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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. For similar triangles - the ratio of their corresponding sides is 2:3. What is the ratio of their areas?
True
180°
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
D/t (distance)/(time)

2. A cylinder has surface area 22pi. If the cylinder has a height of 10 - what is its radius?
C = 2(pi)r
9
41 - 43 - 47
1

3. What is the ratio of the surface area of a cube with an edge of 10 to the surface area of a rectangular solid with dimensions 2 - 4 - and 6?
Members or elements
180°
x²-y²
75:11

4. What is the measure of an exterior angle of a regular pentagon?
72
N! / (k!)(n-k)!
x²-y²
11 - 13 - 17 - 19

5. 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))?
x²+2xy+y²
83.333%
20.5
90

6. Describe the relationship between 3x^2 and 3(x - 1)^2
Edge³
2sqrt6
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.

7. To increase a number by x%
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
x²-y²
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
x²+2xy+y²

8. 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?
Positive
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.
2.592 kg
Undefined - because we can'T divide by 0.

9. Ø is a multiple of
90°
Undefined
1
Every number

10. x^2 = 9. What is the value of x?
3 - -3
x(x - y + 1)
75:11
441000 = 1 10 10 10 21 * 21

11. the measure of a straight angle
180°
A chord is a line segment joining two points on a circle.
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
2sqrt6

12. The reciprocal of any non-zero number is
A+c<b+c
53 - 59
441000 = 1 10 10 10 21 * 21
1/x

13. 1/Ø=null If a>b then
Factors are few - multiples are many.
A<-b
20.5
Add them. i.e. (5^7) * (5^3) = 5^10

14. 30< all primes<40
The sum of its digits is divisible by 3.
Distance=rate×time or d=rt
5 - 12 - 13
31 - 37

15. factored binomial product of (x-y)²
130pi
x²-2xy+y²
28
F(x-c)

16. What are the irrational numbers?

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17. 1 is the
Smallest positive integer
Ø
The greatest value minus the smallest.
Ab-ac

18. Probability of an Event
P(E) = number of favorable outcomes/total number of possible outcomes
2
0
F(x) + c

19. Simplify 9^(1/2) X 4^3 X 2^(-6)?
x²+2xy+y²
6
3
All numbers multiples of 1.

20. Positive integers that have exactly 2 positive divisors are
13
The two xes after factoring.
Prime numbers (2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23)
1

21. The Denominator can never
Smallest positive integer
An arc is a portion of a circumference of a circle.
Be Zero!
1.0843 X 10^11

22. An Angle that'S 180°
Straight Angle
A natural number greater than 1 that has no positive divisors other than 1 and itself
3
Lies opposite the greater angle

23. How to recognize if a # is a multiple of 12
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= (1/2) b*h
angle that is greater than 90° but less than 180°
= (actual decrease/Original amount) x 100%

24. Slope of any line that goes up from left to right
F(x-c)
Positive
Right
2^9 / 2 = 256

25. 1/6 in percent?
Sum of digits is a multiple of 3 and the last digit is even.
NOT A PRIME
Subtract them. i.e (5^7)/(5^3)= 5^4
16.6666%

26. Area of a triangle
6
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%
Positive
A= (1/2) b*h

27. If a product of two numbers is Ø - one number must be
1.0843 X 10^11
180
Ø
360°

28. If 8 schools are in a conference - how many games are played if each team plays each other exactly once?
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
x - x(SR3) - 2x
28. n = 8 - k = 2. n! / k!(n-k)!
1

29. 30 60 90
2
Edge³
5 - 12 - 13
13

30. Evaluate 4/11 + 11/12
20.5
83.333%
1 & 37/132
A percent is a fraction whose denominator is 100.

31. 30 60 90
Pi is the ratio of a circle'S circumference to its diameter.
y2-y1/x2-x1
A subset.
3x - 4x - 5x

32. a^2 - 2ab + b^2
1.7
(a - b)^2
Indeterminable.
6

33. Which is greater? 64^5 or 16^8
2 & 3/7
16^8 64^5 = (4^3)^5 = 4^15 16^8=(4^2)^8 = 4^16
83.333%
A percent is a fraction whose denominator is 100.

34. What are the real numbers?
180
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)
x - x+1 - x+2
1

35. Area of a circle
Add them. i.e. (5^7) * (5^3) = 5^10
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.)
(pi)r²
1

36. What is the common monomial factor in the expression 4(c^3)d - (c^2)(d^2) + 2cd?
2 & 3/7
The empty set - denoted by a circle with a diagonal through it.
Cd
C = 2(pi)r

37. 5/6 in percent?
ODD number
2sqrt6
83.333%
55%

38. Simplify the expression (p^2 - q^2)/ -5(q - p)
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
37.5%
(p + q)/5
An is positive

39. 10<all primes<20
11 - 13 - 17 - 19
2^9 / 2 = 256
180
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)

40. binomial product of (x+y)²
x^(4+7) = x^11
6
(x+y)(x+y)
70

41. What is the intersection of A and B?
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
The set of elements found in both A and B.
37.5%
Sector area = (n/360) X (pi)r^2

42. The ratio of the areas of two similar polygons is ...
1
An expression with just one term (-6x - 2a^2)
... the square of the ratios of the corresponding sides.
True

43. How do you solve proportions? a/b=c/d
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
The sum of digits is divisible by 9.
Cross multiplication a/b=c/d 4/6=10/15 4(15)=6(10) 60=60
D/t (distance)/(time)

44. 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?
x^(6-3) = x^3
Do not have slopes!
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
2.592 kg

45. What transformation occurs if point C is reflected over the x-axis and then the y-axis?
A reflection about the axis.
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
10
The greatest value minus the smallest.

46. Distance
(rate)(time) d=rt
Be Zero!
A-b is negative
Null

47. 10^6 has how many zeroes?
441000 = 1 10 10 10 21 * 21
6
2
(x+y)(x+y)

48. Probability of Event all cases
Ø=P(E)=1
1.7
The two xes after factoring.
10

49. Perimeter of a rectangle
x²-y²
The set of output values for a function.
P= 2L + 2w
Cd

50. 4.809 X 10^7 =
.0004809 X 10^11
The union of A and B.
Even
The shortest arc between points A and B on a circle'S diameter.