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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. Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
2^9 / 2 = 256
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
413.03 / 10^4 (move the decimal point 4 places to the left)
1 & 37/132

2. What is the name for a grouping of the members within a set based on a shared characteristic?
A subset.
180 degrees
4:5
0

3. Define an 'expression'.
9 : 25
6 : 1 : 2
From northeast - counterclockwise. I - II - III - IV
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. Legs 6 - 8. Hypotenuse?
The set of output values for a function.
10
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
An isosceles right triangle.

5. 10^6 has how many zeroes?
The empty set - denoted by a circle with a diagonal through it.
10
6
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)

6. 60 < all primes <70
F(x + c)
61 - 67
3
Move the decimal point to the right x places

7. What is a subset?
A grouping of the members within a set based on a shared characteristic.
28. n = 8 - k = 2. n! / k!(n-k)!
441000 = 1 10 10 10 21 * 21
Angle/360 x 2(pi)r

8. Which quadrant is the lower left hand?
4a^2(b)
(amount of increase/original price) x 100%
Yes. [i.e. f(x) = x^2 - 1
III

9. Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14
2 & 3/7
A reflection about the origin.
F(x) - c
1/(x^y)

10. Suppose that the graph of f(x) is the result of stretching y=x + 5 away from the x-axis by a factor of 2. What is the new equation for the graph f(x)?
A circle centered on the origin with radius 8.
y = (x + 5)/2
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
Relationship cannot be determined (what if x is negative?)

11. P and r are factors of 100. What is greater - pr or 100?
Indeterminable.
7 / 1000
Infinite.
31 - 37

12. How to determine percent increase?
(amount of increase/original price) x 100%
IV
Lies opposite the greater angle
x= (1.2)(.8)lw

13. 20<all primes<30
23 - 29
20.5
The greatest value minus the smallest.
The set of input values for a function.

14. Can you simplify sqrt72?
70
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
$3 -500 in the 9% and $2 -500 in the 7%.
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)

15. Can the input value of a function have more than one output value (i.e. x: y - y1)?
A circle centered on the origin with radius 8.
The point of intersection of the systems.
No - the input value has exactly one output.
1

16. When the 'a' in the parabola is negative...
3
The curve opens downward and the vertex is the maximum point on the graph.
Its divisible by 2 and by 3.
Yes - like radicals can be added/subtracted.

17. Which is greater? 27^(-4) or 9^(-8)
A set with no members - denoted by a circle with a diagonal through it.
70
A 30-60-90 triangle.
27^(-4)

18. Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
2sqrt6
1
(a + b)^2
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15

19. 70 < all primes< 80
The interesection of A and B.
Arc length = (n/360) x pi(2r) where n is the number of degrees.
71 - 73 - 79
When the function is not defined for all real numbers -; only a subset of the real numbers.

20. What is the 'Range' of a series of numbers?
(a - b)(a + b)
Yes - like radicals can be added/subtracted.
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
The greatest value minus the smallest.

21. Which is greater? 64^5 or 16^8
True
No - only like radicals can be added.
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16

22. Simplify the expression (p^2 - q^2)/ -5(q - p)
The curve opens upward and the vertex is the minimal point on the graph.
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
(p + q)/5
...multiply by 100.

23. What is the ratio of the sides of an isosceles right triangle?
IV
The set of elements found in both A and B.
1:1:sqrt2
Undefined - because we can'T divide by 0.

24. 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)
7 / 1000
The empty set - denoted by a circle with a diagonal through it.
1.7
4.25 - 6 - 22

25. 413.03 x 10^(-4) =
413.03 / 10^4 (move the decimal point 4 places to the left)
Yes. [i.e. f(x) = x^2 - 1
When the function is not defined for all real numbers -; only a subset of the real numbers.
The point of intersection of the systems.

26. Max and Min lengths for a side of a triangle?
The third side is greater than the difference and less than the sum.
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
9 : 25
F(x-c)

27. What is the third quartile of the following data set: 44 - 58 - 63 - 63 - 68 - 70 - 82
70
N! / (k!)(n-k)!
90 degrees
Angle/360 x 2(pi)r

28. Write 10 -843 X 10^7 in scientific notation
G(x) = {x}
1.0843 X 10^11
Indeterminable.
Even

29. In a regular polygon with n sides - the formula for the sum of interior angles
A = pi(r^2)
1.0843 X 10^11
(n-2) x 180
Members or elements

30. 1:1:sqrt2 is the ratio of the sides of what kind of triangle?
$3 -500 in the 9% and $2 -500 in the 7%.
y = 2x^2 - 3
An isosceles right triangle.
37.5%

31. What is the 'union' of A and B?
Cd
2 & 3/7
A set with no members - denoted by a circle with a diagonal through it.
The set of elements which can be found in either A or B.

32. If 10800 is invested at a simple interest rate of 4% - what is the value of the investment after 18 months?
Lies opposite the greater angle
$11 -448
2 & 3/7
Sqrt 12

33. 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?
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
Infinite.
1 & 37/132
y = 2x^2 - 3

34. 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?
52
The interesection of A and B.
$11 -448
Ax^2 + bx + c where a -b and c are constants and a /=0

35. The larger the absolute value of the slope...
Yes. [i.e. f(x) = x^2 - 1
The two xes after factoring.
The steeper the slope.
F(x-c)

36. 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
Indeterminable.
4.25 - 6 - 22
F(x-c)

37. 0^0
A reflection about the origin.
12.5%
Undefined
180 degrees

38. What is the 'Solution' for a set of inequalities.
Yes. [i.e. f(x) = x^2 - 1
The overlapping sections.
N! / (k!)(n-k)!
1

39. What is it called when a point is reflected to the quadrant opposite it (i.e. I to III or II to IV)?
The set of elements which can be found in either A or B.
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
F(x-c)
A reflection about the origin.

40. From a box of 12 candles - you are to remove 5. How many different sets of 5 candles could you remove?
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
12! / 5!7! = 792
Two angles whose sum is 90.
III

41. What does the graph (x+2)^2 + (y+2)^2 = 9 look like?
A circle centered at -2 - -2 with radius 3.
(a + b)^2
The steeper the slope.
Members or elements

42. Formula to find a circle'S circumference from its radius?
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
Undefined - because we can'T divide by 0.
The empty set - denoted by a circle with a diagonal through it.
C = 2(pi)r

43. x^(-y)=
3sqrt4
2.592 kg
Its negative reciprocal. (-b/a)
1/(x^y)

44. 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?
Cd
1/a^6
12! / 5!7! = 792
10! / (10-3)! = 720

45. 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
1:sqrt3:2
18
C = (pi)d
13pi / 2

46. 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
6 : 1 : 2
441000 = 1 10 10 10 21 * 21
IV

47. If 8 schools are in a conference - how many games are played if each team plays each other exactly once?
Arc length = (n/360) x pi(2r) where n is the number of degrees.
28. n = 8 - k = 2. n! / k!(n-k)!
Lies opposite the greater angle
III

48. What is the slope of a horizontal line?
The sum of digits is divisible by 9.
A 30-60-90 triangle.
0
When the function is not defined for all real numbers -; only a subset of the real numbers.

49. If the two sides of a triangle are unequal then the longer side...
1:1:sqrt2
Lies opposite the greater angle
x= (1.2)(.8)lw
83.333%

50. The slope of a line perpendicular to (a/b)?
Its negative reciprocal. (-b/a)
10! / 3!(10-3)! = 120
10
20.5