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GRE Math: All In One

Subjects : gre, math

Instructions:

Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
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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. binomial product of (x+y)²
An infinite set.
41 - 43 - 47
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%
(x+y)(x+y)

2. If a is positive - an is
10
Positive
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 3 (i.e. 45 ... 4 + 5 = 9 so the whole thing is a multiple of 3)

3. What is the area of a regular hexagon with side 6?
3 - -3
The set of elements found in both A and B.
An expression with just one term (-6x - 2a^2)
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.

4. If a is inversely porportional to b - what does it equal?
3
x²-2xy+y²
Ab=k (k is a constant)
The set of output values for a function.

5. What is a subset?
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)
A grouping of the members within a set based on a shared characteristic.
Negative
Undefined - because we can'T divide by 0.

6. The four angles around a point measure y - 2y - 35 and 55 respectively. What is the value of y?
83.333%
Two (Ø×2=Ø)
4725
90

7. What is the 'Solution' for a system of linear equations?
y/x is a constant
Every number
The point of intersection of the systems.
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)

8. How many sides does a hexagon have?
Infinite.
The set of output values for a function.
6
Diameter(Pi)

9. Formula for the area of a circle?
A set with a number of elements which can be counted.
A = pi(r^2)
5
2²

10. What are the roots of the quadrinomial x^2 + 2x + 1?
62.5%
The two xes after factoring.
EVEN
Add them. i.e. (5^7) * (5^3) = 5^10

11. Positive integers that have exactly 2 positive divisors are
6 : 1 : 2
28. n = 8 - k = 2. n! / k!(n-k)!
(x+y)(x-y)
Prime numbers (2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23)

12. Pythagorean theorem
The set of input values for a function.
(length)(width)(height)
5 - 12 - 13
A²+b²=c²

13. a^2 - b^2
67 - 71 - 73
x²-y²
(a - b)^2
(a - b)(a + b)

14. 4.809 X 10^7 =
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)
.0004809 X 10^11
$3 -500 in the 9% and $2 -500 in the 7%.
An arc is a portion of a circumference of a circle.

15. b¹
1
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
Null

16. Volume of a rectangular solid
62.5%
(length)(width)(height)
... the square of the ratios of the corresponding sides.
Ø=P(E)=1

17. What is the set of elements found in both A and B?
The interesection of A and B.
Sector area = (n/360) X (pi)r^2
12! / 5!7! = 792
Ø Ø=Ø

18. If an inequality is multiplied or divided by a negative number....
The direction of the inequality is reversed.
D=rt so r= d/t and t=d/r
5 - 12 - 13
(x+y)(x-y)

19. Legs 5 - 12. Hypotenuse?
Infinite.
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...
3 - 4 - 5
13

20. 25^(1/2) or sqrt. 25 =
Edge³
5 OR -5
The two xes after factoring.
The direction of the inequality is reversed.

21. (x-y)(x+y)
x²-y²
x²+2xy+y²
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%
A= (1/2) b*h

22. 5/8 in percent?
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
The empty set - denoted by a circle with a diagonal through it.
angle that is greater than 90° but less than 180°
62.5%

23. What is a set with no members called?
The empty set - denoted by a circle with a diagonal through it.
Ø
4.25 - 6 - 22
(base*height) / 2

24. Simplify (a^2 + b)^2 - (a^2 - b)^2
The sum of digits is divisible by 9.
4a^2(b)
Factors are few - multiples are many.
An is positive

25. How many digits are there between the decimal point and the first even digit in the decimal equivalent of 1/[(2^8)(5^3)]
Even
EVEN
0
x^(2(4)) =x^8 = (x^4)^2

26. Number of degrees in a triangle
180
Pi(diameter)
An infinite set.
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%

27. An Angle that'S 180°
Straight Angle
2sqrt6
A set with no members - denoted by a circle with a diagonal through it.
28

28. What is a chord of a circle?
A chord is a line segment joining two points on a circle.
13
The direction of the inequality is reversed.
31 - 37

29. What are the integers?
Sum of digits is a multiple of 3 and the last digit is even.
The direction of the inequality is reversed.
= (actual decrease/Original amount) x 100%
All numbers multiples of 1.

30. Describe the relationship between the graphs of x^2 and (1/2)x^2
90°
An arc is a portion of a circumference of a circle.
288 (8 9 4)
The second graph is less steep.

31. 1/6 in percent?
23 - 29
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - 29
16.6666%

32. If the 80th percentile of the measurements is 72degrees - about how many measurments are between 69 degrees and 72 degrees? Round your answer to the nearest tenth
Indeterminable.
(n-2) x 180
18
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225

33. The Perimeter of a Square
180°
P=4s (s=side)
7 / 1000
(pi)r²

34. Ø is a multiple of
(2x7)³
Every number
Straight Angle
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)

35. Ø is
(x+y)(x+y)
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
(n-2) x 180
A multiple of every integer

36. What is the 'domain' of a function?
3
An is positive
70
The set of input values for a function.

37. 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?
48
x²+2xy+y²
(rate)(time) d=rt
A=(base)(height)

38. What is it called when a point is reflected to the quadrant opposite it (i.e. I to III or II to IV)?
A reflection about the origin.
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
$11 -448
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50

39. If 4500 is invested at a simple interest rate of 6% - what is the value of the investment after 10 months?
Two equal sides and two equal angles.
Cd
9 & 6/7
4725

40. Which is greater? 64^5 or 16^8
No - only like radicals can be added.
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
16^8 64^5 = (4^3)^5 = 4^15 16^8=(4^2)^8 = 4^16
An angle which is supplementary to an interior angle.

41. Evaluate (4^3)^2
Move the decimal point to the right x places
4096
(a + b)^2
90

42. 2³×7³
Parallelogram
180°
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
(2x7)³

43. 1:1:sqrt2 is the ratio of the sides of what kind of triangle?
An isosceles right triangle.
5
Two angles whose sum is 180.
360°

44. If E is certain
53 - 59
P(E) = 1/1 = 1
A percent is a fraction whose denominator is 100.
288 (8 9 4)

45. What is the empty set?
Even prime number
Relationship cannot be determined (what if x is negative?)
A set with no members - denoted by a circle with a diagonal through it.
The point of intersection of the systems.

46. 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°
Sum of digits is a multiple of 3 and the last digit is even.
2.592 kg
Negative

47. 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)]?
28. n = 8 - k = 2. n! / k!(n-k)!
P(E) = 1/1 = 1
True
1/xn i.e. 5^-3 = 1/(5^3) = 1/ 125 = .008

48. Evaluate 3& 2/7 / 1/3
9 & 6/7
360°
2^9 / 2 = 256
(12/2) x (sqrt15 / sqrt5) = 6sqrt3

49. What is the ratio of the sides of a 30-60-90 triangle?
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
1:sqrt3:2
A<-b
360/n

50. What is a minor arc?

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GRE Math: All In One

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