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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. (12sqrt15) / (2sqrt5) =
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
... the square of the ratios of the corresponding sides.
y/x is a constant
Pi is the ratio of a circle'S circumference to its diameter.

2. What is a subset?
(a + b)^2
A grouping of the members within a set based on a shared characteristic.
Arc length = (n/360) x pi(2r) where n is the number of degrees.
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15

3. Vertical lines
Do not have slopes!
x²-2xy+y²
Ø
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).

4. (2²)³
41 - 43 - 47
26
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 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - 29

5. Suppose that the graph of f(x) is the result of stretching y=x + 5 away from the x-axis by a factor of 2. What is the new equation for the graph f(x)?
... the square of the ratios of the corresponding sides.
6 : 1 : 2
y = (x + 5)/2
1 & 37/132

6. 1 is the
A=(base)(height)
1
Smallest positive integer
Its last two digits are divisible by 4.

7. There are 10 finalists for the school spelling bee. A first - second - and third place trophy will be awarded. How many different people can get the three prizes?
10! / 3!(10-3)! = 120
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.
1/x
x(x - y + 1)

8. x^4 + x^7 =
The sum of the digits is a multiple of 9.
angle that is greater than 90° but less than 180°
y/x is a constant
x^(4+7) = x^11

9. What is the 'Solution' for a system of linear equations?
1.0843 X 10^11
Smallest positive integer
The point of intersection of the systems.
The second graph is less steep.

10. How to determine percent decrease?
(amount of decrease/original price) x 100%
N! / (n-k)!
1
Even

11. a(b-c)
A = length x width
All numbers multiples of 1.
13pi / 2
Ab-ac

12. 1n
1
The two xes after factoring.
zero
angle that is greater than 90° but less than 180°

13. If Madagascar'S exports totaled 1.3 billion in 2009 - and 4% came from China - what was the value in millions of the country'S exports to China?
3 - 4 - 5
31 - 37
52
16.6666%

14. formula for the volume of a cube
The set of output values for a function.
A natural number greater than 1 that has no positive divisors other than 1 and itself
V=side³
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.

15. Important properties of a 30-60-90 triangle?
Even
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
Move the decimal point to the right x places
Even prime number

16. How to recognize a # as a multiple of 3
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
x(x - y + 1)
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)
Even

17. 0^0
Negative
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225
Undefined
23 - 29

18. Slope given 2 points
P=4s (s=side)
M= (Y1-Y2)/(X1-X2)
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
y2-y1/x2-x1

19. 3 is the opposite of
C = 2(pi)r
3
Ab-ac
12.5%

20. Factor a^2 + 2ab + b^2
X
(a + b)^2
500
An is positive

21. -3³
1 & 37/132
P(E) = number of favorable outcomes/total number of possible outcomes
27
An expression with just one term (-6x - 2a^2)

22. What is a finite set?
A set with a number of elements which can be counted.
Triangles with same measure and same side lengths.
An arc is a portion of a circumference of a circle.
A=½bh

23. 30< all primes<40
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
31 - 37
(a + b)^2

24. How many multiples does a given number have?
Infinite.
288 (8 9 4)
1/a^6
An arc is a portion of a circumference of a circle.

25. If E is certain
(pi)r²
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
(a + b)^2
P(E) = 1/1 = 1

26. Circumference of a Circle
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)
C=2 x pi x r OR pi x D
2.592 kg
3x - 4x - 5x

27. 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)]?
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.)
Positive
y2-y1/x2-x1
True

28. An Angle that'S 180°
Straight Angle
2 & 3/7
A = pi(r^2)
Every number

29. What are the rational numbers?
2
y/x is a constant
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.

30. If 8 schools are in a conference - how many games are played if each team plays each other exactly once?
28. n = 8 - k = 2. n! / k!(n-k)!
1
Its divisible by 2 and by 3.
an angle that is less than 90°

31. 200 <_ x <_ 300. How many values of x are divisible by 5 & 8?
1/2 times 7/3
3
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)
9 & 6/7

32. Reduce: 4.8 : 0.8 : 1.6
Two angles whose sum is 180.
Its divisible by 2 and by 3.
6 : 1 : 2
Undefined

33. For what values should the domain be restricted for the function f(x) = sqrt(x + 8)
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
1
8
An infinite set.

34. 30 60 90
x - x(SR3) - 2x
9 & 6/7
75:11
(a - b)^2

35. What is the ratio of the sides of an isosceles right triangle?
67 - 71 - 73
An isosceles right triangle.
D=rt so r= d/t and t=d/r
1:1:sqrt2

36. To decrease a number by x%
28
Sector area = (n/360) X (pi)r^2
67 - 71 - 73
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50

37. When does a function automatically have a restricted domain (2)?
V=Lwh
B?b?b (where b is used as a factor n times)
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
(a - b)(a + b)

38. What is the relationship between lengths of the sides of a triangle and the measure of the angles of the triangle?
(a - b)(a + b)
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.
37.5%
55%

39. The product of odd number of negative numbers
Negative
61 - 67
A<-b
500

40. Which is greater? 200x^295 or 10x^294?
(a - b)(a + b)
$3 -500 in the 9% and $2 -500 in the 7%.
Relationship cannot be determined (what if x is negative?)
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]

41. 1/Ø=null If a>b then
A<-b
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225
1
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)

42. The reciprocal of any non-zero #x is
The greatest value minus the smallest.
2
1/x
Smallest positive integer

43. What is a major arc?

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44. 1:1:sqrt2 is the ratio of the sides of what kind of triangle?
ODD number
A set with no members - denoted by a circle with a diagonal through it.
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
An isosceles right triangle.

45. 1:sqrt3:2 is the ratio of the sides of what kind of 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.
2(pi)r
6
A 30-60-90 triangle.

46. 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
55%
y/x is a constant
Reciprocal

47. x^2 = 9. What is the value of x?
x²-y²
3 - -3
55%
Null

48. If a<b - then
A+c<b+c
N! / (k!)(n-k)!
1
180°

49. 25/2³
Indeterminable.
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=½bh
2²

50. a<b then a - b is positive or negative?
A 30-60-90 triangle.
180 degrees
A-b is negative
Ø