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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 a percent?
A percent is a fraction whose denominator is 100.
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
1
3/2 - 5/3

2. Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
27^(-4)
No - only like radicals can be added.
(pi)r²
2sqrt6

3. (a^-1)/a^5
Null
1/a^6
130pi
F(x-c)

4. If a is negative and n is even then an is (positive or negative?)
10! / (10-3)! = 720
An is positive
61 - 67
5 - 12 - 13

5. What are 'Supplementary angles?'
Ab-ac
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
Two angles whose sum is 180.
C = 2(pi)r

6. a(b+c)
Ab+ac
C=2 x pi x r OR pi x D
F(x) + c
Right

7. Ø is
Even
87.5%
12sqrt2
Ab=k (k is a constant)

8. Ø divided by 7
Ø
x²-y²
B?b?b (where b is used as a factor n times)
90pi

9. 200 <_ x <_ 300. How many values of x are divisible by 5 & 8?
3
12sqrt2
Indeterminable.
180 degrees

10. a^2 + 2ab + b^2
9 : 25
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.)
(a + b)^2
Prime numbers (2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23)

11. Probability of E not occurring:
1 - P(E)
(length)(width)(height)
EVEN
Two equal sides and two equal angles.

12. Write 10 -843 X 10^7 in scientific notation
87.5%
1.0843 X 10^11
Negative
(a + b)^2

13. Can you add sqrt 3 and sqrt 5?
Cross multiplication a/b=c/d 4/6=10/15 4(15)=6(10) 60=60
The greatest value minus the smallest.
No - only like radicals can be added.
zero

14. 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?
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
13pi / 2
C = (pi)d
(2x7)³

15. Simplify 9^(1/2) X 4^3 X 2^(-6)?
Parallelogram
3
x²-2xy+y²
x - x(SR3) - 2x

16. How to recognize a # as a multiple of 4
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.)
Members or elements
Undefined
41 - 43 - 47

17. When does a function automatically have a restricted domain (2)?
Diameter(Pi)
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
... the square of the ratios of the corresponding sides.
37.5%

18. What is a minor arc?

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19. What are the roots of the quadrinomial x^2 + 2x + 1?
C = 2(pi)r
Undefined
2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - 29
The two xes after factoring.

20. What are the real numbers?
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)
C = (pi)d
10! / 3!(10-3)! = 120
37.5%

21. If E is certain
1:1:sqrt2
P(E) = 1/1 = 1
Pi is the ratio of a circle'S circumference to its diameter.
A percent is a fraction whose denominator is 100.

22. What is the coefficient of the x^2 term in the product of (x + 1)(x + 2)(x -1)?
A subset.
y = (x + 5)/2
2
Ø

23. What is a set with no members called?
The empty set - denoted by a circle with a diagonal through it.
5 - 12 - 13
x^(2(4)) =x^8 = (x^4)^2
Even

24. What is the graph of f(x) shifted left c units or spaces?
F(x + c)
2 & 3/7
A 30-60-90 triangle.
A = length x width

25. What is the set of elements found in both A and B?
A grouping of the members within a set based on a shared characteristic.
The interesection of A and B.
1/x
360°

26. What is a tangent?
Negative
A tangent is a line that only touches one point on the circumference of a circle.
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
The longest arc between points A and B on a circle'S diameter.

27. 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?
x - x+1 - x+2
Its divisible by 2 and by 3.
2.592 kg
x²-y²

28. 7 divided by Ø
D/t (distance)/(time)
P(E) = 1/1 = 1
x - x+1 - x+2
Null

29. Simplify the expression (p^2 - q^2)/ -5(q - p)
Every number
(p + q)/5
P= 2L + 2w
The sum of digits is divisible by 9.

30. Number of degrees in a triangle
$11 -448
180
Ab=k (k is a constant)
4a^2(b)

31. The reciprocal of any non-zero number is
90
A=pi*(r^2)
Every number
1/x

32. Area of a circle
The interesection of A and B.
(pi)r²
Every number
Ab-ac

33. Probability of an Event
P(E) = number of favorable outcomes/total number of possible outcomes
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.)
1
4096

34. What is the 'domain' of a function?
The set of input values for a function.
A=pi*(r^2)
Move the decimal point to the right x places
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.

35. Define an 'expression'.
90pi
An algebraic expression is a combination of one of more terms. Terms in an expression are separated by either addition or subtraction signs. (3xy - 4ab - -5cd - x^2 + x - 1)
A chord is a line segment joining two points on a circle.
Negative

36. Circumference of a circle
360°
(x+y)(x-y)
2(pi)r
130pi

37. What is the maximum value for the function g(x) = (-2x^2) -1?
360/n
2^9 / 2 = 256
Cross multiplication a/b=c/d 4/6=10/15 4(15)=6(10) 60=60
1

38. Formula to find a circle'S circumference from its radius?
C = 2(pi)r
Cross multiplication a/b=c/d 4/6=10/15 4(15)=6(10) 60=60
The union of A and B.
A set with a number of elements which can be counted.

39. What is the common monomial factor in the expression 4(c^3)d - (c^2)(d^2) + 2cd?
Cd
(amount of decrease/original price) x 100%
(a - b)^2
Can be negative - zero - or positive

40. Rate
(x+y)(x-y)
The sum of its digits is divisible by 3.
D/t (distance)/(time)
2(pi)r

41. 25^(1/2) or sqrt. 25 =
Pi is the ratio of a circle'S circumference to its diameter.
5 OR -5
x²-y²
A-b is negative

42. 1:sqrt3:2 is the ratio of the sides of what kind of triangle?
A 30-60-90 triangle.
No - only like radicals can be added.
2(pi)r
D=rt so r= d/t and t=d/r

43. Volume of a rectangular solid
A = pi(r^2)
A 30-60-90 triangle.
55%
(length)(width)(height)

44. What number between 70 & 75 - inclusive - has the greatest number of factors?
72
31 - 37
Ab+ac
The direction of the inequality is reversed.

45. A quadrilateral where two diagonals bisect each other
Parallelogram
Ø
An infinite set.
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.

46. If a product of two numbers is Ø - one number must be
The sum of the digits is a multiple of 9.
(p + q)/5
x^(4+7) = x^11
Ø

47. For what values should the domain be restricted for the function f(x) = sqrt(x + 8)
0
All numbers multiples of 1.
8
an angle that is less than 90°

48. The reciprocal of any non-zero #x is
F(x + c)
Cross multiplication a/b=c/d 4/6=10/15 4(15)=6(10) 60=60
x^(6-3) = x^3
1/x

49. What is the surface area of a cylinder with radius 5 and height 8?
Its divisible by 2 and by 3.
Move the decimal point to the right x places
130pi
Ø=P(E)=1

50. 70 < all primes< 80
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
Its last two digits are divisible by 4.
71 - 73 - 79
A+c<b+c