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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. What are the smallest three prime numbers greater than 65?
Its last two digits are divisible by 4.
Two angles whose sum is 180.
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
67 - 71 - 73

2. How to determine percent decrease?
Diameter(Pi)
(amount of decrease/original price) x 100%
A central angle is an angle formed by 2 radii.
An arc is a portion of a circumference of a circle.

3. x^6 / x^3
83.333%
x^(6-3) = x^3
From northeast - counterclockwise. I - II - III - IV
An isosceles right triangle.

4. What is a major arc?

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5. Which is greater? 200x^295 or 10x^294?
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
Relationship cannot be determined (what if x is negative?)
Cd
F(x + c)

6. P and r are factors of 100. What is greater - pr or 100?
The set of input values for a function.
Indeterminable.
Ax^2 + bx + c where a -b and c are constants and a /=0
6 : 1 : 2

7. Define a 'monomial'
Area of the base X height = (pi)hr^2
53 - 59
180 degrees
An expression with just one term (-6x - 2a^2)

8. 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?
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
N! / (n-k)!
The point of intersection of the systems.
The set of input values for a function.

9. What is a finite set?
67 - 71 - 73
3
Diameter(Pi)
A set with a number of elements which can be counted.

10. Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
2^9 / 2 = 256
41 - 43 - 47
(b + c)
N! / (n-k)!

11. a^2 + 2ab + b^2
(a + b)^2
Sector area = (n/360) X (pi)r^2
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
Two equal sides and two equal angles.

12. Can you subtract 3sqrt4 from sqrt4?
Yes - like radicals can be added/subtracted.
4725
x(x - y + 1)
F(x) + c

13. What are 'Supplementary angles?'
Two angles whose sum is 180.
A grouping of the members within a set based on a shared characteristic.
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
Its divisible by 2 and by 3.

14. 20<all primes<30
23 - 29
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
Undefined

15. 8.84 / 5.2
1.7
All numbers multiples of 1.
2 & 3/7
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

16. (-1)^3 =
Yes. [i.e. f(x) = x^2 - 1
6
1
10

17. 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
5
The empty set - denoted by a circle with a diagonal through it.
The curve opens downward and the vertex is the maximum point on the graph.

18. 1/2 divided by 3/7 is the same as
2(pi)r^2 + 2(pi)rh
48
No - the input value has exactly one output.
1/2 times 7/3

19. 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.
The set of output values for a function.
12sqrt2
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)

20. Write 10 -843 X 10^7 in scientific notation
3/2 - 5/3
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
1.0843 X 10^11
7 / 1000

21. 70 < all primes< 80
71 - 73 - 79
(base*height) / 2
An angle which is supplementary to an interior angle.
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.

22. What is the surface area of a cylinder with radius 5 and height 8?
4725
130pi
12! / 5!7! = 792
(a + b)^2

23. A number is divisible by 6 if...
A grouping of the members within a set based on a shared characteristic.
(a + b)^2
1
Its divisible by 2 and by 3.

24. Evaluate 4/11 + 11/12
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
1 & 37/132
(b + c)
y = (x + 5)/2

25. Max and Min lengths for a side of a triangle?
A = pi(r^2)
The sum of digits is divisible by 9.
...multiply by 100.
The third side is greater than the difference and less than the sum.

26. What is the slope of a vertical line?

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27. The slope of a line perpendicular to (a/b)?
3
11 - 13 - 17 - 19
90pi
Its negative reciprocal. (-b/a)

28. (a^-1)/a^5
90pi
1/a^6
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
90 degrees

29. What is the side length of an equilateral triangle with altitude 6?
Relationship cannot be determined (what if x is negative?)
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...
1:sqrt3:2
2^9 / 2 = 256

30. What is the order of operations?
The set of input values for a function.
The curve opens downward and the vertex is the maximum point on the graph.
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
Two angles whose sum is 180.

31. What is the ratio of the sides of an isosceles right triangle?
61 - 67
C = (pi)d
1:1:sqrt2
180

32. What is the area of a regular hexagon with side 6?
72
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
A 30-60-90 triangle.

33. (-1)^2 =
18
1
The sum of digits is divisible by 9.
3/2 - 5/3

34. How many multiples does a given number have?
Infinite.
41 - 43 - 47
61 - 67
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]

35. In a triangle inscribed inside a circle - where the diameter is one side of the triangle - which angle is largest?
Indeterminable.
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
0
Members or elements

36. 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))?
20.5
3
11 - 13 - 17 - 19
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a

37. a^0 =
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
1
Its divisible by 2 and by 3.
Undefined - because we can'T divide by 0.

38. A number is divisible by 9 if...
28. n = 8 - k = 2. n! / k!(n-k)!
No - only like radicals can be added.
III
The sum of digits is divisible by 9.

39. The perimeter of a square is 48 inches. The length of its diagonal is:
Move the decimal point to the right x places
Indeterminable.
5 OR -5
12sqrt2

40. Can you add sqrt 3 and sqrt 5?
No - only like radicals can be added.
Yes. [i.e. f(x) = x^2 - 1
Move the decimal point to the right x places
The longest arc between points A and B on a circle'S diameter.

41. 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?
The overlapping sections.
G(x) = {x}
48
The set of elements found in both A and B.

42. A cylinder has surface area 22pi. If the cylinder has a height of 10 - what is its radius?
12sqrt2
Arc length = (n/360) x pi(2r) where n is the number of degrees.
1
1/(x^y)

43. Which quadrant is the lower left hand?
75:11
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
III

44. What is a piecewise equation?
13pi / 2
The set of elements found in both A and B.
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
Pi is the ratio of a circle'S circumference to its diameter.

45. Which is greater? 64^5 or 16^8
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
The empty set - denoted by a circle with a diagonal through it.
The set of elements found in both A and B.
28. n = 8 - k = 2. n! / k!(n-k)!

46. In a regular polygon with n sides - the formula for the sum of interior angles
2^9 / 2 = 256
1.7
(amount of decrease/original price) x 100%
(n-2) x 180

47. How to find the circumference of a circle which circumscribes a square?
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
(a + b)^2
Yes - like radicals can be added/subtracted.
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...

48. sqrt 2(sqrt 6)=
Pi is the ratio of a circle'S circumference to its diameter.
2.592 kg
Sqrt 12
.0004809 X 10^11

49. Pi is a ratio of what to what?

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50. What is the 'Restricted domain of a function'?
F(x) - c
When the function is not defined for all real numbers -; only a subset of the real numbers.
4a^2(b)
N! / (n-k)!