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GRE Math: Common Errors

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
Yes - like radicals can be added/subtracted.
(a - b)(a + b)
12.5%
A = pi(r^2)

2. What are the rational numbers?
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
Triangles with same measure and same side lengths.
Two angles whose sum is 90.
90pi

3. What is the set of elements which can be found in either A or B?
The union of A and B.
F(x) + c
Sqrt 12
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).

4. 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
90pi
Its last two digits are divisible by 4.
Arc length = (n/360) x pi(2r) where n is the number of degrees.
18

5. Formula of rectangle where l increases by 20% and w decreases by 20%
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
Even
The two xes after factoring.
x= (1.2)(.8)lw

6. The number of degrees in the largest angle of a triangle inscribed in a circle - in which the diameter of the circle is one side of the triangle.
90 degrees
... the square of the ratios of the corresponding sides.
The objects within a set.
3 - -3

7. What is the name of set with a number of elements which cannot be counted?
61 - 67
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
4.25 - 6 - 22
An infinite set.

8. 7/8 in percent?
70
288 (8 9 4)
87.5%
F(x + c)

9. Which is greater? 64^5 or 16^8
8
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
The shortest arc between points A and B on a circle'S diameter.
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.

10. What percent of 40 is 22?
(base*height) / 2
C = (pi)d
55%
Diameter(Pi)

11. 413.03 x 10^(-4) =
II
Undefined - because we can'T divide by 0.
413.03 / 10^4 (move the decimal point 4 places to the left)
53 - 59

12. How to determine percent decrease?
C = (pi)d
(amount of decrease/original price) x 100%
12! / 5!7! = 792
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]

13. What number between 70 & 75 - inclusive - has the greatest number of factors?
72
180
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
10! / (10-3)! = 720

14. Simplify (a^2 + b)^2 - (a^2 - b)^2
87.5%
F(x + c)
2.592 kg
4a^2(b)

15. What is a minor arc?

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16. When does a function automatically have a restricted domain (2)?
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...
Arc length = (n/360) x pi(2r) where n is the number of degrees.
A chord is a line segment joining two points on a circle.
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.

17. (-1)^3 =
1
The empty set - denoted by a circle with a diagonal through it.
Yes - like radicals can be added/subtracted.
2

18. If an inequality is multiplied or divided by a negative number....
True
Part = Percent X Whole
N! / (n-k)!
The direction of the inequality is reversed.

19. From a box of 12 candles - you are to remove 5. How many different sets of 5 candles could you remove?
(a - b)^2
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
A circle centered on the origin with radius 8.
12! / 5!7! = 792

20. 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?
Yes. [i.e. f(x) = x^2 - 1
A chord is a line segment joining two points on a circle.
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
48

21. 4.809 X 10^7 =
(amount of increase/original price) x 100%
.0004809 X 10^11
37.5%
3

22. What is the graph of f(x) shifted downward c units or spaces?
83.333%
A reflection about the axis.
.0004809 X 10^11
F(x) - c

23. There are 10 finalists for the school spelling bee. A first - second - and third place trophy will be awarded. How many different people can get the three prizes?
71 - 73 - 79
10! / 3!(10-3)! = 120
An expression with just one term (-6x - 2a^2)
4:5

24. What is the intersection of A and B?
2 & 3/7
The set of elements found in both A and B.
(n-2) x 180
x^(6-3) = x^3

25. What is the common monomial factor in the expression 4(c^3)d - (c^2)(d^2) + 2cd?
Cd
(amount of decrease/original price) x 100%
6
A chord is a line segment joining two points on a circle.

26. Describe the relationship between 3x^2 and 3(x - 1)^2
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
C = (pi)d
500
Two equal sides and two equal angles.

27. Can the input value of a function have more than one output value (i.e. x: y - y1)?
The direction of the inequality is reversed.
No - the input value has exactly one output.
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
62.5%

28. If r - t - s & u are distinct - consecutive prime numbers - less than 31 - which of the following could be an average of them (4 - 4.25 - 6 - 9 - 24 - 22 - 24)
(a + b)^2
(base*height) / 2
4.25 - 6 - 22
Undefined

29. 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?
A 30-60-90 triangle.
500
Two angles whose sum is 90.
The set of input values for a function.

30. How many sides does a hexagon have?
Move the decimal point to the right x places
6
Lies opposite the greater angle
3/2 - 5/3

31. What does scientific notation mean?
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
72
When the function is not defined for all real numbers -; only a subset of the real numbers.
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).

32. 10^6 has how many zeroes?
6
A circle centered at -2 - -2 with radius 3.
From northeast - counterclockwise. I - II - III - IV
The objects within a set.

33. How many digits are there between the decimal point and the first even digit in the decimal equivalent of 1/[(2^8)(5^3)]
Factors are few - multiples are many.
0
F(x-c)
6 : 1 : 2

34. 25^(1/2) or sqrt. 25 =
0
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
5 OR -5
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).

35. Max and Min lengths for a side of a triangle?
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
No - the input value has exactly one output.
The third side is greater than the difference and less than the sum.
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15

36. 6w^2 - w - 15 = 0
A reflection about the origin.
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
3/2 - 5/3
180

37. What is the formula for computing simple interest?
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)
Move the decimal point to the right x places
A = I (1 + rt)
Cd

38. What are the members or elements of a set?
x^(4+7) = x^11
72
The objects within a set.
Move the decimal point to the right x places

39. Length of an arc of a circle?
Even
II
The third side is greater than the difference and less than the sum.
Angle/360 x 2(pi)r

40. 40 < all primes<50
41 - 43 - 47
(n-2) x 180
87.5%
Factors are few - multiples are many.

41. T or F? Given d -e &f =/ 0 - [(d^3)e(f^5)] / 2d(e^3) / [3(d^2)(e^3)(f^7)] / [6(e^5)(f^2)]?
The set of output values for a function.
41 - 43 - 47
A subset.
True

42. Formula to find a circle'S circumference from its diameter?
An isosceles right triangle.
C = (pi)d
70
All numbers multiples of 1.

43. 3/8 in percent?
A tangent is a line that only touches one point on the circumference of a circle.
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
3
37.5%

44. What are the integers?
All numbers multiples of 1.
IV
The longest arc between points A and B on a circle'S diameter.
(amount of increase/original price) x 100%

45. What is an arc of a circle?
1.0843 X 10^11
180 degrees
An arc is a portion of a circumference of a circle.
67 - 71 - 73

46. Factor a^2 + 2ab + b^2
(a + b)^2
The point of intersection of the systems.
A reflection about the axis.
The two xes after factoring.

47. 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?
1/a^6
2.592 kg
The point of intersection of the systems.
Arc length = (n/360) x pi(2r) where n is the number of degrees.

48. 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...
6
The direction of the inequality is reversed.
The empty set - denoted by a circle with a diagonal through it.

49. (x^2)^4
10
An arc is a portion of a circumference of a circle.
x^(2(4)) =x^8 = (x^4)^2
Part = Percent X Whole

50. Legs 5 - 12. Hypotenuse?
A subset.
1 & 37/132
13
(p + q)/5