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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. Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
70
A-b is negative
The sum of its digits is divisible by 3.
2^9 / 2 = 256

2. How to find the circumference of a circle which circumscribes a square?
Yes - like radicals can be added/subtracted.
An infinite set.
an angle that is less than 90°
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).

3. A number is divisible by 4 is...
(rate)(time) d=rt
Its last two digits are divisible by 4.
Move the decimal point to the right x places
Every number

4. Ø²
V=l×w×h
Cross multiplication a/b=c/d 4/6=10/15 4(15)=6(10) 60=60
Ø
2sqrt6

5. Time
(distance)/(rate) d/r
A natural number greater than 1 that has no positive divisors other than 1 and itself
The sum of digits is divisible by 9.
83.333%

6. What is the ratio of the sides of an isosceles right triangle?
90pi
1:1:sqrt2
An angle which is supplementary to an interior angle.
y2-y1/x2-x1

7. 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)
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
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)
C=2 x pi x r OR pi x D

8. 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?
A subset.
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
angle that is greater than 90° but less than 180°
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]

9. How to recognize a # as a multiple of 3
441000 = 1 10 10 10 21 * 21
18
Negative
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)

10. Suppose that the graph of f(x) is the result of sliding the graph of y=2x^2 down 3 units of spaces. What is the new equation?
4725
y = 2x^2 - 3
F(x-c)
D/t (distance)/(time)

11. 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?
2.592 kg
75:11
(a - b)^2
1/x

12. Area of a triangle?
D/t (distance)/(time)
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
(base*height) / 2
1/xn i.e. 5^-3 = 1/(5^3) = 1/ 125 = .008

13. What is the name of set with a number of elements which cannot be counted?
10! / 3!(10-3)! = 120
C = 2(pi)r
An infinite set.
Do not have slopes!

14. (x^2)^4
x(x - y + 1)
F(x-c)
x^(2(4)) =x^8 = (x^4)^2
An isosceles right triangle.

15. Rate
Ø=P(E)=1
D/t (distance)/(time)
Edge³
Indeterminable.

16. To decrease a number by x%
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
16.6666%
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
P= 2L + 2w

17. Define an 'expression'.
31 - 37
360°
13
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)

18. x^4 + x^7 =
4a^2(b)
Even prime number
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...
x^(4+7) = x^11

19. What is the coefficient of the x^2 term in the product of (x + 1)(x + 2)(x -1)?
All numbers multiples of 1.
5 OR -5
2
F(x + c)

20. What is the measure of an exterior angle of a regular pentagon?
72
The objects within a set.
C = 2(pi)r
The direction of the inequality is reversed.

21. What is the slope of a horizontal line?
The second graph is less steep.
0
V=side³
Parallelogram

22. Legs 6 - 8. Hypotenuse?
Lies opposite the greater angle
12! / 5!7! = 792
90
10

23. a(b-c)
18
1/a^6
Positive
Ab-ac

24. What are the smallest three prime numbers greater than 65?
A 30-60-90 triangle.
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
67 - 71 - 73
Every number

25. What is a set with no members called?
y = 2x^2 - 3
The empty set - denoted by a circle with a diagonal through it.
Be Zero!
x(x - y + 1)

26. If a<b - then
1
2(pi)r
Ab+ac
A+c<b+c

27. If 4500 is invested at a simple interest rate of 6% - what is the value of the investment after 10 months?
4725
The second graph is less steep.
Null
Sector area = (n/360) X (pi)r^2

28. Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14
A-b is positive
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
90pi
2 & 3/7

29. What is the sum of the angles of a triangle?
1
180 degrees
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
61 - 67

30. If a is negative and n is even then an is (positive or negative?)
P=4s (s=side)
Ø
An is positive
Reciprocal

31. If the two sides of a triangle are unequal then the longer side.................
Lies opposite the greater angle
x^(4+7) = x^11
4a^2(b)
Triangles with same measure and same side lengths.

32. a>b then a - b is positive or negative?
4096
180°
Right
A-b is positive

33. First 10 prime #s
A-b is positive
2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - 29
The union of A and B.
(pi)r²

34. 8.84 / 5.2
Ab+ac
x²-2xy+y²
1.7
7 / 1000

35. In a Regular Polygon - the measure of each exterior angle
0
Ab=k (k is a constant)
x^(2(4)) =x^8 = (x^4)^2
360/n

36. formula for area of a triangle
Members or elements
A natural number greater than 1 that has no positive divisors other than 1 and itself
Triangles with same measure and same side lengths.
A=½bh

37. Simplify (a^2 + b)^2 - (a^2 - b)^2
= (actual decrease/Original amount) x100% = 20/100x100% = 20%
4a^2(b)
Subtract them. i.e (5^7)/(5^3)= 5^4
x²-y²

38. A quadrilateral where two diagonals bisect each other
90pi
A= (1/2) b*h
Parallelogram
The point of intersection of the systems.

39. What is a subset?
The empty set - denoted by a circle with a diagonal through it.
A grouping of the members within a set based on a shared characteristic.
Negative
An infinite set.

40. The perimeter of a square is 48 inches. The length of its diagonal is:
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
12sqrt2
A-b is positive
360°

41. 25^(1/2) or sqrt. 25 =
5 OR -5
Triangles with same measure and same side lengths.
10
V=l×w×h

42. In similar hexagons - the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
The sum of digits is divisible by 9.
(b + c)
4:5
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%

43. 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?
N! / (n-k)!
18
Null
Its divisible by 2 and by 3.

44. Simplify the expression (p^2 - q^2)/ -5(q - p)
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
A subset.
(p + q)/5
360°

45. 30 60 90
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
3x - 4x - 5x
Add them. i.e. (5^7) * (5^3) = 5^10
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.

46. P and r are factors of 100. What is greater - pr or 100?
Arc length = (n/360) x pi(2r) where n is the number of degrees.
Indeterminable.
4a^2(b)
3 - -3

47. What is the graph of f(x) shifted right c units or spaces?
A-b is negative
4725
F(x-c)
A reflection about the axis.

48. For similar triangles - the ratio of their corresponding sides is 2:3. What is the ratio of their areas?
C=2 x pi x r OR pi x D
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
23 - 29
52

49. What is the area of a regular hexagon with side 6?
(pi)r²
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
441000 = 1 10 10 10 21 * 21
1/xn i.e. 5^-3 = 1/(5^3) = 1/ 125 = .008

50. 40 < all primes<50
C=2 x pi x r OR pi x D
9
41 - 43 - 47
NOT A PRIME