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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 is the 'Solution' for a set of inequalities.
The overlapping sections.
Ab-ac
Positive or Negative
500

2. Circumference of a circle?
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
37.5%
Diameter(Pi)
6

3. 30 60 90
3x - 4x - 5x
(2x7)³
A<-b
2

4. If a is positive - an is
A = pi(r^2)
Positive
130pi
An isosceles right triangle.

5. Area of a triangle?
83.333%
(base*height) / 2
2
An infinite set.

6. Circumference of a circle
(p + q)/5
Edge³
2(pi)r
P(E) = number of favorable outcomes/total number of possible outcomes

7. 1/2 divided by 3/7 is the same as
(b + c)
1/2 times 7/3
4a^2(b)
.0004809 X 10^11

8. Legs 5 - 12. Hypotenuse?
Its divisible by 2 and by 3.
13
1
C = 2(pi)r

9. Ø is a multiple of
Every number
P(E) = 1/1 = 1
P= 2L + 2w
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)

10. 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?
A<-b
Smallest positive integer
441000 = 1 10 10 10 21 * 21
Ø

11. Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
A central angle is an angle formed by 2 radii.
(b + c)
Pi(diameter)
2^9 / 2 = 256

12. What is the relationship between lengths of the sides of a triangle and the measure of the angles of the triangle?
Two (Ø×2=Ø)
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...
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.
An infinite set.

13. Solve the quadratic equation ax^2 + bx + c= 0
Yes - like radicals can be added/subtracted.
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.
A 30-60-90 triangle.
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a

14. (x+y)²
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - 29
x²+2xy+y²
1

15. What is the intersection of A and B?
Its divisible by 2 and by 3.
x(x - y + 1)
The set of elements found in both A and B.
52

16. 10^6 has how many zeroes?
6
Every number
The two xes after factoring.
(a + b)^2

17. How to recognize a # as a multiple of 9
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
The sum of the digits is a multiple of 9.
90°
A multiple of every integer

18. 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?
x^(4+7) = x^11
48
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
F(x-c)

19. If a lamp increases from $80 to $100 - what is the percent increase?
x^(2(4)) =x^8 = (x^4)^2
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%
2^9 / 2 = 256
(base*height) / 2

20. What are the integers?
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
A=(base)(height)
x^(2(4)) =x^8 = (x^4)^2
All numbers multiples of 1.

21. 1:sqrt3:2 is the ratio of the sides of what kind of triangle?
A 30-60-90 triangle.
20.5
angle that is greater than 90° but less than 180°
B?b?b (where b is used as a factor n times)

22. What is a set with no members called?
The empty set - denoted by a circle with a diagonal through it.
The set of elements found in both A and B.
A percent is a fraction whose denominator is 100.
90pi

23. How to recognize a # as a multiple of 4
Ab+ac
A²+b²=c²
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 = pi(r^2)

24. 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?
0
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
(a - b)(a + b)
37.5%

25. Find distance when given time and rate
D=rt so r= d/t and t=d/r
1
48
3 - 4 - 5

26. What are congruent triangles?
Triangles with same measure and same side lengths.
y/x is a constant
Factors are few - multiples are many.
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)

27. Find the surface area of a cylinder with radius 3 and height 12.
90pi
Positive
Ø
= (actual decrease/Original amount) x100% = 20/100x100% = 20%

28. binomial product of (x+y)(x-y)
Positive
x²-y²
6
y2-y1/x2-x1

29. What are the irrational numbers?

30. a>b then a - b is positive or negative?
Infinite.
9 : 25
A-b is positive
180

31. the measure of a straight angle
A=½bh
Triangles with same measure and same side lengths.
180°
Lies opposite the greater angle

32. If a product of two numbers is Ø - one number must be
The empty set - denoted by a circle with a diagonal through it.
V=l×w×h
(length)(width)(height)
Ø

33. If r - t - s & u are distinct - consecutive prime numbers - less than 31 - which of the following could be an average of them (4 - 4.25 - 6 - 9 - 24 - 22 - 24)
Triangles with same measure and same side lengths.
Every number
Positive
4.25 - 6 - 22

34. Define a 'Term' -
4a^2(b)
18
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)
An infinite set.

35. Write 10 -843 X 10^7 in scientific notation
A = pi(r^2)
(length)(width)(height)
1.0843 X 10^11
1/xn i.e. 5^-3 = 1/(5^3) = 1/ 125 = .008

36. Whats the difference between factors and multiples?
True
Diameter(Pi)
Factors are few - multiples are many.
Parallelogram

37. Product of any number and Ø is
52
Ø
Ø Ø=Ø
True

38. If Event is impossible
Positive
20.5
2sqrt6
P(E) = ø

39. Factor x^2 - xy + x.
x(x - y + 1)
True
Smallest positive integer
x^(4+7) = x^11

40. If 4500 is invested at a simple interest rate of 6% - what is the value of the investment after 10 months?
NOT A PRIME
Prime numbers (2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23)
4725
3

41. For similar triangles - the ratio of their corresponding sides is 2:3. What is the ratio of their areas?
A set with a number of elements which can be counted.
Even prime number
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
A<-b

42. One is (a prime or not?)
NOT A PRIME
13pi / 2
The set of output values for a function.
x²+2xy+y²

43. a^2 - b^2 =
83.333%
Ø
(p + q)/5
(a - b)(a + b)

44. Any Horizontal line slope
x^(2(4)) =x^8 = (x^4)^2
Two angles whose sum is 180.
zero
23 - 29

45. 7 divided by Ø
Even
A= (1/2) b*h
Null
26

46. The only number that is equal to its opposite
A set with no members - denoted by a circle with a diagonal through it.
Ø Ø=Ø
4725
B?b?b (where b is used as a factor n times)

47. Slope of any line that goes up from left to right
F(x-c)
V=l×w×h
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
Positive

48. If E is certain
0
P(E) = 1/1 = 1
23 - 29
Its last two digits are divisible by 4.

49. How many 3-digit positive integers are even and do not contain the digit 4?
13pi / 2
288 (8 9 4)
Prime numbers (2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23)
8

50. a<b then a - b is positive or negative?
Negative
ODD number
5
A-b is negative