Test your basic knowledge |

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. 6w^2 - w - 15 = 0
61 - 67
3/2 - 5/3
The third side is greater than the difference and less than the sum.
2sqrt6

2. Define an 'expression'.
90pi
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)
Infinite.
The direction of the inequality is reversed.

3. 1:sqrt3:2 is the ratio of the sides of what kind of triangle?
Its negative reciprocal. (-b/a)
(a + b)^2
A 30-60-90 triangle.
1

4. What is an arc of a circle?
Part = Percent X Whole
41 - 43 - 47
An arc is a portion of a circumference of a circle.
The union of A and B.

5. How to determine percent increase?
III
53 - 59
(amount of increase/original price) x 100%
Area of the base X height = (pi)hr^2

6. What is a parabola?
Divide by 100.
Ax^2 + bx + c where a -b and c are constants and a /=0
87.5%
37.5%

7. For similar triangles - the ratio of their corresponding sides is 2:3. What is the ratio of their areas?
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
9 & 6/7
28. n = 8 - k = 2. n! / k!(n-k)!
83.333%

8. Factor x^2 - xy + x.
1/2 times 7/3
(a - b)^2
x(x - y + 1)
(12/2) x (sqrt15 / sqrt5) = 6sqrt3

9. How to determine percent decrease?
12.5%
4a^2(b)
(amount of decrease/original price) x 100%
Members or elements

10. A number is divisible by 3 if ...
11 - 13 - 17 - 19
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
The sum of its digits is divisible by 3.
413.03 / 10^4 (move the decimal point 4 places to the left)

11. 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?
2.592 kg
The shortest arc between points A and B on a circle'S diameter.
90pi
(p + q)/5

12. What is the graph of f(x) shifted left c units or spaces?
5
The set of elements which can be found in either A or B.
48
F(x + c)

13. What is the 'Solution' for a set of inequalities.
Factors are few - multiples are many.
The overlapping sections.
18
55%

14. Factor a^2 + 2ab + b^2
Lies opposite the greater angle
II
(a + b)^2
Cd

15. 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?
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
10! / 3!(10-3)! = 120
Area of the base X height = (pi)hr^2
The set of output values for a function.

16. What is a chord of a circle?
A chord is a line segment joining two points on a circle.
A = pi(r^2)
The objects within a set.
A circle centered on the origin with radius 8.

17. What is the 'Range' of a function?
Move the decimal point to the right x places
4a^2(b)
An expression with just one term (-6x - 2a^2)
The set of output values for a function.

18. What is a finite set?
No - only like radicals can be added.
83.333%
A set with a number of elements which can be counted.
48

19. To convert a percent to a fraction....
x^(2(4)) =x^8 = (x^4)^2
Divide by 100.
The curve opens upward and the vertex is the minimal point on the graph.
An angle which is supplementary to an interior angle.

20. What is the name of set with a number of elements which cannot be counted?
The sum of its digits is divisible by 3.
x(x - y + 1)
An infinite set.
Ax^2 + bx + c where a -b and c are constants and a /=0

21. Simplify (a^2 + b)^2 - (a^2 - b)^2
Diameter(Pi)
A = pi(r^2)
18
4a^2(b)

22. 2sqrt4 + sqrt4 =
3sqrt4
67 - 71 - 73
53 - 59
A reflection about the origin.

23. 7/8 in percent?
87.5%
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
2

24. Describe the relationship between the graphs of x^2 and (1/2)x^2
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
The second graph is less steep.
13
C = 2(pi)r

25. Area of a triangle?
3
(base*height) / 2
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
A 30-60-90 triangle.

26. Legs: 3 - 4. Hypotenuse?
Indeterminable.
5
(base*height) / 2
130pi

27. In a regular polygon with n sides - the formula for the sum of interior angles
180
The steeper the slope.
(n-2) x 180
A = pi(r^2)

28. What is the formula for compounded interest?
Move the decimal point to the right x places
52
Factors are few - multiples are many.
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.

29. What are the members or elements of a set?
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.
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
The objects within a set.

30. What is the measure of an exterior angle of a regular pentagon?
The overlapping sections.
x= (1.2)(.8)lw
I
72

31. 5/8 in percent?
(a - b)^2
Even
An isosceles right triangle.
62.5%

32. x^6 / x^3
x^(6-3) = x^3
Infinite.
(b + c)
The set of output values for a function.

33. sqrt 2(sqrt 6)=
37.5%
Sqrt 12
x^(4+7) = x^11
4a^2(b)

34. If 4500 is invested at a simple interest rate of 6% - what is the value of the investment after 10 months?
The set of elements which can be found in either A or B.
(amount of decrease/original price) x 100%
61 - 67
4725

35. 5/6 in percent?
2^9 / 2 = 256
A reflection about the origin.
2 & 3/7
83.333%

36. How many 3-digit positive integers are even and do not contain the digit 4?
12! / 5!7! = 792
288 (8 9 4)
18
Even

37. Can you subtract 3sqrt4 from sqrt4?
2.592 kg
Yes - like radicals can be added/subtracted.
All numbers multiples of 1.
Area of the base X height = (pi)hr^2

38. 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?
Two angles whose sum is 90.
Pi is the ratio of a circle'S circumference to its diameter.
48
The set of elements which can be found in either A or B.

39. 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)
Two angles whose sum is 90.
The greatest value minus the smallest.
4.25 - 6 - 22
10! / (10-3)! = 720

40. 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.
1
90 degrees
Its negative reciprocal. (-b/a)
Part = Percent X Whole

41. (6sqrt3) x (2sqrt5) =
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
55%
The second graph is less steep.
Yes - like radicals can be added/subtracted.

42. 4.809 X 10^7 =
The curve opens downward and the vertex is the maximum point on the graph.
.0004809 X 10^11
A grouping of the members within a set based on a shared characteristic.
72

43. P and r are factors of 100. What is greater - pr or 100?
Its last two digits are divisible by 4.
Indeterminable.
Pi is the ratio of a circle'S circumference to its diameter.
130pi

44. Is 0 even or odd?
4725
Even
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
28. n = 8 - k = 2. n! / k!(n-k)!

45. What is a subset?
A reflection about the origin.
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 grouping of the members within a set based on a shared characteristic.
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a

46. What is the empty set?
An infinite set.
C = 2(pi)r
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
A set with no members - denoted by a circle with a diagonal through it.

47. Can you simplify sqrt72?
Factors are few - multiples are many.
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
...multiply by 100.
13pi / 2

48. What is the ratio of the sides of an isosceles right triangle?
1:1:sqrt2
1
2^9 / 2 = 256
C = 2(pi)r

49. 25^(1/2) or sqrt. 25 =
A subset.
5 OR -5
(a + b)^2
Its negative reciprocal. (-b/a)

50. If Madagascar'S exports totaled 1.3 billion in 2009 - and 4% came from China - what was the value in millions of the country'S exports to China?
4096
52
The steeper the slope.
Part = Percent X Whole