Test your basic knowledge |

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 is the side length of an equilateral triangle with altitude 6?
4sqrt3. The triangle can be divided into two equal 30-60-90 triangles with side 6 as the side in which 6 = xsqrt3. So x =2sqrt3...
12sqrt2
The shortest arc between points A and B on a circle'S diameter.
Two angles whose sum is 90.

2. -3³
27
31 - 37
$3 -500 in the 9% and $2 -500 in the 7%.
(amount of decrease/original price) x 100%

3. What are the real numbers?
Be Zero!
The greatest value minus the smallest.
A chord is a line segment joining two points on a circle.
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)

4. Obtuse Angle
angle that is greater than 90° but less than 180°
A natural number greater than 1 that has no positive divisors other than 1 and itself
90
180°

5. Ø is a multiple of
Two (Ø×2=Ø)
28. n = 8 - k = 2. n! / k!(n-k)!
1/2 times 7/3
Ab+ac

6. How to recognize a # as a multiple of 3
1 - P(E)
The two xes after factoring.
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)
4.25 - 6 - 22

7. If a is inversely porportional to b - what does it equal?
Ab=k (k is a constant)
2^9 / 2 = 256
13
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)

8. What are congruent triangles?
Pi(diameter)
Triangles with same measure and same side lengths.
1
(12/2) x (sqrt15 / sqrt5) = 6sqrt3

9. If 10800 is invested at a simple interest rate of 4% - what is the value of the investment after 18 months?
$11 -448
The sum of its digits is divisible by 3.
An expression with just one term (-6x - 2a^2)
An arc is a portion of a circumference of a circle.

10. If y is directly proportional to x - what does it equal?
A=½bh
y/x is a constant
A-b is positive
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225

11. For any number x
28. n = 8 - k = 2. n! / k!(n-k)!
Can be negative - zero - or positive
zero
y/x is a constant

12. Formula to find a circle'S circumference from its radius?
26
C = 2(pi)r
A set with a number of elements which can be counted.
x²+2xy+y²

13. If the two sides of a triangle are unequal then the longer side.................
1/x
Ø
Lies opposite the greater angle
1:sqrt3:2

14. 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?
Positive
52
7 / 1000
x^(2(4)) =x^8 = (x^4)^2

15. 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?
1
90
48
23 - 29

16. What is the third quartile of the following data set: 44 - 58 - 63 - 63 - 68 - 70 - 82
4.25 - 6 - 22
Be Zero!
70
0

17. What does scientific notation mean?
No - only like radicals can be added.
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
The steeper the slope.
A natural number greater than 1 that has no positive divisors other than 1 and itself

18. How to find the circumference of a circle which circumscribes a square?
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
F(x-c)

19. In a Regular Polygon - the measure of each exterior angle
13pi / 2
360/n
(base*height) / 2
27^(-4)

20. What is an exterior angle?
An angle which is supplementary to an interior angle.
The interesection of A and B.
6 : 1 : 2
The set of output values for a function.

21. How do you solve proportions? a/b=c/d
The shortest arc between points A and B on a circle'S diameter.
A percent is a fraction whose denominator is 100.
Cross multiplication a/b=c/d 4/6=10/15 4(15)=6(10) 60=60
Indeterminable.

22. a^2 - 2ab + b^2
Arc length = (n/360) x pi(2r) where n is the number of degrees.
(a - b)^2
41 - 43 - 47
1

23. 1:1:sqrt2 is the ratio of the sides of what kind of triangle?
An isosceles right triangle.
A-b is positive
The set of elements found in both A and B.
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%

24. 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
Ø
(pi)r²
F(x) - c

25. 25^(1/2) or sqrt. 25 =
The sum of the digits is a multiple of 9.
1/a^6
28
5 OR -5

26. Area of a circle
Sector area = (n/360) X (pi)r^2
A natural number greater than 1 that has no positive divisors other than 1 and itself
Right
A=pi*(r^2)

27. Formula to find a circle'S circumference from its diameter?
Negative
Right
x - x(SR3) - 2x
C = (pi)d

28. An Angle that'S 180°
26
5
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
Straight Angle

29. Slope given 2 points
3
Two equal sides and two equal angles.
M= (Y1-Y2)/(X1-X2)
Prime numbers (2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23)

30. To multiply a number by 10^x
Even
Move the decimal point to the right x places
$3 -500 in the 9% and $2 -500 in the 7%.
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)

31. binomial product of (x+y)(x-y)
441000 = 1 10 10 10 21 * 21
55%
x²-y²
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).

32. In a rectangle - all angles are
Right
4725
Prime numbers (2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23)
The set of input values for a function.

33. 5/6 in percent?
83.333%
Sum of digits is a multiple of 3 and the last digit is even.
F(x + c)
1.0843 X 10^11

34. (x-y)(x+y)
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225
x²-y²
A+c<b+c
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.

35. To decrease a number by x%
Add them. i.e. (5^7) * (5^3) = 5^10
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
1/xn i.e. 5^-3 = 1/(5^3) = 1/ 125 = .008
0

36. How to determine percent decrease?
Cross multiplication a/b=c/d 4/6=10/15 4(15)=6(10) 60=60
55%
(amount of decrease/original price) x 100%
= (actual decrease/Original amount) x100% = 20/100x100% = 20%

37. If Event is impossible
Can be negative - zero - or positive
1
P(E) = ø
A=(base)(height)

38. x^2 = 9. What is the value of x?
3 - -3
A<-b
C = 2(pi)r
Sector area = (n/360) X (pi)r^2

39. What is the order of operations?
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.
180
90°
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)

40. Factor x^2 - xy + x.
3x - 4x - 5x
1.7
x(x - y + 1)
Ø Ø=Ø

41. A number is divisible by 9 if...
An isosceles right triangle.
x - x(SR3) - 2x
16^8 64^5 = (4^3)^5 = 4^15 16^8=(4^2)^8 = 4^16
The sum of digits is divisible by 9.

42. 70 < all primes< 80
87.5%
71 - 73 - 79
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225
(x+y)(x+y)

43. Is 0 even or odd?
Edge³
3x - 4x - 5x
V=Lwh
Even

44. Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
2sqrt6
Right
y2-y1/x2-x1

45. In any polygon - all external angles equal up to
A²+b²=c²
Negative
360°
The greatest value minus the smallest.

46. What is the set of elements which can be found in either A or B?
y = 2x^2 - 3
V=Lwh
360°
The union of A and B.

47. 60 < all primes <70
3 - 4 - 5
61 - 67
48
P(E) = 1/1 = 1

48. The Perimeter of a Square
1.7
(x+y)(x-y)
(length)(width)(height)
P=4s (s=side)

49. Describe the relationship between the graphs of x^2 and (1/2)x^2
53 - 59
(x+y)(x-y)
The second graph is less steep.
62.5%

50. What is the set of elements found in both A and B?
The interesection of A and B.
2(pi)r
A set with no members - denoted by a circle with a diagonal through it.
Relationship cannot be determined (what if x is negative?)