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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 is the maximum value for the function g(x) = (-2x^2) -1?
N! / (k!)(n-k)!
1
Ab=k (k is a constant)
Factors are few - multiples are many.

2. What is a percent?
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
A percent is a fraction whose denominator is 100.
67 - 71 - 73
(b + c)

3. A number is divisible by 3 if ...
The sum of its digits is divisible by 3.
1
C = (pi)d
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)

4. a(b+c)
288 (8 9 4)
Ab+ac
(a + b)^2
The objects within a set.

5. a^2 - b^2
Undefined
71 - 73 - 79
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
(a - b)(a + b)

6. 6w^2 - w - 15 = 0
Positive
3/2 - 5/3
2(pi)r
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.

7. 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-b is negative
Positive
5
$3 -500 in the 9% and $2 -500 in the 7%.

8. What is the empty set?
Null
(pi)r²
A set with no members - denoted by a circle with a diagonal through it.
500

9. Employee X is paid 19.50 per hour no matter how many a week. Employee Y earns 18 for the first 40 and 1.5 the hourly wage for every hour after that. If both earned the same amount and worked the same in one week - how many did each work?
48
X
1/x
12! / 5!7! = 792

10. A triangle is inscribed in a semi circle with legs 5 and 12. What is the circumfermence of the semicircle?
13pi / 2
28
Its last two digits are divisible by 4.
72

11. What number between 70 & 75 - inclusive - has the greatest number of factors?
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
V=Lwh
Diameter(Pi)
72

12. What is the set of elements found in both A and B?
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
3 - -3
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
The interesection of A and B.

13. The negative exponent x?n is equivalent to what?
27^(-4)
1/xn i.e. 5^-3 = 1/(5^3) = 1/ 125 = .008
ODD number
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.

14. 1/2 divided by 3/7 is the same as
16^8 64^5 = (4^3)^5 = 4^15 16^8=(4^2)^8 = 4^16
(distance)/(rate) d/r
Indeterminable.
1/2 times 7/3

15. Time
Even prime number
V=side³
5 OR -5
(distance)/(rate) d/r

16. Volume of a rectangular solid
C = 2(pi)r
6 : 1 : 2
Ab-ac
(length)(width)(height)

17. To decrease a number by x%
The shortest arc between points A and B on a circle'S diameter.
Multiply by 1-x% i.e. 100 x (1-50%)=100x.5=50
10! / 3!(10-3)! = 120
Positive or Negative

18. X is the opposite of
X
P= 2L + 2w
A natural number greater than 1 that has no positive divisors other than 1 and itself
Undefined - because we can'T divide by 0.

19. The perimeter of a square is 48 inches. The length of its diagonal is:
12sqrt2
67 - 71 - 73
x²+2xy+y²
18

20. a^2 + 2ab + b^2
M
Negative
Two equal sides and two equal angles.
(a + b)^2

21. 2³×7³
(2x7)³
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
4a^2(b)
1

22. Formula for the area of a sector of a circle?
Sector area = (n/360) X (pi)r^2
An angle which is supplementary to an interior angle.
x²+2xy+y²
Ab-ac

23. Ø²
Parallelogram
(a - b)(a + b)
Ø
83.333%

24. Simplify the expression [(b^2 - c^2) / (b - c)]
(b + c)
ODD number
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
71 - 73 - 79

25. 1/8 in percent?
5 OR -5
12.5%
Ab=k (k is a constant)
X

26. a>b then a - b is positive or negative?
A-b is positive
F(x) - c
Undefined
Positive

27. What is the slope of a vertical line?

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28. -3³
Can be negative - zero - or positive
55%
x²-y²
27

29. Circumference of a circle
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
70
Pi(diameter)
3 - 4 - 5

30. The sum of the measures of the n angles in a polygon with n sides
Every number
(n-2) x 180
The shortest arc between points A and B on a circle'S diameter.
The greatest value minus the smallest.

31. Solve the quadratic equation ax^2 + bx + c= 0
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
2²
The set of output values for a function.
360°

32. In a rectangle - all angles are
Right
x - x(SR3) - 2x
Ø
Positive or Negative

33. For any number x
90°
2(pi)r
4.25 - 6 - 22
Can be negative - zero - or positive

34. bn
B?b?b (where b is used as a factor n times)
D/t (distance)/(time)
Even prime number
An infinite set.

35. 5/6 in percent?
83.333%
90°
Ab-ac
62.5%

36. factored binomial product of (x-y)²
x²-2xy+y²
A-b is negative
13
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.

37. 25+2³
28
360°
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.)
2.592 kg

38. What are the real numbers?
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)
x^(4+7) = x^11
441000 = 1 10 10 10 21 * 21
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%

39. (x-y)(x+y)
A reflection about the axis.
(p + q)/5
x²-y²
The set of elements found in both A and B.

40. 30 60 90
1/a^6
3 - 4 - 5
A grouping of the members within a set based on a shared characteristic.
Arc length = (n/360) x pi(2r) where n is the number of degrees.

41. What is the 'union' of A and B?
= 25%. = (actual increase/original amount) x 100% = 20/80 x 100% = 1/4 x 100% = 25%
A= (1/2) b*h
Edge³
The set of elements which can be found in either A or B.

42. Formula to find a circle'S circumference from its diameter?
C=2 x pi x r OR pi x D
C = (pi)d
The set of elements found in both A and B.
A subset.

43. What is the coefficient of the x^2 term in the product of (x + 1)(x + 2)(x -1)?
27^(-4)
2
Ab+ac
(a + b)^2

44. If a is inversely porportional to b - what does it equal?
Prime numbers (2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23)
P(E) = 1/1 = 1
Ab=k (k is a constant)
The two xes after factoring.

45. Acute Angle
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
(rate)(time) d=rt
an angle that is less than 90°
Two angles whose sum is 90.

46. -3²
The set of output values for a function.
Cd
9
Null

47. Ø is
A multiple of every integer
x²-2xy+y²
5 - 12 - 13
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)

48. Can you subtract 3sqrt4 from sqrt4?
Positive
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)
Yes - like radicals can be added/subtracted.
A = length x width

49. 70 < all primes< 80
71 - 73 - 79
The sum of its digits is divisible by 3.
F(x + c)
(distance)/(rate) d/r

50. Simplify 9^(1/2) X 4^3 X 2^(-6)?
(a + b)^2
13pi / 2
3
Indeterminable.