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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. (x^2)^4
1:1:sqrt2
x^(2(4)) =x^8 = (x^4)^2
The sum of digits is divisible by 9.
Indeterminable.

2. What are complementary angles?
1
Its last two digits are divisible by 4.
Two angles whose sum is 90.
I

3. Find the surface area of a cylinder with radius 3 and height 12.
90pi
18
The curve opens upward and the vertex is the minimal point on the graph.
48

4. Evaluate 4/11 + 11/12
1 & 37/132
A tangent is a line that only touches one point on the circumference of a circle.
Factors are few - multiples are many.
Lies opposite the greater angle

5. 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?
A reflection about the origin.
75:11
9 : 25
(a - b)(a + b)

6. 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?
Its divisible by 2 and by 3.
2.592 kg
(a - b)(a + b)
9 & 6/7

7. Volume for a cylinder?
The direction of the inequality is reversed.
61 - 67
Area of the base X height = (pi)hr^2
... the square of the ratios of the corresponding sides.

8. Length of an arc of a circle?
The curve opens upward and the vertex is the minimal point on the graph.
Angle/360 x 2(pi)r
Factors are few - multiples are many.
413.03 / 10^4 (move the decimal point 4 places to the left)

9. What is the maximum value for the function g(x) = (-2x^2) -1?
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
The union of A and B.
1
70

10. A number is divisible by 6 if...
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 direction of the inequality is reversed.
Its divisible by 2 and by 3.
The set of output values for a function.

11. 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)]?
500
Its negative reciprocal. (-b/a)
A = I (1 + rt)
True

12. What are the integers?
(p + q)/5
All numbers multiples of 1.
1:1:sqrt2
N! / (n-k)!

13. What is the 'union' of A and B?
The set of elements found in both A and B.
The set of elements which can be found in either A or B.
413.03 / 10^4 (move the decimal point 4 places to the left)
1 & 37/132

14. What is the name of set with a number of elements which cannot be counted?
130pi
An infinite set.
Even
A set with a number of elements which can be counted.

15. a^2 - 2ab + b^2
Relationship cannot be determined (what if x is negative?)
$11 -448
23 - 29
(a - b)^2

16. Which is greater? 64^5 or 16^8
The second graph is less steep.
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
7 / 1000
28. n = 8 - k = 2. n! / k!(n-k)!

17. 200 <_ x <_ 300. How many values of x are divisible by 5 & 8?
7 / 1000
The set of elements found in both A and B.
3 - -3
3

18. If 8 schools are in a conference - how many games are played if each team plays each other exactly once?
Its divisible by 2 and by 3.
Part = Percent X Whole
9 : 25
28. n = 8 - k = 2. n! / k!(n-k)!

19. How many digits are there between the decimal point and the first even digit in the decimal equivalent of 1/[(2^8)(5^3)]
The union of A and B.
1:1:sqrt2
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
0

20. 6w^2 - w - 15 = 0
2
3/2 - 5/3
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
1.7

21. What number between 70 & 75 - inclusive - has the greatest number of factors?
A subset.
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
1
72

22. Surface area for a cylinder?
The sum of its digits is divisible by 3.
2(pi)r^2 + 2(pi)rh
Lies opposite the greater angle
From northeast - counterclockwise. I - II - III - IV

23. Legs 5 - 12. Hypotenuse?
13
Undefined - because we can'T divide by 0.
The third side is greater than the difference and less than the sum.
Lies opposite the greater angle

24. To multiply a number by 10^x
Move the decimal point to the right x places
72
48
1.0843 X 10^11

25. Describe the relationship between 3x^2 and 3(x - 1)^2
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
1:1:sqrt2
Two angles whose sum is 180.
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.

26. 10^6 has how many zeroes?
1
6
Angle/360 x 2(pi)r
Arc length = (n/360) x pi(2r) where n is the number of degrees.

27. The slope of a line perpendicular to (a/b)?
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
Its negative reciprocal. (-b/a)
Divide by 100.
5

28. Which quadrant is the upper right hand?
71 - 73 - 79
I
A 30-60-90 triangle.
Factors are few - multiples are many.

29. What is the sum of the angles of a triangle?
1.7
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
180 degrees
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)

30. What are the irrational numbers?

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31. 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?
Its last two digits are divisible by 4.
20.5
The steeper the slope.
y = 2x^2 - 3

32. What is the surface area of a cylinder with radius 5 and height 8?
.0004809 X 10^11
1
130pi
The third side is greater than the difference and less than the sum.

33. What is the 'Restricted domain of a function'?
...multiply by 100.
x^(6-3) = x^3
Pi is the ratio of a circle'S circumference to its diameter.
When the function is not defined for all real numbers -; only a subset of the real numbers.

34. 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?
48
Yes. [i.e. f(x) = x^2 - 1
413.03 / 10^4 (move the decimal point 4 places to the left)
180 degrees

35. A number is divisible by 4 is...
An arc is a portion of a circumference of a circle.
Its last two digits are divisible by 4.
7 / 1000
The interesection of A and B.

36. 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?
2^9 / 2 = 256
61 - 67
10! / (10-3)! = 720
0

37. 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?
Move the decimal point to the right x places
$3 -500 in the 9% and $2 -500 in the 7%.
Sector area = (n/360) X (pi)r^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.

38. When the 'a' in a parabola is positive....
3
The curve opens upward and the vertex is the minimal point on the graph.
13pi / 2
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. In similar hexagons - the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
8
4:5
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)
3sqrt4

40. What is the slope of a vertical line?

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41. When the 'a' in the parabola is negative...
G(x) = {x}
An isosceles right triangle.
The curve opens downward and the vertex is the maximum point on the graph.
A grouping of the members within a set based on a shared characteristic.

42. A cylinder has a surface area of 22pi. If the cylinder has a height of 10 - what is the radius?
1
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
37.5%
53 - 59

43. 2sqrt4 + sqrt4 =
1
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
3sqrt4
The greatest value minus the smallest.

44. Can the input value of a function have more than one output value (i.e. x: y - y1)?
75:11
83.333%
F(x) + c
No - the input value has exactly one output.

45. What are the rational numbers?
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
A = pi(r^2)
1/a^6
10! / 3!(10-3)! = 120

46. What is the area of a regular hexagon with side 6?
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
12.5%
18

47. 413.03 x 10^(-4) =
28. n = 8 - k = 2. n! / k!(n-k)!
1
413.03 / 10^4 (move the decimal point 4 places to the left)
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).

48. 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?
Move the decimal point to the right x places
An arc is a portion of a circumference of a circle.
90
N! / (n-k)!

49. Can you add sqrt 3 and sqrt 5?
No - only like radicals can be added.
441000 = 1 10 10 10 21 * 21
62.5%
(a + b)^2

50. What is the slope of a horizontal line?
0
The shortest arc between points A and B on a circle'S diameter.
(a + b)^2
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]