisible by 2 and by 3.
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)

32. How to find the circumference of a circle which circumscribes a square?
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
180°
A percent is a fraction whose denominator is 100.

33. Which is greater? 27^(-4) or 9^(-8)
27^(-4)
3
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.)

34. 1 is an
ODD number
10! / 3!(10-3)! = 120
(amount of decrease/original price) x 100%
180

35. 1/6 in percent?
A natural number greater than 1 that has no positive divisors other than 1 and itself
16.6666%
The overlapping sections.
Ø Ø=Ø

36. What is an arc of a circle?
A=(base)(height)
4a^2(b)
An arc is a portion of a circumference of a circle.
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]

37. If 8 schools are in a conference - how many games are played if each team plays each other exactly once?
P=2(l+w)
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225
3
28. n = 8 - k = 2. n! / k!(n-k)!

38. formula for distance problems
Can be negative - zero - or positive
Distance=rate×time or d=rt
Two angles whose sum is 90.
31 - 37

39. Which is greater? 200x^295 or 10x^294?
x(x - y + 1)
Relationship cannot be determined (what if x is negative?)
(pi)r²
28

40. If a is negative and n is even then an is (positive or negative?)
Even
An is positive
12sqrt2
A 30-60-90 triangle.

41. Is 0 even or odd?
Members or elements
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
Even
13

42. The perimeter of a square is 48 inches. The length of its diagonal is:
12sqrt2
10! / (10-3)! = 720
6
Subtract them. i.e (5^7)/(5^3)= 5^4

43. 5/8 in percent?
x^(2(4)) =x^8 = (x^4)^2
62.5%
y/x is a constant
Cd

44. 1/2 divided by 3/7 is the same as
1/2 times 7/3
1/x
V=Lwh
An angle which is supplementary to an interior angle.

45. What is a set with no members called?
All numbers multiples of 1.
A-b is negative
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
The empty set - denoted by a circle with a diagonal through it.

46. Circumference of a circle?
71 - 73 - 79
Diameter(Pi)
Null
EVEN

47. 1:sqrt3:2 is the ratio of the sides of what kind of triangle?
Negative
Null
27^(-4)
A 30-60-90 triangle.

48. To increase a number by x%
B?b?b (where b is used as a factor n times)
P(E) = 1/1 = 1
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
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150

49. Define a 'Term' -
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)
The direction of the inequality is reversed.
(2x7)³
1/x

50. Simplify (a^2 + b)^2 - (a^2 - b)^2
27^(-4)
1/xn i.e. 5^-3 = 1/(5^3) = 1/ 125 = .008
4a^2(b)
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.)