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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 it called when a point is reflected to the quadrant opposite it (i.e. I to III or II to IV)?
x²-y²
Positive
A reflection about the origin.
Every number

2. Area of a triangle
A= (1/2) b*h
5 - 12 - 13
12! / 5!7! = 792
x²-y²

3. Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
$3 -500 in the 9% and $2 -500 in the 7%.
Right
2sqrt6
1/xn i.e. 5^-3 = 1/(5^3) = 1/ 125 = .008

4. Legs 5 - 12. Hypotenuse?
(p + q)/5
The set of elements which can be found in either A or B.
441000 = 1 10 10 10 21 * 21
13

5. formula for the volume of a cube
0
31 - 37
V=side³
Diameter(Pi)

6. Ø is a multiple of
3
Two (Ø×2=Ø)
18
The second graph is less steep.

7. 25^(1/2) or sqrt. 25 =
Cross multiplication a/b=c/d 4/6=10/15 4(15)=6(10) 60=60
F(x + c)
x²-y²
5 OR -5

8. Vertical lines
Do not have slopes!
28
Add them. i.e. (5^7) * (5^3) = 5^10
Two angles whose sum is 180.

9. What is the side length of an equilateral triangle with altitude 6?
A subset.
Triangles with same measure and same side lengths.
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 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. binomial product of (x-y)²
Diameter(Pi)
(x+y)(x-y)
Yes - like radicals can be added/subtracted.
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50

11. The ratio of the areas of two similar polygons is ...
x - x(SR3) - 2x
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
67 - 71 - 73
... the square of the ratios of the corresponding sides.

12. How to recognize a multiple of 6
Sector area = (n/360) X (pi)r^2
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
Sum of digits is a multiple of 3 and the last digit is even.
x²-2xy+y²

13. Describe the relationship between 3x^2 and 3(x - 1)^2
180
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
Ø=P(E)=1
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.

14. What are the roots of the quadrinomial x^2 + 2x + 1?
The two xes after factoring.
An expression with just one term (-6x - 2a^2)
No - only like radicals can be added.
1.0843 X 10^11

15. a^2 + 2ab + b^2
(a + b)^2
27
Two (Ø×2=Ø)
A= (1/2) b*h

16. For any number x
V=Lwh
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 triangle is a right triangle. The triangle is isosceles (AC=BC). The ratio of the lengths of the three sides is x:x:xv2.
Can be negative - zero - or positive

17. What is the intersection of A and B?
12! / 5!7! = 792
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
The set of elements found in both A and B.
The union of A and B.

18. P and r are factors of 100. What is greater - pr or 100?
3 - -3
Indeterminable.
An expression with just one term (-6x - 2a^2)
16.6666%

19. How many multiples does a given number have?
x²-y²
Infinite.
90
The set of elements found in both A and B.

20. When does a function automatically have a restricted domain (2)?
P=2(l+w)
The overlapping sections.
The shortest arc between points A and B on a circle'S diameter.
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.

21. A number is divisible by 3 if ...
The direction of the inequality is reversed.
NOT A PRIME
(base*height) / 2
The sum of its digits is divisible by 3.

22. Product of any number and Ø is
Add them. i.e. (5^7) * (5^3) = 5^10
2
Every number
Ø

23. Find the surface area of a cylinder with radius 3 and height 12.
B?b?b (where b is used as a factor n times)
90pi
A subset.
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.)

24. The reciprocal of any non-zero #x is
1/x
X
x²+2xy+y²
Ab+ac

25. Can you simplify sqrt72?
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
2.592 kg
V=side³
NOT A PRIME

26. (a^-1)/a^5
(base*height) / 2
Null
1/a^6
A-b is positive

27. Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
2^9 / 2 = 256
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)
16.6666%
Pi is the ratio of a circle'S circumference to its diameter.

28. Which is greater? 200x^295 or 10x^294?
Relationship cannot be determined (what if x is negative?)
4:5
1
An arc is a portion of a circumference of a circle.

29. b¹
Positive
D=rt so r= d/t and t=d/r
an angle that is less than 90°
1

30. Formula for the area of a sector of a circle?
70
B?b?b (where b is used as a factor n times)
Sector area = (n/360) X (pi)r^2
9 & 6/7

31. What is the surface area of a cylinder with radius 5 and height 8?
1
P=2(l+w)
130pi
M

32. (x-y)²
x²-2xy+y²
Every number
7 / 1000
(length)(width)(height)

33. What is the 'Range' of a function?
NOT A PRIME
Edge³
360°
The set of output values for a function.

34. What is the name for a grouping of the members within a set based on a shared characteristic?
A subset.
37.5%
Null
55%

35. binomial product of (x+y)(x-y)
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
x²-y²
360/n
2^9 / 2 = 256

36. Area of a circle
P=4s (s=side)
9
6
A=pi*(r^2)

37. What is the 'Range' of a series of numbers?
The greatest value minus the smallest.
Ø
The steeper the slope.
16.6666%

38. What number between 70 & 75 - inclusive - has the greatest number of factors?
72
(x+y)(x+y)
M
1/x

39. 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)
C=2 x pi x r OR pi x D
1
x²-y²
4.25 - 6 - 22

40. Find distance when given time and rate
D=rt so r= d/t and t=d/r
F(x + c)
28. n = 8 - k = 2. n! / k!(n-k)!
The two xes after factoring.

41. Simplify (a^2 + b)^2 - (a^2 - b)^2
The direction of the inequality is reversed.
4a^2(b)
x²-y²
1 & 37/132

42. 6w^2 - w - 15 = 0
A set with a number of elements which can be counted.
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
A multiple of every integer
3/2 - 5/3

43. An Angle that'S 180°
Straight Angle
31 - 37
Members or elements
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.)

44. How many sides does a hexagon have?
67 - 71 - 73
The direction of the inequality is reversed.
6
16^8 64^5 = (4^3)^5 = 4^15 16^8=(4^2)^8 = 4^16

45. binomial product of (x+y)²
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
Even
(x+y)(x+y)
True

46. What transformation occurs if point C is reflected over the x-axis and then the y-axis?
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.
Ø
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
A reflection about the axis.

47. formula for area of a triangle
3/2 - 5/3
55%
y = (x + 5)/2
A=½bh

48. Area of a circle
Ab+ac
V=Lwh
The interesection of A and B.
(pi)r²

49. What is the set of elements which can be found in either A or B?
A multiple of every integer
(distance)/(rate) d/r
The union of A and B.
87.5%

50. If y is directly proportional to x - what does it equal?
x²+2xy+y²
90
The sum of the digits is a multiple of 9.
y/x is a constant