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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 an arc of a circle?
3
An arc is a portion of a circumference of a circle.
4096
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.

2. What is the percent formula?
2(pi)r^2 + 2(pi)rh
An arc is a portion of a circumference of a circle.
Part = Percent X Whole
4096

3. To multiply a number by 10^x
83.333%
1
Angle/360 x (pi)r^2
Move the decimal point to the right x places

4. If an inequality is multiplied or divided by a negative number....
0
(a - b)^2
N! / (k!)(n-k)!
The direction of the inequality is reversed.

5. Legs 5 - 12. Hypotenuse?
6
A tangent is a line that only touches one point on the circumference of a circle.
13
(a - b)(a + b)

6. What are the real numbers?
When the function is not defined for all real numbers -; only a subset of the real numbers.
Divide by 100.
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)
55%

7. A number is divisible by 9 if...
Ax^2 + bx + c where a -b and c are constants and a /=0
Sector area = (n/360) X (pi)r^2
The sum of digits is divisible by 9.
Area of the base X height = (pi)hr^2

8. In a triangle inscribed inside a circle - where the diameter is one side of the triangle - which angle is largest?
Even
70
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
62.5%

9. 1/6 in percent?
16.6666%
No - only like radicals can be added.
10! / (10-3)! = 720
413.03 / 10^4 (move the decimal point 4 places to the left)

10. What is the graph of f(x) shifted left c units or spaces?
(b + c)
3/2 - 5/3
1
F(x + c)

11. a^2 - b^2
An angle which is supplementary to an interior angle.
(a - b)(a + b)
The set of output values for a function.
The set of elements which can be found in either A or B.

12. 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)
Lies opposite the greater angle
4.25 - 6 - 22
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
1/a^6

13. Can you simplify sqrt72?
$3 -500 in the 9% and $2 -500 in the 7%.
Two angles whose sum is 90.
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
16.6666%

14. (-1)^2 =
0
Pi is the ratio of a circle'S circumference to its diameter.
1
87.5%

15. To convert a decimal to a percent...
...multiply by 100.
83.333%
An isosceles right triangle.
4096

16. The perimeter of a square is 48 inches. The length of its diagonal is:
3
12sqrt2
A set with a number of elements which can be counted.
Area of the base X height = (pi)hr^2

17. What is the third quartile of the following data set: 44 - 58 - 63 - 63 - 68 - 70 - 82
.0004809 X 10^11
0
70
1

18. Evaluate (4^3)^2
1/a^6
4096
A tangent is a line that only touches one point on the circumference of a circle.
3sqrt4

19. What is the 'Restricted domain of a function'?
The direction of the inequality is reversed.
1
When the function is not defined for all real numbers -; only a subset of the real numbers.
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.

20. Pi is a ratio of what to what?

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21. What is the set of elements found in both A and B?
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
The sum of its digits is divisible by 3.
70
The interesection of A and B.

22. What number between 70 & 75 - inclusive - has the greatest number of factors?
72
2
Its last two digits are divisible by 4.
4096

23. If 8 schools are in a conference - how many games are played if each team plays each other exactly once?
$11 -448
28. n = 8 - k = 2. n! / k!(n-k)!
A grouping of the members within a set based on a shared characteristic.
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).

24. What is the graph of f(x) shifted downward c units or spaces?
Its negative reciprocal. (-b/a)
4096
F(x) - c
x^(6-3) = x^3

25. 200 <_ x <_ 300. How many values of x are divisible by 5 & 8?
3
A circle centered at -2 - -2 with radius 3.
53 - 59
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.

26. What is the 'domain' of a function?
Relationship cannot be determined (what if x is negative?)
The set of input values for a function.
1:1:sqrt2
Yes - like radicals can be added/subtracted.

27. What are the smallest three prime numbers greater than 65?
The union of A and B.
1.0843 X 10^11
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
67 - 71 - 73

28. Convert 0.7% to a fraction.
413.03 / 10^4 (move the decimal point 4 places to the left)
No - the input value has exactly one output.
7 / 1000
1

29. 50 < all primes< 60
Two equal sides and two equal angles.
53 - 59
5
31 - 37

30. When the 'a' in the parabola is negative...
The curve opens downward and the vertex is the maximum point on the graph.
31 - 37
Angle/360 x (pi)r^2
180

31. 0^0
1
Angle/360 x 2(pi)r
Undefined
Divide by 100.

32. What percent of 40 is 22?
55%
Even
10! / (10-3)! = 720
A term is a numerical constant or the product (or quotient) of a numerical constant and one or more variables. (3x - 4x^2 and 2a/c)

33. When does a function automatically have a restricted domain (2)?
y = (x + 5)/2
1:1:sqrt2
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
The two xes after factoring.

34. Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
441000 = 1 10 10 10 21 * 21
3
Yes - like radicals can be added/subtracted.
2sqrt6

35. 1/2 divided by 3/7 is the same as
$3 -500 in the 9% and $2 -500 in the 7%.
.0004809 X 10^11
1/a^6
1/2 times 7/3

36. Can the input value of a function have more than one output value (i.e. x: y - y1)?
No - the input value has exactly one output.
10! / 3!(10-3)! = 120
The longest arc between points A and B on a circle'S diameter.
10

37. Evaluate 3& 2/7 / 1/3
9 & 6/7
Area of the base X height = (pi)hr^2
83.333%
2sqrt6

38. 3/8 in percent?
37.5%
$11 -448
2
Diameter(Pi)

39. Which is greater? 27^(-4) or 9^(-8)
27^(-4)
6
1
71 - 73 - 79

40. 413.03 x 10^(-4) =
413.03 / 10^4 (move the decimal point 4 places to the left)
The set of input values for a function.
Move the decimal point to the right x places
3

41. What is the graph of f(x) shifted upward c units or spaces?
Relationship cannot be determined (what if x is negative?)
x^(6-3) = x^3
4725
F(x) + c

42. What are complementary angles?
7 / 1000
Two angles whose sum is 90.
$11 -448
When the function is not defined for all real numbers -; only a subset of the real numbers.

43. Factor x^2 - xy + x.
x(x - y + 1)
Area of the base X height = (pi)hr^2
F(x) + c
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)

44. What is the name of set with a number of elements which cannot be counted?
An infinite set.
11 - 13 - 17 - 19
The greatest value minus the smallest.
The union of A and B.

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?
The longest arc between points A and B on a circle'S diameter.
$3 -500 in the 9% and $2 -500 in the 7%.
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
Indeterminable.

46. P and r are factors of 100. What is greater - pr or 100?
130pi
Indeterminable.
4:5
An isosceles right triangle.

47. (a^-1)/a^5
(a + b)^2
1/a^6
18
x^(4+7) = x^11

48. 30< all primes<40
31 - 37
1
20.5
70

49. 1:1:sqrt2 is the ratio of the sides of what kind of triangle?
The set of elements which can be found in either A or B.
An isosceles right triangle.
90pi
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...

50. Ratio of ages of Anna and Emma is 3:5 and of Emma and Nicolas is 3:5. What is the ratio of Anna to Nicholas' ages?
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
9 : 25
Triangles with same measure and same side lengths.
1/a^6