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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 empty set?
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
2(pi)r^2 + 2(pi)rh
A set with no members - denoted by a circle with a diagonal through it.
83.333%

2. 6w^2 - w - 15 = 0
Two equal sides and two equal angles.
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)
3/2 - 5/3
4096

3. Simplify (a^2 + b)^2 - (a^2 - b)^2
4a^2(b)
C = (pi)d
52
From northeast - counterclockwise. I - II - III - IV

4. 60 < all primes <70
$3 -500 in the 9% and $2 -500 in the 7%.
4:5
61 - 67
The shortest arc between points A and B on a circle'S diameter.

5. 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)!
11 - 13 - 17 - 19
A chord is a line segment joining two points on a circle.
F(x + c)

6. How to determine percent increase?
55%
2.592 kg
9 : 25
(amount of increase/original price) x 100%

7. Formula to calculate arc length?
A set with a number of elements which can be counted.
Arc length = (n/360) x pi(2r) where n is the number of degrees.
62.5%
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)

8. What is a piecewise equation?
(a - b)^2
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
0
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

9. Formula of rectangle where l increases by 20% and w decreases by 20%
x= (1.2)(.8)lw
N! / (k!)(n-k)!
(a + b)^2
9 & 6/7

10. Simplify the expression (p^2 - q^2)/ -5(q - p)
The set of elements which can be found in either A or B.
(p + q)/5
52
6

11. The ratio of the areas of two similar polygons is ...
N! / (k!)(n-k)!
The sum of its digits is divisible by 3.
... the square of the ratios of the corresponding sides.
The set of input values for a function.

12. What is the formula for computing simple interest?
130pi
10! / (10-3)! = 720
70
A = I (1 + rt)

13. A number is divisible by 4 is...
$3 -500 in the 9% and $2 -500 in the 7%.
Its last two digits are divisible by 4.
8
6

14. Find the surface area of a cylinder with radius 3 and height 12.
The sum of its digits is divisible by 3.
500
90pi
61 - 67

15. 20<all primes<30
Its last two digits are divisible by 4.
A = I (1 + rt)
71 - 73 - 79
23 - 29

16. How many digits are there between the decimal point and the first even digit in the decimal equivalent of 1/[(2^8)(5^3)]
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
(a + b)^2
$11 -448
0

17. What is the percent formula?
Undefined - because we can'T divide by 0.
x= (1.2)(.8)lw
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
Part = Percent X Whole

18. What is a minor arc?

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19. 1:sqrt3:2 is the ratio of the sides of what kind of triangle?
9 : 25
6
A 30-60-90 triangle.
The union of A and B.

20. What is the area of a regular hexagon with side 6?
2
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
2(pi)r^2 + 2(pi)rh
An isosceles right triangle.

21. What does the graph (x+2)^2 + (y+2)^2 = 9 look like?
A circle centered at -2 - -2 with radius 3.
1:sqrt3:2
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.
1/(x^y)

22. How to determine percent decrease?
A set with a number of elements which can be counted.
(amount of increase/original price) x 100%
Move the decimal point to the right x places
(amount of decrease/original price) x 100%

23. 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?
9 : 25
16.6666%
An arc is a portion of a circumference of a circle.
2^9 / 2 = 256

24. Can you simplify sqrt72?
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
An arc is a portion of a circumference of a circle.
True
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.

25. The perimeter of a square is 48 inches. The length of its diagonal is:
(a - b)^2
1
The objects within a set.
12sqrt2

26. 1/2 divided by 3/7 is the same as
441000 = 1 10 10 10 21 * 21
1/2 times 7/3
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
4.25 - 6 - 22

27. Order of quadrants:
Move the decimal point to the right x places
From northeast - counterclockwise. I - II - III - IV
An infinite set.
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)

28. x^6 / x^3
x^(6-3) = x^3
A = pi(r^2)
Lies opposite the greater angle
Pi is the ratio of a circle'S circumference to its diameter.

29. a^2 - b^2
.0004809 X 10^11
(a - b)(a + b)
A reflection about the axis.
9 : 25

30. What is a finite set?
The greatest value minus the smallest.
A = pi(r^2)
A set with a number of elements which can be counted.
71 - 73 - 79

31. Which quadrant is the upper left hand?
Cd
Infinite.
II
1

32. Which quadrant is the lower left hand?
180
...multiply by 100.
The curve opens downward and the vertex is the maximum point on the graph.
III

33. 40 < all primes<50
...multiply by 100.
41 - 43 - 47
3 - -3
The empty set - denoted by a circle with a diagonal through it.

34. 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?
y = (x + 5)/2
10! / (10-3)! = 720
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

35. 5x^2 - 35x -55 = 0
C = (pi)d
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
No - only like radicals can be added.

36. What is the 'domain' of a function?
Area of the base X height = (pi)hr^2
The set of input values for a function.
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
1/a^6

37. Length of an arc of a circle?
10! / (10-3)! = 720
6
A 30-60-90 triangle.
Angle/360 x 2(pi)r

38. Define a 'Term' -
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)
62.5%
31 - 37
(12/2) x (sqrt15 / sqrt5) = 6sqrt3

39. What is an exterior angle?
An infinite set.
Relationship cannot be determined (what if x is negative?)
An angle which is supplementary to an interior angle.
70

40. Pi is a ratio of what to what?

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41. What are the smallest three prime numbers greater than 65?
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
67 - 71 - 73
A circle centered at -2 - -2 with radius 3.
10! / 3!(10-3)! = 120

42. What is the intersection of A and B?
An expression with just one term (-6x - 2a^2)
Lies opposite the greater angle
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
The set of elements found in both A and B.

43. What is a subset?
An expression with just one term (-6x - 2a^2)
A grouping of the members within a set based on a shared characteristic.
Cd
(a + b)^2

44. Evaluate 4/11 + 11/12
1 & 37/132
The interesection of A and B.
2(pi)r^2 + 2(pi)rh
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...

45. Which is greater? 64^5 or 16^8
Its negative reciprocal. (-b/a)
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
The sum of digits is divisible by 9.

46. What are the real numbers?
G(x) = {x}
6 : 1 : 2
Factors are few - multiples are many.
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)

47. To convert a decimal to a percent...
37.5%
...multiply by 100.
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
9 & 6/7

48. For similar triangles - the ratio of their corresponding sides is 2:3. What is the ratio of their areas?
Area of the base X height = (pi)hr^2
2 & 3/7
N! / (n-k)!
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.

49. a^2 - b^2 =
x^(6-3) = x^3
Two angles whose sum is 180.
180
(a - b)(a + b)

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?
13
Two angles whose sum is 180.
3
2.592 kg