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GRE Math: Common Errors

Subjects : gre, math

Instructions:

Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
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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 a set with no members called?
2
No - only like radicals can be added.
A reflection about the axis.
The empty set - denoted by a circle with a diagonal through it.

2. 1/6 in percent?
16.6666%
1.7
2sqrt6
4725

3. Which quadrant is the upper right hand?
Triangles with same measure and same side lengths.
F(x) + c
I
(a + b)^2

4. 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?
A 30-60-90 triangle.
75:11
$3 -500 in the 9% and $2 -500 in the 7%.
The curve opens upward and the vertex is the minimal point on the graph.

5. Which is greater? 64^5 or 16^8
(a + b)^2
A circle centered on the origin with radius 8.
(amount of increase/original price) x 100%
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16

6. Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14
9 : 25
2 & 3/7
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
20.5

7. 2sqrt4 + sqrt4 =
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
4725
3sqrt4
72

8. How many digits are there between the decimal point and the first even digit in the decimal equivalent of 1/[(2^8)(5^3)]
0
Factors are few - multiples are many.
The second graph is less steep.
1.7

9. A triangle is inscribed in a semi circle with legs 5 and 12. What is the circumfermence of the semicircle?
x^(6-3) = x^3
13pi / 2
Factors are few - multiples are many.
10! / (10-3)! = 720

10. (6sqrt3) x (2sqrt5) =
Factors are few - multiples are many.
6
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
The second graph is less steep.

11. What percent of 40 is 22?
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...
55%
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
IV

12. If 8 schools are in a conference - how many games are played if each team plays each other exactly once?
28. n = 8 - k = 2. n! / k!(n-k)!
Infinite.
1
The set of elements found in both A and B.

13. 70 < all primes< 80
Two angles whose sum is 90.
An angle which is supplementary to an interior angle.
18
71 - 73 - 79

14. A number is divisible by 3 if ...
6 : 1 : 2
The sum of its digits is divisible by 3.
All numbers multiples of 1.
Diameter(Pi)

15. Describe the relationship between 3x^2 and 3(x - 1)^2
From northeast - counterclockwise. I - II - III - IV
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
Indeterminable.
F(x + c)

16. Can you simplify sqrt72?
x^(2(4)) =x^8 = (x^4)^2
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
55%
1

17. 60 < all primes <70
Undefined - because we can'T divide by 0.
A grouping of the members within a set based on a shared characteristic.
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
61 - 67

18. (-1)^3 =
1
70
C = 2(pi)r
Divide by 100.

19. What is the name for a grouping of the members within a set based on a shared characteristic?
A subset.
1/a^6
The sum of digits is divisible by 9.
Angle/360 x 2(pi)r

20. To convert a decimal to a percent...
1.7
Factors are few - multiples are many.
10! / 3!(10-3)! = 120
...multiply by 100.

21. What is the formula for compounded interest?
F(x-c)
G(x) = {x}
11 - 13 - 17 - 19
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.

22. 3/8 in percent?
1/a^6
The curve opens downward and the vertex is the maximum point on the graph.
37.5%
The objects within a set.

23. 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))?
2
The empty set - denoted by a circle with a diagonal through it.
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
20.5

24. Find the surface area of a cylinder with radius 3 and height 12.
A chord is a line segment joining two points on a circle.
90pi
4:5
From northeast - counterclockwise. I - II - III - IV

25. Can the input value of a function have more than one output value (i.e. x: y - y1)?
2sqrt6
No - the input value has exactly one output.
A tangent is a line that only touches one point on the circumference of a circle.
Area of the base X height = (pi)hr^2

26. Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
10! / (10-3)! = 720
F(x + c)
75:11
2sqrt6

27. What is the slope of a horizontal line?
0
Part = Percent X Whole
An angle which is supplementary to an interior angle.
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.

28. 8.84 / 5.2
The set of elements which can be found in either A or B.
1.7
C = 2(pi)r
II

29. What is the graph of f(x) shifted upward c units or spaces?
9 & 6/7
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
F(x-c)
F(x) + c

30. x^(-y)=
10! / (10-3)! = 720
A reflection about the origin.
1/(x^y)
Diameter(Pi)

31. The ratio of the areas of two similar polygons is ...
62.5%
... the square of the ratios of the corresponding sides.
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
Arc length = (n/360) x pi(2r) where n is the number of degrees.

32. 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?
A reflection about the origin.
48
F(x) - c
F(x) + c

33. Evaluate 3& 2/7 / 1/3
28. n = 8 - k = 2. n! / k!(n-k)!
1 & 37/132
9 & 6/7
The shortest arc between points A and B on a circle'S diameter.

34. 10^6 has how many zeroes?
72
6
41 - 43 - 47
A 30-60-90 triangle.

35. The objects in a set are called two names:
The third side is greater than the difference and less than the sum.
Members or elements
The set of elements found in both A and B.
2.592 kg

36. What number between 70 & 75 - inclusive - has the greatest number of factors?
1
The greatest value minus the smallest.
72
3sqrt4

37. A cylinder has surface area 22pi. If the cylinder has a height of 10 - what is its radius?
9 & 6/7
1
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)
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.

38. The slope of a line perpendicular to (a/b)?
9 : 25
Factors are few - multiples are many.
y = 2x^2 - 3
Its negative reciprocal. (-b/a)

39. What is the 'Solution' for a system of linear equations?
Angle/360 x 2(pi)r
An angle which is supplementary to an interior angle.
1/a^6
The point of intersection of the systems.

40. Surface area for a cylinder?
500
2(pi)r^2 + 2(pi)rh
90
II

41. How to determine percent increase?
Sector area = (n/360) X (pi)r^2
The interesection of A and B.
8
(amount of increase/original price) x 100%

42. A number is divisible by 9 if...
55%
The sum of digits is divisible by 9.
Part = Percent X Whole
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.

43. A cylinder has a surface area of 22pi. If the cylinder has a height of 10 - what is the radius?
1
4a^2(b)
Angle/360 x (pi)r^2
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.

44. For similar triangles - the ratio of their corresponding sides is 2:3. What is the ratio of their areas?
52
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
67 - 71 - 73
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.

45. What does the graph (x+2)^2 + (y+2)^2 = 9 look like?
4.25 - 6 - 22
A circle centered at -2 - -2 with radius 3.
The second graph is less steep.
1/a^6

46. 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?
1
75:11
413.03 / 10^4 (move the decimal point 4 places to the left)
3/2 - 5/3

47. What is a tangent?
A tangent is a line that only touches one point on the circumference of a circle.
2 & 3/7
12.5%
Sector area = (n/360) X (pi)r^2

48. What are 'Supplementary angles?'
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
41 - 43 - 47
Indeterminable.
Two angles whose sum is 180.

49. In a triangle where the two legs are 4 and 3 - what is the value of a line directly intersecting the middle coming from the meeting point of the two legs?
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
3sqrt4
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
The empty set - denoted by a circle with a diagonal through it.

50. What is the absolute value function?
55%
F(x) + c
G(x) = {x}
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.

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GRE Math: Common Errors

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