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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 is the common monomial factor in the expression 4(c^3)d - (c^2)(d^2) + 2cd?
55%
Cd
The set of elements which can be found in either A or B.
An expression with just one term (-6x - 2a^2)

2. 10<all primes<20
90pi
Factors are few - multiples are many.
11 - 13 - 17 - 19
1

3. What is the set of elements found in both A and B?
Infinite.
The interesection of A and B.
4a^2(b)
180

4. Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
Arc length = (n/360) x pi(2r) where n is the number of degrees.
(a + b)^2
2^9 / 2 = 256
180 degrees

5. Formula to find a circle'S circumference from its diameter?
Ax^2 + bx + c where a -b and c are constants and a /=0
61 - 67
1
C = (pi)d

6. A number is divisible by 3 if ...
A 30-60-90 triangle.
The sum of its digits is divisible by 3.
13pi / 2
N! / (k!)(n-k)!

7. What is the 'domain' of a function?
The objects within a set.
1/a^6
2^9 / 2 = 256
The set of input values for a function.

8. (x^2)^4
x^(4+7) = x^11
Sector area = (n/360) X (pi)r^2
The interesection of A and B.
x^(2(4)) =x^8 = (x^4)^2

9. What is the third quartile of the following data set: 44 - 58 - 63 - 63 - 68 - 70 - 82
A chord is a line segment joining two points on a circle.
70
The set of elements found in both A and B.
1

10. How many sides does a hexagon have?
Yes - like radicals can be added/subtracted.
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
6
Arc length = (n/360) x pi(2r) where n is the number of degrees.

11. A number is divisible by 6 if...
Its divisible by 2 and by 3.
0
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
Two angles whose sum is 180.

12. 6w^2 - w - 15 = 0
The sum of its digits is divisible by 3.
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
3/2 - 5/3
Relationship cannot be determined (what if x is negative?)

13. What is a set with no members called?
The interesection of A and B.
The empty set - denoted by a circle with a diagonal through it.
F(x) - c
72

14. In similar hexagons - the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
(b + c)
4:5
1
5 OR -5

15. Simplify the expression (p^2 - q^2)/ -5(q - p)
288 (8 9 4)
(p + q)/5
Its negative reciprocal. (-b/a)
A circle centered at -2 - -2 with radius 3.

16. What is the 'union' of A and B?
The set of elements which can be found in either A or B.
(a - b)(a + b)
Diameter(Pi)
0

17. Factor x^2 - xy + x.
1
x(x - y + 1)
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

18. Legs 6 - 8. Hypotenuse?
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
Factors are few - multiples are many.
10
Two angles whose sum is 90.

19. What is it called when a point is reflected to the quadrant opposite it (i.e. I to III or II to IV)?
37.5%
52
90pi
A reflection about the origin.

20. What is the empty set?
The set of input values for a function.
2sqrt6
A set with no members - denoted by a circle with a diagonal through it.
1

21. 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
27^(-4)
500
2^9 / 2 = 256

22. (-1)^3 =
Cd
1
10! / 3!(10-3)! = 120
Yes. [i.e. f(x) = x^2 - 1

23. 413.03 x 10^(-4) =
x(x - y + 1)
x= (1.2)(.8)lw
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
413.03 / 10^4 (move the decimal point 4 places to the left)

24. The perimeter of a square is 48 inches. The length of its diagonal is:
The union of A and B.
2(pi)r^2 + 2(pi)rh
3sqrt4
12sqrt2

25. Legs 5 - 12. Hypotenuse?
Relationship cannot be determined (what if x is negative?)
75:11
13
1/a^6

26. What does the graph x^2 + y^2 = 64 look like?
6 : 1 : 2
A circle centered on the origin with radius 8.
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
180

27. x^2 = 9. What is the value of x?
3 - -3
Its negative reciprocal. (-b/a)
(a - b)(a + b)
90

28. What is the graph of f(x) shifted downward c units or spaces?
F(x) - c
F(x + c)
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/(x^y)

29. If Madagascar'S exports totaled 1.3 billion in 2009 - and 4% came from China - what was the value in millions of the country'S exports to China?
The greatest value minus the smallest.
52
1.7
3/2 - 5/3

30. What is a major arc?

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31. 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^(4+7) = x^11
(amount of decrease/original price) x 100%
Undefined - because we can'T divide by 0.

32. 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?
67 - 71 - 73
The shortest arc between points A and B on a circle'S diameter.
0
y = 2x^2 - 3

33. 200 <_ x <_ 300. How many values of x are divisible by 5 & 8?
3
No - only like radicals can be added.
The set of elements which can be found in either A or B.
1/2 times 7/3

34. 1/2 divided by 3/7 is the same as
288 (8 9 4)
55%
1/2 times 7/3
83.333%

35. 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)
2(pi)r^2 + 2(pi)rh
1
Yes. [i.e. f(x) = x^2 - 1

36. What are the members or elements of a set?
Arc length = (n/360) x pi(2r) where n is the number of degrees.
4096
The objects within a set.
1 & 37/132

37. Find the surface area of a cylinder with radius 3 and height 12.
1
13
10! / (10-3)! = 720
90pi

38. a^0 =
1
A 30-60-90 triangle.
67 - 71 - 73
Divide by 100.

39. Write 10 -843 X 10^7 in scientific notation
1.0843 X 10^11
75:11
Its divisible by 2 and by 3.
A grouping of the members within a set based on a shared characteristic.

40. 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)
4.25 - 6 - 22
A set with a number of elements which can be counted.
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
I

41. x^(-y)=
1/(x^y)
Angle/360 x 2(pi)r
83.333%
52

42. If 4500 is invested at a simple interest rate of 6% - what is the value of the investment after 10 months?
4725
The shortest arc between points A and B on a circle'S diameter.
11 - 13 - 17 - 19
0

43. What is the set of elements which can be found in either A or B?
10! / (10-3)! = 720
6 : 1 : 2
The union of A and B.
27^(-4)

44. 70 < all primes< 80
70
The two xes after factoring.
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
71 - 73 - 79

45. 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?
4096
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
Undefined - because we can'T divide by 0.
$3 -500 in the 9% and $2 -500 in the 7%.

46. What is a chord of a circle?
(n-2) x 180
13
A chord is a line segment joining two points on a circle.
II

47. What number between 70 & 75 - inclusive - has the greatest number of factors?
72
6 : 1 : 2
The curve opens upward and the vertex is the minimal point on the graph.
Yes - like radicals can be added/subtracted.

48. 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).
5 OR -5
The second graph is less steep.
Two angles whose sum is 180.

49. Circumference of a circle?
1 & 37/132
1/2 times 7/3
Diameter(Pi)
(a + b)^2

50. 50 < all primes< 60
53 - 59
Undefined - because we can'T divide by 0.
The shortest arc between points A and B on a circle'S diameter.
12! / 5!7! = 792