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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 rational numbers?
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
Smallest positive integer
Relationship cannot be determined (what if x is negative?)
360°

2. (x+y)²
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
x²+2xy+y²
90pi
1 & 37/132

3. What percent of 40 is 22?
55%
EVEN
Undefined
x²-y²

4. If 4500 is invested at a simple interest rate of 6% - what is the value of the investment after 10 months?
The greatest value minus the smallest.
Indeterminable.
(a - b)(a + b)
4725

5. 1:sqrt3:2 is the ratio of the sides of what kind of triangle?
A 30-60-90 triangle.
The steeper the slope.
Ø
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

6. a^2 + 2ab + b^2
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
Parallelogram
(a + b)^2
Be Zero!

7. A number is divisible by 9 if...
41 - 43 - 47
N! / (k!)(n-k)!
The sum of digits is divisible by 9.
The set of elements found in both A and B.

8. What is the intersection of A and B?
Positive or Negative
The set of elements found in both A and B.
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...
All numbers multiples of 1.

9. If a lamp increases from $80 to $100 - what is the percent increase?
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%
A= (1/2) b*h
A=pi*(r^2)
Infinite.

10. The larger the absolute value of the slope...
The set of output values for a function.
A multiple of every integer
The set of elements which can be found in either A or B.
The steeper the slope.

11. a>b then a - b is positive or negative?
A-b is positive
A tangent is a line that only touches one point on the circumference of a circle.
(distance)/(rate) d/r
x²+2xy+y²

12. The only number that is equal to its opposite
Ab+ac
Prime numbers (2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23)
Ø Ø=Ø
y/x is a constant

13. 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?
Even
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
10! / 3!(10-3)! = 120
Ab-ac

14. 30 60 90
6
20.5
3
5 - 12 - 13

15. What transformation occurs if point C is reflected over the x-axis and then the y-axis?
M
Relationship cannot be determined (what if x is negative?)
A reflection about the axis.
Ø

16. A prime number (or a prime)
Sector area = (n/360) X (pi)r^2
The greatest value minus the smallest.
A natural number greater than 1 that has no positive divisors other than 1 and itself
An isosceles right triangle.

17. Area of a rectangle
F(x) - c
A = length x width
x^(2(4)) =x^8 = (x^4)^2
67 - 71 - 73

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?
An expression with just one term (-6x - 2a^2)
The sum of its digits is divisible by 3.
The interesection of A and B.
48

19. What is a percent?
31 - 37
= (actual decrease/Original amount) x100% = 20/100x100% = 20%
A percent is a fraction whose denominator is 100.
3 - -3

20. binomial product of (x-y)²
A percent is a fraction whose denominator is 100.
(x+y)(x-y)
1
27^(-4)

21. Area of a triangle?
x²-y²
8
A = length x width
(base*height) / 2

22. Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
angle that is greater than 90° but less than 180°
(a - b)^2
Positive or Negative
2sqrt6

23. Circumference of a Circle
A=pi*(r^2)
C=2 x pi x r OR pi x D
3x - 4x - 5x
Be Zero!

24. One is (a prime or not?)
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
Ø
... the square of the ratios of the corresponding sides.
NOT A PRIME

25. Convert 0.7% to a fraction.
7 / 1000
360°
angle that is greater than 90° but less than 180°
Null

26. P and r are factors of 100. What is greater - pr or 100?
75:11
Indeterminable.
71 - 73 - 79
The union of A and B.

27. In any polygon - all external angles equal up to
360°
6 : 1 : 2
The objects within a set.
(length)(width)(height)

28. Find distance when given time and rate
A 30-60-90 triangle.
D=rt so r= d/t and t=d/r
(base*height) / 2
1:1:sqrt2

29. What is the common monomial factor in the expression 4(c^3)d - (c^2)(d^2) + 2cd?
Infinite.
C = 2(pi)r
2(pi)r
Cd

30. Ø is
All numbers multiples of 1.
Even
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
(pi)r²

31. 5/6 in percent?
83.333%
9
x²-y²
5 - 12 - 13

32. What is the coefficient of the x^2 term in the product of (x + 1)(x + 2)(x -1)?
360°
Ø
y = 2x^2 - 3
2

33. Pi is a ratio of what to what?

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34. In similar hexagons - the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
75:11
4:5
A subset.
No - only like radicals can be added.

35. Which is greater? 200x^295 or 10x^294?
(n-2) x 180
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%
72
Relationship cannot be determined (what if x is negative?)

36. Factor a^2 + 2ab + b^2
1
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
P(E) = 1/1 = 1
(a + b)^2

37. What is the 'Solution' for a set of inequalities.
An isosceles right triangle.
The point of intersection of the systems.
The overlapping sections.
3/2 - 5/3

38. x^4 + x^7 =
P=4s (s=side)
11 - 13 - 17 - 19
x^(4+7) = x^11
The sum of the digits is a multiple of 9.

39. 10^6 has how many zeroes?
A 30-60-90 triangle.
6
F(x + c)
A chord is a line segment joining two points on a circle.

40. Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
1
x²-y²
16^8 64^5 = (4^3)^5 = 4^15 16^8=(4^2)^8 = 4^16
2^9 / 2 = 256

41. What is the set of elements found in both A and B?
The interesection of A and B.
Factors are few - multiples are many.
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.

42. What is the area of a regular hexagon with side 6?
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
(x+y)(x-y)
Indeterminable.

43. What is the graph of f(x) shifted upward c units or spaces?
A tangent is a line that only touches one point on the circumference of a circle.
F(x) + c
P=2(l+w)
The point of intersection of the systems.

44. How to recognize if a # is a multiple of 12
M
Ø=P(E)=1
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)
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.)

45. What is a minor arc?

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46. (x-y)²
x²-2xy+y²
x²+2xy+y²
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.)
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.

47. 8.84 / 5.2
x²-y²
1.7
360°
Positive

48. 7/8 in percent?
Null
The two xes after factoring.
87.5%
(length)(width)(height)

49. What is the ratio of the sides of a 30-60-90 triangle?
1:sqrt3:2
8
an angle that is less than 90°
1 - P(E)

50. What is a finite set?
Ø
A set with a number of elements which can be counted.
70
3 - -3