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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 are the integers?
180 degrees
Yes. [i.e. f(x) = x^2 - 1
All numbers multiples of 1.
87.5%

2. a^2 - 2ab + b^2
A reflection about the axis.
2sqrt6
II
(a - b)^2

3. When the 'a' in a parabola is positive....
12sqrt2
The curve opens upward and the vertex is the minimal point on the graph.
2
Angle/360 x (pi)r^2

4. 3/8 in percent?
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
37.5%
41 - 43 - 47
The second graph is less steep.

5. 20<all primes<30
37.5%
23 - 29
The shortest arc between points A and B on a circle'S diameter.
Factors are few - multiples are many.

6. What is the 'union' of A and B?
The set of elements which can be found in either A or B.
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
The second graph is less steep.
Yes. [i.e. f(x) = x^2 - 1

7. 5 bakeries sell an average of 300 muffins per bakery per day. If 2 stop making muffins but the total muffins sold stays the same - what is the average of muffins per bakery sold among the remaining?
Diameter(Pi)
500
A chord is a line segment joining two points on a circle.
1.0843 X 10^11

8. Evaluate (4^3)^2
Undefined - because we can'T divide by 0.
Indeterminable.
4096
Two angles whose sum is 90.

9. 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?
3
9 : 25
500
Triangles with same measure and same side lengths.

10. A number is divisible by 6 if...
53 - 59
10! / (10-3)! = 720
Its divisible by 2 and by 3.
(amount of decrease/original price) x 100%

11. Area of a triangle?
(base*height) / 2
0
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
An isosceles right triangle.

12. What is the slope of a horizontal line?
I
0
441000 = 1 10 10 10 21 * 21
10! / (10-3)! = 720

13. x^4 + x^7 =
90
x^(4+7) = x^11
Part = Percent X Whole
288 (8 9 4)

14. How many 3-digit positive integers are even and do not contain the digit 4?
441000 = 1 10 10 10 21 * 21
The set of elements found in both A and B.
2
288 (8 9 4)

15. P and r are factors of 100. What is greater - pr or 100?
Arc length = (n/360) x pi(2r) where n is the number of degrees.
The set of output values for a function.
A circle centered on the origin with radius 8.
Indeterminable.

16. a^2 - b^2
C = (pi)d
(a - b)(a + b)
The curve opens downward and the vertex is the maximum point on the graph.
x= (1.2)(.8)lw

17. What is the side length of an equilateral triangle with altitude 6?
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...
1:sqrt3:2
F(x + c)
2(pi)r^2 + 2(pi)rh

18. 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?
Yes. [i.e. f(x) = x^2 - 1
N! / (k!)(n-k)!
Arc length = (n/360) x pi(2r) where n is the number of degrees.
441000 = 1 10 10 10 21 * 21

19. Max and Min lengths for a side of a triangle?
(a - b)^2
The third side is greater than the difference and less than the sum.
2^9 / 2 = 256
3/2 - 5/3

20. How to find the circumference of a circle which circumscribes a square?
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
A reflection about the origin.
The set of input values for a function.
1.0843 X 10^11

21. 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?
7 / 1000
3
Its divisible by 2 and by 3.
48

22. Define a 'monomial'
3
N! / (k!)(n-k)!
A set with a number of elements which can be counted.
An expression with just one term (-6x - 2a^2)

23. Pi is a ratio of what to what?

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24. Legs: 3 - 4. Hypotenuse?
62.5%
5
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
12.5%

25. Which quadrant is the upper right hand?
70
4.25 - 6 - 22
I
Two angles whose sum is 180.

26. 7/8 in percent?
x^(6-3) = x^3
500
61 - 67
87.5%

27. What are congruent triangles?
Undefined
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)
x(x - y + 1)
Triangles with same measure and same side lengths.

28. 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?
N! / (n-k)!
(a + b)^2
An expression with just one term (-6x - 2a^2)
A = I (1 + rt)

29. 2sqrt4 + sqrt4 =
The curve opens downward and the vertex is the maximum point on the graph.
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
37.5%
3sqrt4

30. What is a set with no members called?
The empty set - denoted by a circle with a diagonal through it.
A tangent is a line that only touches one point on the circumference of a circle.
3/2 - 5/3
90

31. The objects in a set are called two names:
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
Members or elements
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...
4096

32. What is a minor arc?

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33. To convert a percent to a fraction....
(a + b)^2
10! / 3!(10-3)! = 120
Divide by 100.
When the function is not defined for all real numbers -; only a subset of the real numbers.

34. From a box of 12 candles - you are to remove 5. How many different sets of 5 candles could you remove?
31 - 37
12! / 5!7! = 792
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)
All numbers multiples of 1.

35. sqrt 2(sqrt 6)=
An infinite set.
Sqrt 12
8
23 - 29

36. 1/6 in percent?
16.6666%
The point of intersection of the systems.
A = pi(r^2)
Sqrt 12

37. If 4500 is invested at a simple interest rate of 6% - what is the value of the investment after 10 months?
4725
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
A chord is a line segment joining two points on a circle.
(12/2) x (sqrt15 / sqrt5) = 6sqrt3

38. 1:1:sqrt2 is the ratio of the sides of what kind of triangle?
10! / 3!(10-3)! = 120
An isosceles right triangle.
6
12! / 5!7! = 792

39. In a regular polygon with n sides - the formula for the sum of interior angles
A central angle is an angle formed by 2 radii.
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
(n-2) x 180
The sum of digits is divisible by 9.

40. Formula to find a circle'S circumference from its radius?
F(x) - c
The set of elements found in both A and B.
5
C = 2(pi)r

41. 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
1.0843 X 10^11
2.592 kg
4725

42. 4.809 X 10^7 =
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
.0004809 X 10^11
37.5%
x^(2(4)) =x^8 = (x^4)^2

43. What is the set of elements found in both A and B?
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
The interesection of A and B.
(a - b)(a + b)
1/a^6

44. Legs 6 - 8. Hypotenuse?
Relationship cannot be determined (what if x is negative?)
10
72
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15

45. 413.03 x 10^(-4) =
413.03 / 10^4 (move the decimal point 4 places to the left)
(a + b)^2
The objects within a set.
1

46. 30< all primes<40
90 degrees
31 - 37
Arc length = (n/360) x pi(2r) where n is the number of degrees.
1

47. What does the graph (x+2)^2 + (y+2)^2 = 9 look like?
12! / 5!7! = 792
5
F(x) + c
A circle centered at -2 - -2 with radius 3.

48. Simplify 9^(1/2) X 4^3 X 2^(-6)?
(b + c)
From northeast - counterclockwise. I - II - III - IV
3
A subset.

49. Which quadrant is the upper left hand?
II
(a + b)^2
Two equal sides and two equal angles.
441000 = 1 10 10 10 21 * 21

50. What is the empty set?
The set of input values for a function.
A set with no members - denoted by a circle with a diagonal through it.
Indeterminable.
(12/2) x (sqrt15 / sqrt5) = 6sqrt3

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GRE Math: Common Errors

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