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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. a^2 - b^2
(base*height) / 2
(a - b)(a + b)
Negative
1:1:sqrt2

2. What are the smallest three prime numbers greater than 65?
67 - 71 - 73
Arc length = (n/360) x pi(2r) where n is the number of degrees.
A central angle is an angle formed by 2 radii.
Its divisible by 2 and by 3.

3. What is the coefficient of the x^2 term in the product of (x + 1)(x + 2)(x -1)?
2²
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
2
Undefined - because we can'T divide by 0.

4. When does a function automatically have a restricted domain (2)?
V=Lwh
x²-y²
1/x
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.

5. 5/6 in percent?
Infinite.
2
(base*height) / 2
83.333%

6. If a=-1 and b=3 - what is the value of (4(a^3)(b^2) - 12(a^2)(b^5)) / (16(a^3)(b^2))?
The sum of its digits is divisible by 3.
x²+2xy+y²
20.5
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.

7. In a rectangle - all angles are
Pi(diameter)
Ø
Right
1

8. Ratio of ages of Anna and Emma is 3:5 and of Emma and Nicolas is 3:5. What is the ratio of Anna to Nicholas' ages?
1.0843 X 10^11
A=(base)(height)
70
9 : 25

9. First 10 prime #s
2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - 29
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
The set of output values for a function.
(p + q)/5

10. (2²)³
P(E) = ø
1/a^6
26
P(E) = 1/1 = 1

11. Volume of a cube
2sqrt6
1/xn i.e. 5^-3 = 1/(5^3) = 1/ 125 = .008
Edge³
Distance=rate×time or d=rt

12. Ø is
Its last two digits are divisible by 4.
9 : 25
A multiple of every integer
(p + q)/5

13. What is the set of elements which can be found in either A or B?
The union of A and B.
A=½bh
y2-y1/x2-x1
5 - 12 - 13

14. 25^(1/2) or sqrt. 25 =
5 OR -5
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
(a + b)^2
A=(base)(height)

15. 50 < all primes< 60
$3 -500 in the 9% and $2 -500 in the 7%.
53 - 59
3
Pi(diameter)

16. Area of a circle
1/a^6
1 & 37/132
(length)(width)(height)
(pi)r²

17. What number between 70 & 75 - inclusive - has the greatest number of factors?
P=2(l+w)
72
18
441000 = 1 10 10 10 21 * 21

18. In similar hexagons - the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
M= (Y1-Y2)/(X1-X2)
(b + c)
The direction of the inequality is reversed.
4:5

19. Can you simplify sqrt72?
Pi is the ratio of a circle'S circumference to its diameter.
(rate)(time) d=rt
1 & 37/132
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.

20. (6sqrt3) x (2sqrt5) =
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
P=4s (s=side)
(a + b)^2

21. The sum of all angles around a point
A 30-60-90 triangle.
1/a^6
N! / (n-k)!
360°

22. 200 <_ x <_ 300. How many values of x are divisible by 5 & 8?
y2-y1/x2-x1
Sum of digits is a multiple of 3 and the last digit is even.
$11 -448
3

23. X is the opposite of
Edge³
X
A²+b²=c²
x^(6-3) = x^3

24. How to recognize a # as a multiple of 9
The sum of the digits is a multiple of 9.
The two xes after factoring.
2.592 kg
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a

25. 1 is an
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
The point of intersection of the systems.
7 / 1000
ODD number

26. Describe the relationship between the graphs of x^2 and (1/2)x^2
= (actual decrease/Original amount) x 100%
D/t (distance)/(time)
The second graph is less steep.
A central angle is an angle formed by 2 radii.

27. 25/2³
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)
Ø=P(E)=1
2²
1

28. Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14
2 & 3/7
Cd
Positive
$3 -500 in the 9% and $2 -500 in the 7%.

29. a/Ø
A multiple of every integer
Ab+ac
1
Null

30. A number is divisible by 9 if...
The sum of digits is divisible by 9.
A set with no members - denoted by a circle with a diagonal through it.
F(x) + c
V=l×w×h

31. One is (a prime or not?)
NOT A PRIME
Null
Edge³
Sum of digits is a multiple of 3 and the last digit is even.

32. The only number that is equal to its opposite
(a - b)^2
Ø Ø=Ø
Ø
26

33. b¹
360°
(length)(width)(height)
Every number
1

34. The ratio of the areas of two similar polygons is ...
... the square of the ratios of the corresponding sides.
5 OR -5
M= (Y1-Y2)/(X1-X2)
All numbers multiples of 1.

35. What is the relationship between lengths of the sides of a triangle and the measure of the angles of the triangle?
20.5
$3 -500 in the 9% and $2 -500 in the 7%.
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.
Undefined - because we can'T divide by 0.

36. Solve the quadratic equation ax^2 + bx + c= 0
P(E) = 1/1 = 1
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150
C = 2(pi)r
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a

37. Area of a circle
1
A=pi*(r^2)
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)
(12/2) x (sqrt15 / sqrt5) = 6sqrt3

38. A company places a 6-symbol code on each product. The code consists of the letter T - followed by 3 numerical digits - and then 2 consonants (Y is a conson). How many codes are possible?
(a - b)^2
True
13pi / 2
441000 = 1 10 10 10 21 * 21

39. Circumference of a circle?
Diameter(Pi)
(pi)r²
1 - 4 - 9 - 16 - 25 - 36 - 49 - 64 - 81 - 100 - 121 - 144 - 169 - 196 - 225
8

40. 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?
x^(2(4)) =x^8 = (x^4)^2
C = 2(pi)r
y = 2x^2 - 3
x²-y²

41. If a lamp decreases to $80 - from $100 - what is the decrease in price?
6 : 1 : 2
= (actual decrease/Original amount) x100% = 20/100x100% = 20%
(p + q)/5
41 - 43 - 47

42. If a<b - then
A+c<b+c
Be Zero!
4096
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.

43. the slope of a line in y=mx+b
72
1:sqrt3:2
M
12! / 5!7! = 792

44. Perimeter of a rectangle
A tangent is a line that only touches one point on the circumference of a circle.
(a + b)^2
P= 2L + 2w
0

45. Define a 'Term' -
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)
The sum of its digits is divisible by 3.
The union of A and B.
$11 -448

46. What is the graph of f(x) shifted upward c units or spaces?
(b + c)
Ab=k (k is a constant)
F(x) + c
1 & 37/132

47. How to recognize a # as a multiple of 4
10
6 : 1 : 2
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.)
Multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150

48. The perimeter of a square is 48 inches. The length of its diagonal is:
... the square of the ratios of the corresponding sides.
180
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)
12sqrt2

49. What is the measure of an exterior angle of a regular pentagon?
1
90
x²-2xy+y²
72

50. Any Horizontal line slope
(a - b)(a + b)
3 - 4 - 5
The direction of the inequality is reversed.
zero