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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 percent of 40 is 22?
55%
18
5 - 12 - 13
A set with a number of elements which can be counted.

2. 3/8 in percent?
180
37.5%
Relationship cannot be determined (what if x is negative?)
= (actual decrease/Original amount) x100% = 20/100x100% = 20%

3. 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?
Sum of digits is a multiple of 3 and the last digit is even.
An arc is a portion of a circumference of a circle.
A set with no members - denoted by a circle with a diagonal through it.
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

4. Ø is
x^(2(4)) =x^8 = (x^4)^2
P=4s (s=side)
A multiple of every integer
An expression with just one term (-6x - 2a^2)

5. Simplify (a^2 + b)^2 - (a^2 - b)^2
P= 2L + 2w
(x+y)(x+y)
Ab-ac
4a^2(b)

6. x^4 + x^7 =
x^(4+7) = x^11
V=side³
Pi(diameter)
M

7. What is the intersection of A and B?
The set of elements found in both A and B.
1 - P(E)
500
EVEN

8. What is the name for a grouping of the members within a set based on a shared characteristic?
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
A 30-60-90 triangle.
A subset.
26

9. What does scientific notation mean?
x²-2xy+y²
Ab-ac
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
2 & 3/7

10. Ø Is neither
F(x + c)
(base*height) / 2
Positive or Negative
angle that is greater than 90° but less than 180°

11. Formula for the area of a sector of a circle?
Sector area = (n/360) X (pi)r^2
EVEN
(x+y)(x-y)
1/a^6

12. When does a function automatically have a restricted domain (2)?
Positive or Negative
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
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=pi*(r^2)

13. Convert 0.7% to a fraction.
7 / 1000
A=½bh
1
1

14. How to recognize if a # is a multiple of 12
The sum of digits is divisible by 9.
Do not have slopes!
180°
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.)

15. How do you solve proportions? a/b=c/d
y = 2x^2 - 3
The longest arc between points A and B on a circle'S diameter.
Cross multiplication a/b=c/d 4/6=10/15 4(15)=6(10) 60=60
Even

16. If y is directly proportional to x - what does it equal?
A = length x width
y/x is a constant
83.333%
The union of A and B.

17. What are the integers?
All numbers multiples of 1.
13
The direction of the inequality is reversed.
V=side³

18. 10^6 has how many zeroes?
6
Positive
90°
83.333%

19. 60 < all primes <70
70
61 - 67
1
(rate)(time) d=rt

20. Describe the relationship between 3x^2 and 3(x - 1)^2
An infinite set.
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
4725
D=rt so r= d/t and t=d/r

21. Slope of any line that goes up from left to right
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
130pi
C = 2(pi)r
Positive

22. 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
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
12.5%

23. 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)!
A 30-60-90 triangle.
1/a^6
Relationship cannot be determined (what if x is negative?)

24. Distance
Add them. i.e. (5^7) * (5^3) = 5^10
(rate)(time) d=rt
180
(x+y)(x-y)

25. 20<all primes<30
The point of intersection of the systems.
23 - 29
(pi)r²
y = 2x^2 - 3

26. The Denominator can never
A²+b²=c²
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
Two angles whose sum is 180.
Be Zero!

27. The only number that is equal to its opposite
90°
Ø Ø=Ø
1/a^6
$3 -500 in the 9% and $2 -500 in the 7%.

28. If a lamp decreases to $80 - from $100 - what is the decrease in price?
= (actual decrease/Original amount) x100% = 20/100x100% = 20%
2.592 kg
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
The greatest value minus the smallest.

29. a^2 + 2ab + b^2
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%
zero
(a + b)^2
The steeper the slope.

30. Reduce: 4.8 : 0.8 : 1.6
28. n = 8 - k = 2. n! / k!(n-k)!
6 : 1 : 2
16.6666%
Yes - like radicals can be added/subtracted.

31. Whats the difference between factors and multiples?
A²+b²=c²
Factors are few - multiples are many.
6
Subtract them. i.e (5^7)/(5^3)= 5^4

32. What are the roots of the quadrinomial x^2 + 2x + 1?
1 & 37/132
No - only like radicals can be added.
The two xes after factoring.
an angle that is less than 90°

33. Ø Is
Factors are few - multiples are many.
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%
C = 2(pi)r
EVEN

34. What is the common monomial factor in the expression 4(c^3)d - (c^2)(d^2) + 2cd?
D/t (distance)/(time)
67 - 71 - 73
5 - 12 - 13
Cd

35. The Perimeter of a Square
26
A=(base)(height)
P=4s (s=side)
C = 2(pi)r

36. The objects in a set are called two names:
Members or elements
61 - 67
Ø=P(E)=1
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)

37. The product of any number x and its reciprocal
4:5
1
75:11
$3 -500 in the 9% and $2 -500 in the 7%.

38. 2³×7³
Arc length = (n/360) x pi(2r) where n is the number of degrees.
(2x7)³
A chord is a line segment joining two points on a circle.
(length)(width)(height)

39. 1/6 in percent?
x²-y²
(a + b)^2
1
16.6666%

40. Consecutive integers
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
C=2 x pi x r OR pi x D
The set of input values for a function.
x - x+1 - x+2

41. How many 3-digit positive integers are even and do not contain the digit 4?
x²-y²
180°
180 degrees
288 (8 9 4)

42. Can you subtract 3sqrt4 from sqrt4?
P(E) = number of favorable outcomes/total number of possible outcomes
A percent is a fraction whose denominator is 100.
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
Yes - like radicals can be added/subtracted.

43. If 10800 is invested at a simple interest rate of 4% - what is the value of the investment after 18 months?
$11 -448
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%
10! / (10-3)! = 720
3

44. The sum of all angles around a point
An isosceles right triangle.
Even
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
360°

45. What are 'Supplementary angles?'
D/t (distance)/(time)
Two angles whose sum is 180.
71 - 73 - 79
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)

46. 30 60 90
Right
x - x(SR3) - 2x
A-b is negative
90pi

47. Probability of Event all cases
28
Ø=P(E)=1
C = 2(pi)r
37.5%

48. Formula to calculate arc length?
Arc length = (n/360) x pi(2r) where n is the number of degrees.
0
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
x^(2(4)) =x^8 = (x^4)^2

49. Slope
52
y2-y1/x2-x1
Every number
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.

50. What is the measure of an exterior angle of a regular pentagon?
Add them. i.e. (5^7) * (5^3) = 5^10
72
2sqrt6
37.5%