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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. 10^6 has how many zeroes?
180°
87.5%
y = (x + 5)/2
6

2. Slope of any line that goes down as you move from left to right is
an angle that is less than 90°
Negative
C=2 x pi x r OR pi x D
Two (Ø×2=Ø)

3. Write 10 -843 X 10^7 in scientific notation
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...
Can be negative - zero - or positive
1.0843 X 10^11
48

4. Positive integers that have exactly 2 positive divisors are
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
Prime numbers (2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23)
y2-y1/x2-x1
Subtract them. i.e (5^7)/(5^3)= 5^4

5. The sum of all angles around a point
360°
3x - 4x - 5x
ODD number
(pi)r²

6. The four angles around a point measure y - 2y - 35 and 55 respectively. What is the value of y?
x²-y²
90
360°
Positive or Negative

7. The reciprocal of any non-zero #x is
Straight Angle
B?b?b (where b is used as a factor n times)
1/x
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225

8. 2 is the only
An angle which is supplementary to an interior angle.
Even prime number
EVEN
Cross multiplication a/b=c/d 4/6=10/15 4(15)=6(10) 60=60

9. The sum of the measures of the n angles in a polygon with n sides
Parallelogram
(n-2) x 180
6
4:5

10. a<b then a - b is positive or negative?
Add them. i.e. (5^7) * (5^3) = 5^10
A-b is negative
Every number
1.7

11. Evaluate (4^3)^2
2(pi)r
A-b is positive
Positive or Negative
4096

12. (x-y)²
x²-2xy+y²
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
1
2^9 / 2 = 256

13. What is the name for a grouping of the members within a set based on a shared characteristic?
Even
A subset.
Ø
Arc length = (n/360) x pi(2r) where n is the number of degrees.

14. the slope of a line in y=mx+b
The interesection of A and B.
20.5
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...
M

15. In a Regular Polygon - the measure of each exterior angle
A²+b²=c²
360/n
27
Two angles whose sum is 90.

16. Simplify 9^(1/2) X 4^3 X 2^(-6)?
3
An isosceles right triangle.
2²
x(x - y + 1)

17. Which is greater? 64^5 or 16^8
16^8 64^5 = (4^3)^5 = 4^15 16^8=(4^2)^8 = 4^16
Add them. i.e. (5^7) * (5^3) = 5^10
Every number
The direction of the inequality is reversed.

18. a^2 - 2ab + b^2
The point of intersection of the systems.
6 : 1 : 2
V=side³
(a - b)^2

19. If a lamp decreases to $80 - from $100 - what is the decrease in price?
Can be negative - zero - or positive
2
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
= (actual decrease/Original amount) x100% = 20/100x100% = 20%

20. What is the side length of an equilateral triangle with altitude 6?
6 : 1 : 2
1 & 37/132
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)
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...

21. The Perimeter of a rectangle
2^9 / 2 = 256
No - only like radicals can be added.
Add them. i.e. (5^7) * (5^3) = 5^10
P=2(l+w)

22. Suppose that the graph of f(x) is the result of sliding the graph of y=2x^2 down 3 units of spaces. What is the new equation?
1
True
Ab=k (k is a constant)
y = 2x^2 - 3

23. What is a set with no members called?
0
Triangles with same measure and same side lengths.
6
The empty set - denoted by a circle with a diagonal through it.

24. Area of a triangle
18
A= (1/2) b*h
12! / 5!7! = 792
Undefined - because we can'T divide by 0.

25. x^6 / x^3
1.7
x^(6-3) = x^3
1/a^6
Yes - like radicals can be added/subtracted.

26. Volume of a rectangular box
Every number
4725
13
V=Lwh

27. What are the smallest three prime numbers greater than 65?
62.5%
Right
(x+y)(x-y)
67 - 71 - 73

28. Important properties of a 30-60-90 triangle?
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
.0004809 X 10^11
72
Lies opposite the greater angle

29. (12sqrt15) / (2sqrt5) =
360°
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
y2-y1/x2-x1
(12/2) x (sqrt15 / sqrt5) = 6sqrt3

30. 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)
The set of elements which can be found in either A or B.
4.25 - 6 - 22
No - only like radicals can be added.
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)

31. 25+2³
1
55%
90
28

32. If a is inversely porportional to b - what does it equal?
1
Ab=k (k is a constant)
20.5
28

33. X is the opposite of
x^(6-3) = x^3
Sum of digits is a multiple of 3 and the last digit is even.
X
Lies opposite the greater angle

34. What number between 70 & 75 - inclusive - has the greatest number of factors?
72
y/x is a constant
Triangles with same measure and same side lengths.
A percent is a fraction whose denominator is 100.

35. 20<all primes<30
Ø=P(E)=1
23 - 29
(pi)r²
6

36. Product of any number and Ø is
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.)
an angle that is less than 90°
An is positive
Ø

37. Find the surface area of a cylinder with radius 3 and height 12.
F(x) - c
12sqrt2
90pi
An is positive

38. 3 is the opposite of
3
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.)
Ø
1

39. 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?
20.5
x²-y²
4096
2.592 kg

40. Suppose you have a set of n objects - and you want to select k of them - but the order doesn'T matter. What formula do you use to determine the number of combinations of n objects taken k at a time?
N! / (k!)(n-k)!
61 - 67
The interesection of A and B.
4725

41. 1n
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.
(length)(width)(height)
(x+y)(x+y)
1

42. Slope of any line that goes up from left to right
4096
M= (Y1-Y2)/(X1-X2)
Positive
2²

43. The Perimeter of a Square
75:11
P=4s (s=side)
Its divisible by 2 and by 3.
31 - 37

44. In similar hexagons - the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
y/x is a constant
4:5
P=2(l+w)
52

45. Formula to calculate arc length?
x²-2xy+y²
The set of elements which can be found in either A or B.
F(x-c)
Arc length = (n/360) x pi(2r) where n is the number of degrees.

46. 1/6 in percent?
2
M= (Y1-Y2)/(X1-X2)
16.6666%
(12/2) x (sqrt15 / sqrt5) = 6sqrt3

47. 200 <_ x <_ 300. How many values of x are divisible by 5 & 8?
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
Distance=rate×time or d=rt
3
360°

48. Solve the quadratic equation ax^2 + bx + c= 0
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
Cd
Null
True

49. How to recognize a # as a multiple of 3
A 30-60-90 triangle.
Cross multiplication a/b=c/d 4/6=10/15 4(15)=6(10) 60=60
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)
F(x-c)

50. 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
x²-y²
18
Even
The point of intersection of the systems.