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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. 5x^2 - 35x -55 = 0
12.5%
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
2
y = 2x^2 - 3

2. If a lamp decreases to $80 - from $100 - what is the decrease in price?
= (actual decrease/Original amount) x100% = 20/100x100% = 20%
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
D=rt so r= d/t and t=d/r
The empty set - denoted by a circle with a diagonal through it.

3. If Madagascar'S exports totaled 1.3 billion in 2009 - and 4% came from China - what was the value in millions of the country'S exports to China?
52
The interesection of A and B.
An is positive
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)

4. 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?
8
1/2 times 7/3
True
10! / (10-3)! = 720

5. a^0 =
1
Ø
9
Relationship cannot be determined (what if x is negative?)

6. A number is divisible by 4 is...
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
5 OR -5
Its last two digits are divisible by 4.
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.)

7. 5 bakeries sell an average of 300 muffins per bakery per day. If 2 stop making muffins but the total muffins sold stays the same - what is the average of muffins per bakery sold among the remaining?
(x+y)(x-y)
500
Positive
Ø

8. Factor a^2 + 2ab + b^2
9
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
288 (8 9 4)

9. How to recognize a # as a multiple of 4
An infinite set.
B?b?b (where b is used as a factor n times)
4:5
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.)

10. What is an arc of a circle?
1
A<-b
180
An arc is a portion of a circumference of a circle.

11. 1:sqrt3:2 is the ratio of the sides of what kind of triangle?
(a - b)(a + b)
ODD number
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
A 30-60-90 triangle.

12. (2²)³
A tangent is a line that only touches one point on the circumference of a circle.
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%
26
Ab+ac

13. 30 60 90
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225
The set of elements found in both A and B.
Prime numbers (2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23)
x - x(SR3) - 2x

14. What is the 'union' of A and B?
90pi
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.)
The set of elements which can be found in either A or B.
The set of elements found in both A and B.

15. If a is positive - an is
A 30-60-90 triangle.
Positive
(a + b)^2
= (actual decrease/Original amount) x100% = 20/100x100% = 20%

16. 25^(1/2) or sqrt. 25 =
Add them. i.e. (5^7) * (5^3) = 5^10
5 OR -5
(a - b)^2
360/n

17. Area of a triangle?
2²
... the square of the ratios of the corresponding sides.
(base*height) / 2
Even

18. What are the irrational numbers?

19. a<b then a - b is positive or negative?
A-b is negative
16^8 64^5 = (4^3)^5 = 4^15 16^8=(4^2)^8 = 4^16
A= (1/2) b*h
D=rt so r= d/t and t=d/r

20. -3³
27
1.0843 X 10^11
0
A = pi(r^2)

21. 25+2³
D=rt so r= d/t and t=d/r
(b + c)
(2x7)³
28

22. If E is certain
P(E) = 1/1 = 1
x²+2xy+y²
The empty set - denoted by a circle with a diagonal through it.
The sum of its digits is divisible by 3.

23. 30 60 90
All numbers multiples of 1.
5 - 12 - 13
True
The sum of the digits is a multiple of 9.

24. 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?
A=pi*(r^2)
$3 -500 in the 9% and $2 -500 in the 7%.
(length)(width)(height)
1/x

25. What does scientific notation mean?
1
The direction of the inequality is reversed.
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
The sum of its digits is divisible by 3.

26. Vertical lines
The set of elements which can be found in either A or B.
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
Do not have slopes!
y = 2x^2 - 3

27. What is the graph of f(x) shifted downward c units or spaces?
F(x) - c
C=2 x pi x r OR pi x D
16^8 64^5 = (4^3)^5 = 4^15 16^8=(4^2)^8 = 4^16
(x+y)(x+y)

28. What is the ratio of the surface area of a cube with an edge of 10 to the surface area of a rectangular solid with dimensions 2 - 4 - and 6?
75:11
72
True
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225

29. What is the side length of an equilateral triangle with altitude 6?
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...
The set of elements which can be found in either A or B.
23 - 29
C = (pi)d

30. How do you solve proportions? a/b=c/d
Cross multiplication a/b=c/d 4/6=10/15 4(15)=6(10) 60=60
1
(2x7)³
10! / 3!(10-3)! = 120

31. Perfect Squares 1-15
V=l×w×h
12! / 5!7! = 792
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225
An isosceles right triangle.

32. 70 < all primes< 80
90°
An expression with just one term (-6x - 2a^2)
71 - 73 - 79
90pi

33. A prime number (or a prime)
4:5
A natural number greater than 1 that has no positive divisors other than 1 and itself
$11 -448
An expression with just one term (-6x - 2a^2)

34. 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
75:11
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
180
18

35. Formula to find a circle'S circumference from its radius?
D/t (distance)/(time)
61 - 67
zero
C = 2(pi)r

36. P and r are factors of 100. What is greater - pr or 100?
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
Indeterminable.
13
180

37. How to determine percent decrease?
(amount of decrease/original price) x 100%
9
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
Positive

38. What is the ratio of the sides of an isosceles right triangle?
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
(x+y)(x-y)
F(x-c)
1:1:sqrt2

39. If a is inversely porportional to b - what does it equal?
Ab=k (k is a constant)
7 / 1000
The shortest arc between points A and B on a circle'S diameter.
Ab+ac

40. First 10 prime #s
2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - 29
(pi)r²
4.25 - 6 - 22
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)

41. The important properties of a 45-45-90 triangle?
70
Positive or Negative
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)
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.

42. The four angles around a point measure y - 2y - 35 and 55 respectively. What is the value of y?
90
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
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.)
P=4s (s=side)

43. What is the set of elements found in both A and B?
N! / (k!)(n-k)!
An isosceles right triangle.
The interesection of A and B.
The longest arc between points A and B on a circle'S diameter.

44. Legs 5 - 12. Hypotenuse?
13
Smallest positive integer
Negative
28. n = 8 - k = 2. n! / k!(n-k)!

45. Ø Is neither
Positive or Negative
A natural number greater than 1 that has no positive divisors other than 1 and itself
4096
M

46. Solve the quadratic equation ax^2 + bx + c= 0
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
4a^2(b)
An arc is a portion of a circumference of a circle.
7 / 1000

47. What is the measure of an exterior angle of a regular pentagon?
72
P(E) = ø
Two angles whose sum is 90.
Even

48. Can you subtract 3sqrt4 from sqrt4?
Yes - like radicals can be added/subtracted.
(2x7)³
The greatest value minus the smallest.
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)

49. Evaluate (4^3)^2
ODD number
4096
x - x(SR3) - 2x
3 - 4 - 5

50. Dividing by a number is the same as multiplying it by its
10! / 3!(10-3)! = 120
The overlapping sections.
Reciprocal
(p + q)/5