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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 'union' of A and B?
The set of elements which can be found in either A or B.
The interesection of A and B.
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
The point of intersection of the systems.

2. What is the intersection of A and B?
90pi
Angle/360 x (pi)r^2
The set of elements found in both A and B.
3sqrt4

3. Solve the quadratic equation ax^2 + bx + c= 0
An isosceles right triangle.
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
x^(6-3) = x^3
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a

4. x^(-y)=
1/(x^y)
Yes - like radicals can be added/subtracted.
1:sqrt3:2
A reflection about the origin.

5. Volume for a cylinder?
12.5%
The interesection of A and B.
Area of the base X height = (pi)hr^2
The steeper the slope.

6. What are the roots of the quadrinomial x^2 + 2x + 1?
The two xes after factoring.
28. n = 8 - k = 2. n! / k!(n-k)!
0
Undefined

7. What is the common monomial factor in the expression 4(c^3)d - (c^2)(d^2) + 2cd?
A 30-60-90 triangle.
Cd
The set of elements found in both A and B.
Even

8. How many 3-digit positive integers are even and do not contain the digit 4?
An expression with just one term (-6x - 2a^2)
288 (8 9 4)
4096
The second graph is less steep.

9. What is the ratio of the surface area of a cube with an edge of 10 to the surface area of a rectangular solid with dimensions 2 - 4 - and 6?
75:11
Ax^2 + bx + c where a -b and c are constants and a /=0
41 - 43 - 47
2.592 kg

10. 1/6 in percent?
16.6666%
An infinite set.
1
The direction of the inequality is reversed.

11. Suppose you have a set of n objects - and you want to select k of them - but the order doesn'T matter. What formula do you use to determine the number of combinations of n objects taken k at a time?
10! / 3!(10-3)! = 120
28. n = 8 - k = 2. n! / k!(n-k)!
1
N! / (k!)(n-k)!

12. 1:1:sqrt2 is the ratio of the sides of what kind of triangle?
1.7
A reflection about the axis.
An isosceles right triangle.
(amount of decrease/original price) x 100%

13. a^2 - 2ab + b^2
Arc length = (n/360) x pi(2r) where n is the number of degrees.
3/2 - 5/3
(a - b)^2
From northeast - counterclockwise. I - II - III - IV

14. 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?
(a - b)^2
23 - 29
A set with no members - denoted by a circle with a diagonal through it.
N! / (n-k)!

15. What does the graph x^2 + y^2 = 64 look like?
A circle centered on the origin with radius 8.
Arc length = (n/360) x pi(2r) where n is the number of degrees.
2.592 kg
27^(-4)

16. 70 < all primes< 80
All numbers multiples of 1.
0
71 - 73 - 79
6

17. From a box of 12 candles - you are to remove 5. How many different sets of 5 candles could you remove?
An angle which is supplementary to an interior angle.
x^(6-3) = x^3
12! / 5!7! = 792
48

18. What does scientific notation mean?
A = pi(r^2)
The two xes after factoring.
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
III

19. 2sqrt4 + sqrt4 =
3
A grouping of the members within a set based on a shared characteristic.
3sqrt4
An arc is a portion of a circumference of a circle.

20. What are the smallest three prime numbers greater than 65?
Its negative reciprocal. (-b/a)
x^(4+7) = x^11
67 - 71 - 73
Relationship cannot be determined (what if x is negative?)

21. What is a finite set?
The set of elements found in both A and B.
A set with a number of elements which can be counted.
90pi
An angle which is supplementary to an interior angle.

22. What number between 70 & 75 - inclusive - has the greatest number of factors?
72
27^(-4)
Two equal sides and two equal angles.
5 OR -5

23. Which is greater? 64^5 or 16^8
52
The sum of its digits is divisible by 3.
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.

24. Pi is a ratio of what to what?

25. Can you subtract 3sqrt4 from sqrt4?
Yes - like radicals can be added/subtracted.
True
The shortest arc between points A and B on a circle'S diameter.
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)

26. a^0 =
441000 = 1 10 10 10 21 * 21
1
288 (8 9 4)
The second graph is less steep.

27. The objects in a set are called two names:
Cd
Members or elements
C = (pi)d
x(x - y + 1)

28. A number is divisible by 4 is...
An expression with just one term (-6x - 2a^2)
1:sqrt3:2
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
Its last two digits are divisible by 4.

29. What is the graph of f(x) shifted upward c units or spaces?
72
N! / (n-k)!
F(x) + c
413.03 / 10^4 (move the decimal point 4 places to the left)

30. A number is divisible by 3 if ...
4.25 - 6 - 22
The objects within a set.
The sum of its digits is divisible by 3.
A reflection about the origin.

31. 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
A set with a number of elements which can be counted.
180 degrees
72

32. Legs 5 - 12. Hypotenuse?
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
13
x^(2(4)) =x^8 = (x^4)^2
4.25 - 6 - 22

33. How to find the diagonal of a rectangular solid?
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
II
10! / 3!(10-3)! = 120
A = I (1 + rt)

34. 200 <_ x <_ 300. How many values of x are divisible by 5 & 8?
3
Area of the base X height = (pi)hr^2
75:11
10

35. Write 10 -843 X 10^7 in scientific notation
1
Sector area = (n/360) X (pi)r^2
An angle which is supplementary to an interior angle.
1.0843 X 10^11

36. What is the 'Solution' for a system of linear equations?
The curve opens downward and the vertex is the maximum point on the graph.
The union of A and B.
y = 2x^2 - 3
The point of intersection of the systems.

37. What is a chord of a circle?
7 / 1000
Undefined
A chord is a line segment joining two points on a circle.
Divide by 100.

38. Formula of rectangle where l increases by 20% and w decreases by 20%
Yes - like radicals can be added/subtracted.
10! / (10-3)! = 720
1
x= (1.2)(.8)lw

39. What are the real numbers?
A reflection about the origin.
Its negative reciprocal. (-b/a)
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)
The steeper the slope.

40. What is the name for a grouping of the members within a set based on a shared characteristic?
1
The union of A and B.
A subset.
0

41. x^2 = 9. What is the value of x?
N! / (k!)(n-k)!
x= (1.2)(.8)lw
An infinite set.
3 - -3

42. Describe the relationship between the graphs of x^2 and (1/2)x^2
A central angle is an angle formed by 2 radii.
The interesection of A and B.
The second graph is less steep.
(p + q)/5

43. Simplify the expression (p^2 - q^2)/ -5(q - p)
The curve opens upward and the vertex is the minimal point on the graph.
I
Angle/360 x 2(pi)r
(p + q)/5

44. 1/2 divided by 3/7 is the same as
A grouping of the members within a set based on a shared characteristic.
1/2 times 7/3
(b + c)
x^(4+7) = x^11

45. What is the set of elements which can be found in either A or B?
The union of A and B.
Sqrt 12
(a + b)^2
Divide by 100.

46. A cylinder has surface area 22pi. If the cylinder has a height of 10 - what is its radius?
10! / 3!(10-3)! = 120
3sqrt4
1
27^(-4)

47. What is the ratio of the sides of a 30-60-90 triangle?
The union of A and B.
The set of elements which can be found in either A or B.
1:sqrt3:2
A grouping of the members within a set based on a shared characteristic.

48. What are complementary angles?
III
Two angles whose sum is 90.
441000 = 1 10 10 10 21 * 21
Relationship cannot be determined (what if x is negative?)

49. What is a central angle?
A central angle is an angle formed by 2 radii.
4725
8
1

50. 1/8 in percent?
All numbers multiples of 1.
1
12! / 5!7! = 792
12.5%