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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. Whats the difference between factors and multiples?
288 (8 9 4)
Factors are few - multiples are many.
55%
No - the input value has exactly one output.

2. There are 10 finalists for the school spelling bee. A first - second - and third place trophy will be awarded. How many different people can get the three prizes?
10! / 3!(10-3)! = 120
An angle which is supplementary to an interior angle.
No - the input value has exactly one output.
An algebraic expression is a combination of one of more terms. Terms in an expression are separated by either addition or subtraction signs. (3xy - 4ab - -5cd - x^2 + x - 1)

3. 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)]?
Two angles whose sum is 90.
The longest arc between points A and B on a circle'S diameter.
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
True

4. 6w^2 - w - 15 = 0
13
23 - 29
Area of the base X height = (pi)hr^2
3/2 - 5/3

5. 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)
x= (1.2)(.8)lw
... the square of the ratios of the corresponding sides.
Part = Percent X Whole
4.25 - 6 - 22

6. Max and Min lengths for a side of a triangle?
10
90 degrees
The third side is greater than the difference and less than the sum.
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.

7. Area of a triangle?
4725
The objects within a set.
37.5%
(base*height) / 2

8. What number between 70 & 75 - inclusive - has the greatest number of factors?
A subset.
Two angles whose sum is 180.
72
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)

9. 5x^2 - 35x -55 = 0
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
Two angles whose sum is 180.
An angle which is supplementary to an interior angle.
G(x) = {x}

10. For similar triangles - the ratio of their corresponding sides is 2:3. What is the ratio of their areas?
The second graph is less steep.
62.5%
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
53 - 59

11. Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
A 30-60-90 triangle.
52
61 - 67
2^9 / 2 = 256

12. The objects in a set are called two names:
x(x - y + 1)
Members or elements
2sqrt6
The empty set - denoted by a circle with a diagonal through it.

13. What is it called when a point is reflected to the quadrant opposite it (i.e. I to III or II to IV)?
A reflection about the origin.
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
70
From northeast - counterclockwise. I - II - III - IV

14. How to determine percent increase?
(amount of increase/original price) x 100%
Two angles whose sum is 180.
2
Its negative reciprocal. (-b/a)

15. 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?
$3 -500 in the 9% and $2 -500 in the 7%.
Lies opposite the greater angle
Indeterminable.
Yes. [i.e. f(x) = x^2 - 1

16. 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?
N! / (k!)(n-k)!
288 (8 9 4)
90 degrees
G(x) = {x}

17. Which quandrant is the lower right hand?
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)
A 30-60-90 triangle.
Yes. [i.e. f(x) = x^2 - 1
IV

18. 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.
A = I (1 + rt)
(a - b)(a + b)
10
90 degrees

19. (6sqrt3) x (2sqrt5) =
6
No - the input value has exactly one output.
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
Angle/360 x (pi)r^2

20. What transformation occurs if point C is reflected over the x-axis and then the y-axis?
4725
Its divisible by 2 and by 3.
A reflection about the axis.
An isosceles right triangle.

21. (-1)^3 =
1
41 - 43 - 47
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
A circle centered at -2 - -2 with radius 3.

22. When does a function automatically have a restricted domain (2)?
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
11 - 13 - 17 - 19
5

23. What are complementary angles?
55%
Two angles whose sum is 90.
1:1:sqrt2
The longest arc between points A and B on a circle'S diameter.

24. If 10800 is invested at a simple interest rate of 4% - what is the value of the investment after 18 months?
61 - 67
$11 -448
1/a^6
3/2 - 5/3

25. 1/8 in percent?
The overlapping sections.
Sector area = (n/360) X (pi)r^2
12.5%
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]

26. The ratio of the areas of two similar polygons is ...
... the square of the ratios of the corresponding sides.
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
(amount of increase/original price) x 100%
83.333%

27. What is the set of elements which can be found in either A or B?
9 & 6/7
Part = Percent X Whole
The union of A and B.
II

28. What is the coefficient of the x^2 term in the product of (x + 1)(x + 2)(x -1)?
2
Its negative reciprocal. (-b/a)
An algebraic expression is a combination of one of more terms. Terms in an expression are separated by either addition or subtraction signs. (3xy - 4ab - -5cd - x^2 + x - 1)
An infinite set.

29. A number is divisible by 6 if...
The point of intersection of the systems.
Its divisible by 2 and by 3.
23 - 29
13pi / 2

30. 2sqrt4 + sqrt4 =
Yes. [i.e. f(x) = x^2 - 1
The set of elements which can be found in either A or B.
A chord is a line segment joining two points on a circle.
3sqrt4

31. Legs 5 - 12. Hypotenuse?
13
The greatest value minus the smallest.
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
72

32. 70 < all primes< 80
37.5%
71 - 73 - 79
1 & 37/132
48

33. Evaluate (4^3)^2
F(x) - c
4096
0
From northeast - counterclockwise. I - II - III - IV

34. The perimeter of a square is 48 inches. The length of its diagonal is:
12sqrt2
2
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
The shortest arc between points A and B on a circle'S diameter.

35. Define a 'Term' -
180
20.5
A set with a number of elements which can be counted.
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)

36. x^6 / x^3
55%
2 & 3/7
No - only like radicals can be added.
x^(6-3) = x^3

37. Evaluate 4/11 + 11/12
1 & 37/132
The greatest value minus the smallest.
288 (8 9 4)
1

38. There are 10 finalists for the school spelling bee. A first - second - and third place trophy will be awarded. In how many ways can the judges award the 3 prizes?
13
y = 2x^2 - 3
3sqrt4
10! / (10-3)! = 720

39. 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).
1.7
A 30-60-90 triangle.
(a - b)(a + b)

40. In similar hexagons - the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
4:5
10! / 3!(10-3)! = 120
71 - 73 - 79
N! / (k!)(n-k)!

41. (-1)^2 =
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)
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
6
1

42. Factor a^2 + 2ab + b^2
4096
(a + b)^2
10! / (10-3)! = 720
27^(-4)

43. a^2 - b^2 =
10
83.333%
(a - b)(a + b)
II

44. What is the 'Range' of a series of numbers?
The greatest value minus the smallest.
Angle/360 x (pi)r^2
90
0

45. How many multiples does a given number have?
Infinite.
(a + b)^2
The third side is greater than the difference and less than the sum.
23 - 29

46. What is the side length of an equilateral triangle with altitude 6?
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
Pi is the ratio of a circle'S circumference to its diameter.
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...
The greatest value minus the smallest.

47. 40 < all primes<50
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
An algebraic expression is a combination of one of more terms. Terms in an expression are separated by either addition or subtraction signs. (3xy - 4ab - -5cd - x^2 + x - 1)
1:sqrt3:2
41 - 43 - 47

48. What is the set of elements found in both A and B?
An arc is a portion of a circumference of a circle.
N! / (k!)(n-k)!
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
The interesection of A and B.

49. What is the slope of a horizontal line?
0
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
(amount of decrease/original price) x 100%
... the square of the ratios of the corresponding sides.

50. What is the order of operations?
72
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
The sum of digits is divisible by 9.
A = pi(r^2)