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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. 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?
10! / 3!(10-3)! = 120
A grouping of the members within a set based on a shared characteristic.
The direction of the inequality is reversed.
31 - 37

2. Solve the quadratic equation ax^2 + bx + c= 0
An arc is a portion of a circumference of a circle.
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
Two angles whose sum is 180.
Sector area = (n/360) X (pi)r^2

3. A cylinder has a surface area of 22pi. If the cylinder has a height of 10 - what is the radius?
87.5%
... the square of the ratios of the corresponding sides.
72
1

4. What are the real numbers?
2
The curve opens upward and the vertex is the minimal point on the graph.
(base*height) / 2
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)

5. A triangle is inscribed in a semi circle with legs 5 and 12. What is the circumfermence of the semicircle?
13pi / 2
13
3
Infinite.

6. Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
Its divisible by 2 and by 3.
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
2^9 / 2 = 256
3

7. When does a function automatically have a restricted domain (2)?
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
1
18

8. What is the third quartile of the following data set: 44 - 58 - 63 - 63 - 68 - 70 - 82
The union of A and B.
70
IV
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)

9. Is 0 even or odd?
Undefined - because we can'T divide by 0.
Even
3
x^(6-3) = x^3

10. What is an arc of a circle?
53 - 59
Undefined - because we can'T divide by 0.
An arc is a portion of a circumference of a circle.
6

11. In a triangle inscribed inside a circle - where the diameter is one side of the triangle - which angle is largest?
2 & 3/7
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.
6
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.

12. Surface area for a cylinder?
x^(6-3) = x^3
12.5%
2(pi)r^2 + 2(pi)rh
Undefined - because we can'T divide by 0.

13. How to determine percent decrease?
(amount of decrease/original price) x 100%
The union of A and B.
Divide by 100.
288 (8 9 4)

14. A number is divisible by 3 if ...
The sum of its digits is divisible by 3.
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
C = 2(pi)r
The set of elements found in both A and B.

15. (-1)^3 =
Relationship cannot be determined (what if x is negative?)
Yes - like radicals can be added/subtracted.
1
I

16. (12sqrt15) / (2sqrt5) =
Angle/360 x 2(pi)r
90pi
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
All numbers multiples of 1.

17. What is a finite set?
Factors are few - multiples are many.
71 - 73 - 79
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
A set with a number of elements which can be counted.

18. What is the sum of the angles of a triangle?
6
N! / (k!)(n-k)!
71 - 73 - 79
180 degrees

19. What is an exterior angle?
An angle which is supplementary to an interior angle.
71 - 73 - 79
413.03 / 10^4 (move the decimal point 4 places to the left)
y = (x + 5)/2

20. 5x^2 - 35x -55 = 0
A reflection about the origin.
6
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
1:sqrt3:2

21. What is the name of set with a number of elements which cannot be counted?
Area of the base X height = (pi)hr^2
The second graph is less steep.
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
An infinite set.

22. 1/8 in percent?
$11 -448
2
12.5%
The objects within a set.

23. Evaluate 3& 2/7 / 1/3
Sqrt 12
72
9 & 6/7
The interesection of A and B.

24. If the 80th percentile of the measurements is 72degrees - about how many measurments are between 69 degrees and 72 degrees? Round your answer to the nearest tenth
18
1.0843 X 10^11
True
90pi

25. What is the side length of an equilateral triangle with altitude 6?
The union of A and B.
A set with a number of elements which can be counted.
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 graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.

26. What are 'Supplementary angles?'
Two angles whose sum is 180.
1.0843 X 10^11
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
87.5%

27. What is the graph of f(x) shifted right c units or spaces?
500
The direction of the inequality is reversed.
Infinite.
F(x-c)

28. How to determine percent increase?
(amount of increase/original price) x 100%
Its last two digits are divisible by 4.
28. n = 8 - k = 2. n! / k!(n-k)!
Angle/360 x 2(pi)r

29. When the 'a' in a parabola is positive....
The curve opens upward and the vertex is the minimal point on the graph.
6
2(pi)r^2 + 2(pi)rh
y = (x + 5)/2

30. What is a major arc?

31. 2sqrt4 + sqrt4 =
F(x-c)
3sqrt4
1
The shortest arc between points A and B on a circle'S diameter.

32. 70 < all primes< 80
x^(4+7) = x^11
71 - 73 - 79
(amount of decrease/original price) x 100%
3 - -3

33. Formula to find a circle'S circumference from its radius?
C = 2(pi)r
53 - 59
87.5%
1 & 37/132

34. Simplify the expression [(b^2 - c^2) / (b - c)]
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
(b + c)
The interesection of A and B.
2sqrt6

35. Which is greater? 64^5 or 16^8
12! / 5!7! = 792
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
10! / (10-3)! = 720
A chord is a line segment joining two points on a circle.

36. What is the maximum value for the function g(x) = (-2x^2) -1?
C = (pi)d
1
4725
6

37. What does the graph x^2 + y^2 = 64 look like?
3sqrt4
A circle centered on the origin with radius 8.
Part = Percent X Whole
The curve opens downward and the vertex is the maximum point on the graph.

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?
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
48
Move the decimal point to the right x places
When the function is not defined for all real numbers -; only a subset of the real numbers.

39. Simplify (a^2 + b)^2 - (a^2 - b)^2
A tangent is a line that only touches one point on the circumference of a circle.
3sqrt4
Relationship cannot be determined (what if x is negative?)
4a^2(b)

40. Which quadrant is the upper left hand?
Angle/360 x 2(pi)r
II
90
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).

41. 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?
...multiply by 100.
$3 -500 in the 9% and $2 -500 in the 7%.
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
(a - b)^2

42. 7/8 in percent?
An infinite set.
13pi / 2
87.5%
The two xes after factoring.

43. What is the 'Solution' for a system of linear equations?
y = (x + 5)/2
The point of intersection of the systems.
7 / 1000
A subset.

44. Describe the relationship between the graphs of x^2 and (1/2)x^2
C = (pi)d
The second graph is less steep.
...multiply by 100.
0

45. What is a subset?
16.6666%
52
A grouping of the members within a set based on a shared characteristic.
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]

46. Formula of rectangle where l increases by 20% and w decreases by 20%
(a - b)^2
4a^2(b)
4725
x= (1.2)(.8)lw

47. 1/2 divided by 3/7 is the same as
18
The steeper the slope.
1/2 times 7/3
2 & 3/7

48. 5/8 in percent?
62.5%
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
$3 -500 in the 9% and $2 -500 in the 7%.
The sum of digits is divisible by 9.

49. 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.
72
4a^2(b)
90 degrees
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

50. Evaluate (4^3)^2
4096
A tangent is a line that only touches one point on the circumference of a circle.
2sqrt6
Angle/360 x (pi)r^2