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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. How many 3-digit positive integers are even and do not contain the digit 4?
x²-y²
1
P=4s (s=side)
288 (8 9 4)

2. Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14
8
2 & 3/7
An expression with just one term (-6x - 2a^2)
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150

3. Distance
(rate)(time) d=rt
(b + c)
A = length x width
x^(6-3) = x^3

4. Can you subtract 3sqrt4 from sqrt4?
Yes - like radicals can be added/subtracted.
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
A = length x width
C = 2(pi)r

5. (x-y)(x+y)
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)
1/xn i.e. 5^-3 = 1/(5^3) = 1/ 125 = .008
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.
x²-y²

6. Ø²
A²+b²=c²
13
C=2 x pi x r OR pi x D
Ø

7. The product of any number x and its reciprocal
Even prime number
Factors are few - multiples are many.
1
5 OR -5

8. 10<all primes<20
y = 2x^2 - 3
11 - 13 - 17 - 19
A = length x width
Undefined

9. What does scientific notation mean?
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
72
1
4.25 - 6 - 22

10. There are 10 finalists for the school spelling bee. A first - second - and third place trophy will be awarded. In how many ways can the judges award the 3 prizes?
The greatest value minus the smallest.
A = pi(r^2)
10! / (10-3)! = 720
The empty set - denoted by a circle with a diagonal through it.

11. formula for volume of a rectangular solid
B?b?b (where b is used as a factor n times)
Edge³
V=l×w×h
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).

12. What is the set of elements found in both A and B?
Sum of digits is a multiple of 3 and the last digit is even.
4.25 - 6 - 22
... the square of the ratios of the corresponding sides.
The interesection of A and B.

13. 1/2 divided by 3/7 is the same as
A subset.
1
12sqrt2
1/2 times 7/3

14. factored binomial product of (x-y)²
x²-2xy+y²
Parallelogram
an angle that is less than 90°
Arc length = (n/360) x pi(2r) where n is the number of degrees.

15. If Event is impossible
P(E) = ø
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.)
Pi is the ratio of a circle'S circumference to its diameter.
Negative

16. Find the surface area of a cylinder with radius 3 and height 12.
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
y = (x + 5)/2
$3 -500 in the 9% and $2 -500 in the 7%.
90pi

17. Convert 0.7% to a fraction.
Undefined
A chord is a line segment joining two points on a circle.
7 / 1000
A reflection about the origin.

18. 40 < all primes<50
A natural number greater than 1 that has no positive divisors other than 1 and itself
41 - 43 - 47
Positive
9 & 6/7

19. Area of a rectangle
x(x - y + 1)
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
500
A = length x width

20. 200 <_ x <_ 300. How many values of x are divisible by 5 & 8?
Members or elements
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...
A-b is negative
3

21. The reciprocal of any non-zero #x is
2 & 3/7
Relationship cannot be determined (what if x is negative?)
D/t (distance)/(time)
1/x

22. How to recognize a multiple of 6
Sum of digits is a multiple of 3 and the last digit is even.
1
1
An isosceles right triangle.

23. bn
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 hypotenuse is twice the length of the shorter leg. The ratio of the length of the three sides is x:xv3:2x
(pi)r²
B?b?b (where b is used as a factor n times)

24. What is the empty set?
Positive
2.592 kg
A set with no members - denoted by a circle with a diagonal through it.
6

25. (12sqrt15) / (2sqrt5) =
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
Arc length = (n/360) x pi(2r) where n is the number of degrees.
130pi

26. Factor a^2 + 2ab + b^2
Straight Angle
Add them. i.e. (5^7) * (5^3) = 5^10
(a + b)^2
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.

27. The Perimeter of a rectangle
7 / 1000
Every number
41 - 43 - 47
P=2(l+w)

28. Which is greater? 64^5 or 16^8
y2-y1/x2-x1
16^8 64^5 = (4^3)^5 = 4^15 16^8=(4^2)^8 = 4^16
x²+2xy+y²
Smallest positive integer

29. The product of odd number of negative numbers
A chord is a line segment joining two points on a circle.
Negative
1
Relationship cannot be determined (what if x is negative?)

30. Volume of a cube
Edge³
An angle which is supplementary to an interior angle.
28. n = 8 - k = 2. n! / k!(n-k)!
4a^2(b)

31. What is the 'domain' of a function?
Its last two digits are divisible by 4.
The set of elements which can be found in either A or B.
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
The set of input values for a function.

32. A number is divisible by 4 is...
x - x(SR3) - 2x
(distance)/(rate) d/r
Its last two digits are divisible by 4.
Ab+ac

33. How to find the circumference of a circle which circumscribes a square?
52
A+c<b+c
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
(length)(width)(height)

34. a(b-c)
Add them. i.e. (5^7) * (5^3) = 5^10
V=l×w×h
A= (1/2) b*h
Ab-ac

35. The ratio of the areas of two similar polygons is ...
... the square of the ratios of the corresponding sides.
The interesection of A and B.
(2x7)³
Indeterminable.

36. If you have a set of n objects - but you only want to order k of them - what formula do you use to determine the number of permutations?
x^(2(4)) =x^8 = (x^4)^2
N! / (n-k)!
The longest arc between points A and B on a circle'S diameter.
A=(base)(height)

37. binomial product of (x+y)²
(x+y)(x+y)
The overlapping sections.
A = pi(r^2)
(12/2) x (sqrt15 / sqrt5) = 6sqrt3

38. 7/8 in percent?
(a - b)(a + b)
87.5%
x(x - y + 1)
90

39. Circumference of a circle?
Diameter(Pi)
(n-2) x 180
C=2 x pi x r OR pi x D
Negative

40. 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.)
6
48
The point of intersection of the systems.

41. Probability of E not occurring:
No - only like radicals can be added.
500
1 - P(E)
A=pi*(r^2)

42. A prime number (or a prime)
Prime numbers (2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23)
A natural number greater than 1 that has no positive divisors other than 1 and itself
6 : 1 : 2
12.5%

43. How to recognize if a # is a multiple of 12
y = 2x^2 - 3
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.)
1.0843 X 10^11
A set with no members - denoted by a circle with a diagonal through it.

44. What is the set of elements which can be found in either A or B?
P(E) = ø
x²-2xy+y²
62.5%
The union of A and B.

45. 1 is a divisor of
Its last two digits are divisible by 4.
Every number
1/x
C = 2(pi)r

46. X is the opposite of
X
37.5%
Ab+ac
1.0843 X 10^11

47. 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)
28
X
1
4.25 - 6 - 22

48. a(b+c)
Ab+ac
28. n = 8 - k = 2. n! / k!(n-k)!
16.6666%
The longest arc between points A and B on a circle'S diameter.

49. Hector invested $6000. Part was invested in account with 9% simple annual interest - and the rest in account with 7% simple annual interest. If he earned $490 in the first year of these investments - how much did he invest in each account?
27
F(x-c)
$3 -500 in the 9% and $2 -500 in the 7%.
(x+y)(x-y)

50. Formula to calculate arc length?
x^(2(4)) =x^8 = (x^4)^2
12sqrt2
Arc length = (n/360) x pi(2r) where n is the number of degrees.
90°