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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. 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?
75:11
N! / (n-k)!
180 degrees
Factors are few - multiples are many.

2. What is the name of set with a number of elements which cannot be counted?
Members or elements
An infinite set.
(a - b)^2
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.

3. What is the slope of a vertical line?

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4. What is the area of a regular hexagon with side 6?
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
Angle/360 x (pi)r^2
x^(2(4)) =x^8 = (x^4)^2
7 / 1000

5. 4.809 X 10^7 =
4725
Arc length = (n/360) x pi(2r) where n is the number of degrees.
37.5%
.0004809 X 10^11

6. What is the graph of f(x) shifted right c units or spaces?
62.5%
1.0843 X 10^11
F(x-c)
No - only like radicals can be added.

7. From a box of 12 candles - you are to remove 5. How many different sets of 5 candles could you remove?
Sector area = (n/360) X (pi)r^2
12! / 5!7! = 792
1.7
130pi

8. 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
The longest arc between points A and B on a circle'S diameter.
12sqrt2
0

9. 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 curve opens downward and the vertex is the maximum point on the graph.
13pi / 2
48
3/2 - 5/3

10. What is the ratio of the sides of an isosceles right triangle?
The sum of digits is divisible by 9.
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
1:1:sqrt2
The interesection of A and B.

11. What is the graph of f(x) shifted upward c units or spaces?
Members or elements
F(x) + c
6
When the function is not defined for all real numbers -; only a subset of the real numbers.

12. 8.84 / 5.2
The second graph is less steep.
1.7
I
Yes. [i.e. f(x) = x^2 - 1

13. What are congruent triangles?
Triangles with same measure and same side lengths.
1/2 times 7/3
52
4:5

14. 60 < all primes <70
The point of intersection of the systems.
2
A reflection about the origin.
61 - 67

15. What is the 'union' of A and B?
0
The set of elements which can be found in either A or B.
The curve opens upward and the vertex is the minimal point on the graph.
72

16. 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
10! / (10-3)! = 720
18
10
C = 2(pi)r

17. Formula for the area of a sector of a circle?
5
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
Sector area = (n/360) X (pi)r^2
The point of intersection of the systems.

18. A number is divisible by 3 if ...
Ax^2 + bx + c where a -b and c are constants and a /=0
The sum of its digits is divisible by 3.
I
61 - 67

19. What is the 'Solution' for a system of linear equations?
x(x - y + 1)
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 sum of its digits is divisible by 3.
The point of intersection of the systems.

20. Solve the quadratic equation ax^2 + bx + c= 0
A chord is a line segment joining two points on a circle.
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
23 - 29

21. For what values should the domain be restricted for the function f(x) = sqrt(x + 8)
Triangles with same measure and same side lengths.
8
75:11
The union of A and B.

22. What are the integers?
.0004809 X 10^11
All numbers multiples of 1.
A set with no members - denoted by a circle with a diagonal through it.
Area of the base X height = (pi)hr^2

23. What is a central angle?
A subset.
An arc is a portion of a circumference of a circle.
9 : 25
A central angle is an angle formed by 2 radii.

24. Can the input value of a function have more than one output value (i.e. x: y - y1)?
II
48
12.5%
No - the input value has exactly one output.

25. If 4500 is invested at a simple interest rate of 6% - what is the value of the investment after 10 months?
23 - 29
83.333%
4725
Cd

26. 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?
(amount of decrease/original price) x 100%
20.5
$3 -500 in the 9% and $2 -500 in the 7%.
.0004809 X 10^11

27. 1/6 in percent?
(base*height) / 2
62.5%
1 & 37/132
16.6666%

28. How to find the area of a sector?
An infinite set.
1/(x^y)
Angle/360 x (pi)r^2
(a + b)^2

29. 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?
y = 2x^2 - 3
The greatest value minus the smallest.
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)
The interesection of A and B.

30. 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)]?
True
6 : 1 : 2
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
Factors are few - multiples are many.

31. Convert 0.7% to a fraction.
Divide by 100.
1
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)
7 / 1000

32. What is the 'Solution' for a set of inequalities.
The overlapping sections.
The third side is greater than the difference and less than the sum.
1/2 times 7/3
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.

33. (x^2)^4
Its negative reciprocal. (-b/a)
An isosceles right triangle.
x^(2(4)) =x^8 = (x^4)^2
83.333%

34. What is an isoceles triangle?
1
Sector area = (n/360) X (pi)r^2
Two equal sides and two equal angles.
7 / 1000

35. Can you simplify sqrt72?
A= I (1 + (r/c))^tC - where I is the investment - C is the number of times compounded annually - and t is the number of years.
True
The third side is greater than the difference and less than the sum.
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.

36. What does scientific notation mean?
No - only like radicals can be added.
A tangent is a line that only touches one point on the circumference of a circle.
3
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.

37. What is the set of elements found in both A and B?
20.5
The interesection of A and B.
Divide by 100.
10! / (10-3)! = 720

38. Max and Min lengths for a side of a triangle?
72
The third side is greater than the difference and less than the sum.
x^(6-3) = x^3
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)

39. Simplify the expression [(b^2 - c^2) / (b - c)]
(b + c)
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
180 degrees
Undefined - because we can'T divide by 0.

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)
A= I (1 + (r/c))^tC - where I is the investment - C is the number of times compounded annually - and t is the number of years.
4.25 - 6 - 22
IV
0

41. 6w^2 - w - 15 = 0
(a + b)^2
(a - b)(a + b)
3/2 - 5/3
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)

42. Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14
288 (8 9 4)
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
Two angles whose sum is 180.
2 & 3/7

43. 200 <_ x <_ 300. How many values of x are divisible by 5 & 8?
3
Pi is the ratio of a circle'S circumference to its diameter.
An isosceles right triangle.
10! / 3!(10-3)! = 120

44. (a^-1)/a^5
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
1
True
1/a^6

45. What is the set of elements which can be found in either A or B?
4a^2(b)
The union of A and B.
The set of input values for a function.
The steeper the slope.

46. What is the formula for computing simple interest?
A = I (1 + rt)
F(x + c)
.0004809 X 10^11
Move the decimal point to the right x places

47. How many sides does a hexagon have?
Diameter(Pi)
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
6
1.0843 X 10^11

48. What are the rational numbers?
10! / (10-3)! = 720
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
Its divisible by 2 and by 3.
441000 = 1 10 10 10 21 * 21

49. What is the absolute value function?
C = (pi)d
2(pi)r^2 + 2(pi)rh
G(x) = {x}
From northeast - counterclockwise. I - II - III - IV

50. 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
Cd
Move the decimal point to the right x places
2.592 kg