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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. Important properties of a 30-60-90 triangle?
Positive
C=2 x pi x r OR pi x D
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
10

2. 10^6 has how many zeroes?
1
Undefined - because we can'T divide by 0.
No - only like radicals can be added.
6

3. Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
5 OR -5
2sqrt6
(distance)/(rate) d/r
4:5

4. 5x^2 - 35x -55 = 0
M
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
The set of input values for a function.

5. 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?
360°
x - x+1 - x+2
2.592 kg
9

6. Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14
2 & 3/7
Sum of digits is a multiple of 3 and the last digit is even.
F(x-c)
20.5

7. 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 reflection about the origin.
90
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.

8. What is an exterior angle?
Two angles whose sum is 180.
P=2(l+w)
An angle which is supplementary to an interior angle.
6

9. What is a finite set?
90pi
The two xes after factoring.
A set with a number of elements which can be counted.
The shortest arc between points A and B on a circle'S diameter.

10. Circumference of a Circle
6
x²-y²
C=2 x pi x r OR pi x D
EVEN

11. Slope of any line that goes up from left to right
2^9 / 2 = 256
(distance)/(rate) d/r
Positive
4096

12. Legs 5 - 12. Hypotenuse?
A²+b²=c²
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
13
Yes - like radicals can be added/subtracted.

13. What is an isoceles triangle?
16^8 64^5 = (4^3)^5 = 4^15 16^8=(4^2)^8 = 4^16
1
4a^2(b)
Two equal sides and two equal angles.

14. Find distance when given time and rate
20.5
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
D=rt so r= d/t and t=d/r
Cd

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

16. Legs 6 - 8. Hypotenuse?
180
3/2 - 5/3
10
Undefined

17. What is the coefficient of the x^2 term in the product of (x + 1)(x + 2)(x -1)?
2
A<-b
20.5
Do not have slopes!

18. How do you solve proportions? a/b=c/d
Cross multiplication a/b=c/d 4/6=10/15 4(15)=6(10) 60=60
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
72
A-b is positive

19. In a Rectangle - each angles measures
90°
= (actual decrease/Original amount) x 100%
11 - 13 - 17 - 19
Every number

20. What is the order of operations?
2sqrt6
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
75:11

21. a^2 + 2ab + b^2
Positive
(a + b)^2
180°
7 / 1000

22. 30 60 90
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)
5 - 12 - 13
37.5%
3x - 4x - 5x

23. What are the roots of the quadrinomial x^2 + 2x + 1?
N! / (k!)(n-k)!
.0004809 X 10^11
The two xes after factoring.
70

24. How to recognize if a # is a multiple of 12
67 - 71 - 73
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.)
3 - 4 - 5
7 / 1000

25. Legs: 3 - 4. Hypotenuse?
Prime numbers (2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23)
Ab-ac
5
A reflection about the axis.

26. What is the name of set with a number of elements which cannot be counted?
An infinite set.
EVEN
1/2 times 7/3
3/2 - 5/3

27. A number is divisible by 3 if ...
A subset.
V=l×w×h
NOT A PRIME
The sum of its digits is divisible by 3.

28. Define an 'expression'.
A-b is positive
V=side³
Move the decimal point to the right x places
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)

29. Which is greater? 27^(-4) or 9^(-8)
$11 -448
ODD number
The overlapping sections.
27^(-4)

30. 5/6 in percent?
83.333%
x²-2xy+y²
Infinite.
67 - 71 - 73

31. What are congruent triangles?
Distance=rate×time or d=rt
The steeper the slope.
Triangles with same measure and same side lengths.
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]

32. 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?
(a - b)(a + b)
52
75:11
61 - 67

33. A quadrilateral where two diagonals bisect each other
Reciprocal
(a + b)^2
Parallelogram
Two angles whose sum is 180.

34. Employee X is paid 19.50 per hour no matter how many a week. Employee Y earns 18 for the first 40 and 1.5 the hourly wage for every hour after that. If both earned the same amount and worked the same in one week - how many did each work?
C = (pi)d
1/a^6
48
2²

35. a(b-c)
1
Ab+ac
Ab-ac
A=½bh

36. 1/Ø=null If a>b then
Parallelogram
A<-b
Ø
(n-2) x 180

37. 1 is the
Parallelogram
28
Smallest positive integer
18

38. What is the slope of a horizontal line?
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)
0
Factors are few - multiples are many.
2

39. To decrease a number by x%
4.25 - 6 - 22
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
Undefined
x - x(SR3) - 2x

40. (x^2)^4
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)
x^(2(4)) =x^8 = (x^4)^2
A chord is a line segment joining two points on a circle.
3 - 4 - 5

41. 30 60 90
A central angle is an angle formed by 2 radii.
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
x - x(SR3) - 2x

42. How to determine percent decrease?
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.
x²-2xy+y²
(amount of decrease/original price) x 100%
2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - 29

43. Evaluate (4^3)^2
Straight Angle
27^(-4)
4096
16.6666%

44. Obtuse Angle
angle that is greater than 90° but less than 180°
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
... the square of the ratios of the corresponding sides.
12! / 5!7! = 792

45. Perfect Squares 1-15
Every number
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225
The sum of digits is divisible by 9.
The sum of the digits is a multiple of 9.

46. Is 0 even or odd?
Even
N! / (k!)(n-k)!
The empty set - denoted by a circle with a diagonal through it.
Positive

47. Acute Angle
A reflection about the origin.
an angle that is less than 90°
The objects within a set.
A percent is a fraction whose denominator is 100.

48. The percent decrease of a quantity
Even
1/2 times 7/3
= (actual decrease/Original amount) x 100%
A²+b²=c²

49. Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
Null
2^9 / 2 = 256
41 - 43 - 47
(12/2) x (sqrt15 / sqrt5) = 6sqrt3

50. (x+y)²
x²+2xy+y²
A=(base)(height)
The set of elements found in both A and B.
A grouping of the members within a set based on a shared characteristic.