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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 are the members or elements of a set?
6 : 1 : 2
The objects within a set.
(a - b)(a + b)
6

2. 20<all primes<30
(2x7)³
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
3 - -3
23 - 29

3. What is the name for a grouping of the members within a set based on a shared characteristic?
A subset.
(p + q)/5
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
12sqrt2

4. Area of a rectangle
(p + q)/5
A = length x width
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
Straight Angle

5. Which is greater? 200x^295 or 10x^294?
Relationship cannot be determined (what if x is negative?)
Parallelogram
P=2(l+w)
Even prime number

6. 40 < all primes<50
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.)
P(E) = ø
41 - 43 - 47
53 - 59

7. 0^0
67 - 71 - 73
48
Undefined
(2x7)³

8. Ø²
360°
6
Ø
23 - 29

9. binomial product of (x+y)²
(x+y)(x+y)
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
2^9 / 2 = 256
Positive

10. A cylinder has surface area 22pi. If the cylinder has a height of 10 - what is its radius?
72
2²
1
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.

11. There are 10 finalists for the school spelling bee. A first - second - and third place trophy will be awarded. In how many ways can the judges award the 3 prizes?
180°
Prime numbers (2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23)
2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - 29
10! / (10-3)! = 720

12. What is the ratio of the sides of a 30-60-90 triangle?
28
1
16^8 64^5 = (4^3)^5 = 4^15 16^8=(4^2)^8 = 4^16
1:sqrt3:2

13. Probability of an Event
P(E) = number of favorable outcomes/total number of possible outcomes
The set of output values for a function.
Relationship cannot be determined (what if x is negative?)
4a^2(b)

14. (2²)³
.0004809 X 10^11
A set with no members - denoted by a circle with a diagonal through it.
26
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.

15. If a is negative and n is even then an is (positive or negative?)
An is positive
Positive
x(x - y + 1)
Pi is the ratio of a circle'S circumference to its diameter.

16. Ø is
An algebraic expression is a combination of one of more terms. Terms in an expression are separated by either addition or subtraction signs. (3xy - 4ab - -5cd - x^2 + x - 1)
A multiple of every integer
A natural number greater than 1 that has no positive divisors other than 1 and itself
C = (pi)d

17. 1n
16.6666%
1
No - only like radicals can be added.
Null

18. Area of a triangle
Ø
An arc is a portion of a circumference of a circle.
EVEN
A= (1/2) b*h

19. If 10800 is invested at a simple interest rate of 4% - what is the value of the investment after 18 months?
Every number
The set of input values for a function.
$11 -448
Ab=k (k is a constant)

20. Circumference of a Circle
A set with no members - denoted by a circle with a diagonal through it.
True
C=2 x pi x r OR pi x D
4:5

21. What is the name of set with a number of elements which cannot be counted?
(a - b)^2
Be Zero!
1
An infinite set.

22. Time
Ø
360°
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
(distance)/(rate) d/r

23. 1 is an
ODD number
A reflection about the axis.
Its last two digits are divisible by 4.
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)

24. An Angle that'S 180°
Straight Angle
9 : 25
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
3/2 - 5/3

25. Pythagorean theorem
72
N! / (n-k)!
y2-y1/x2-x1
A²+b²=c²

26. For any number x
1/a^6
(x+y)(x+y)
Ø
Can be negative - zero - or positive

27. In similar hexagons - the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
M
4:5
72
The shortest arc between points A and B on a circle'S diameter.

28. Formula to find a circle'S circumference from its diameter?
C = (pi)d
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)
The set of input values for a function.
360/n

29. Which is greater? 64^5 or 16^8
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
Null
10

30. A number is divisible by 4 is...
The overlapping sections.
Its last two digits are divisible by 4.
2
P(E) = number of favorable outcomes/total number of possible outcomes

31. 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?
441000 = 1 10 10 10 21 * 21
A set with a number of elements which can be counted.
A-b is positive
288 (8 9 4)

32. If the two sides of a triangle are unequal then the longer side.................
x²-2xy+y²
A=pi*(r^2)
4096
Lies opposite the greater angle

33. a^2 - 2ab + b^2
C = 2(pi)r
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
(a - b)^2
N! / (k!)(n-k)!

34. Ø is a multiple of
P=2(l+w)
A tangent is a line that only touches one point on the circumference of a circle.
1.0843 X 10^11
Every number

35. x^6 / x^3
D=rt so r= d/t and t=d/r
Ab-ac
x^(6-3) = x^3
Even

36. formula for distance problems
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
D=rt so r= d/t and t=d/r
9 & 6/7
Distance=rate×time or d=rt

37. (12sqrt15) / (2sqrt5) =
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
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= (1/2) b*h
Negative

38. Product of any number and Ø is
V=Lwh
Ø
x²-2xy+y²
N! / (k!)(n-k)!

39. 25/2³
2²
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
The overlapping sections.
$3 -500 in the 9% and $2 -500 in the 7%.

40. What is the ratio of the sides of an isosceles right triangle?
The shortest arc between points A and B on a circle'S diameter.
A set with a number of elements which can be counted.
71 - 73 - 79
1:1:sqrt2

41. What is the empty set?
2.592 kg
A set with no members - denoted by a circle with a diagonal through it.
P=2(l+w)
Two angles whose sum is 90.

42. Can you add sqrt 3 and sqrt 5?
zero
C = 2(pi)r
13pi / 2
No - only like radicals can be added.

43. Hector invested $6000. Part was invested in account with 9% simple annual interest - and the rest in account with 7% simple annual interest. If he earned $490 in the first year of these investments - how much did he invest in each account?
Even
9 : 25
$3 -500 in the 9% and $2 -500 in the 7%.
C=2 x pi x r OR pi x D

44. What is an exterior angle?
An angle which is supplementary to an interior angle.
(a + b)^2
(a + b)^2
x - x(SR3) - 2x

45. Formula for the area of a circle?
A = pi(r^2)
31 - 37
20.5
13pi / 2

46. 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
0
180
1/a^6
V=side³

47. Is 0 even or odd?
Even
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
1
Two (Ø×2=Ø)

48. Probability of E not occurring:
A percent is a fraction whose denominator is 100.
Edge³
1 - P(E)
D/t (distance)/(time)

49. Number of degrees in a triangle
180
Every number
2^9 / 2 = 256
The longest arc between points A and B on a circle'S diameter.

50. 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)]?
True
The direction of the inequality is reversed.
N! / (k!)(n-k)!
Sector area = (n/360) X (pi)r^2