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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.
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. If 8 schools are in a conference - how many games are played if each team plays each other exactly once?
An isosceles right triangle.
I
x^(4+7) = x^11
28. n = 8 - k = 2. n! / k!(n-k)!

2. Reduce: 4.8 : 0.8 : 1.6
2.592 kg
N! / (n-k)!
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
6 : 1 : 2

3. How to find the circumference of a circle which circumscribes a square?
Sector area = (n/360) X (pi)r^2
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
48

4. To convert a decimal to a percent...
I
x^(4+7) = x^11
...multiply by 100.
Yes. [i.e. f(x) = x^2 - 1

5. What are the rational numbers?
288 (8 9 4)
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
The interesection of A and B.

6. Formula for the area of a sector of a circle?
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.
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
Sector area = (n/360) X (pi)r^2
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a

7. When the 'a' in a parabola is positive....
The curve opens upward and the vertex is the minimal point on the graph.
Members or elements
A subset.
4a^2(b)

8. 413.03 x 10^(-4) =
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)
1
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...
413.03 / 10^4 (move the decimal point 4 places to the left)

9. If the two sides of a triangle are unequal then the longer side...
$11 -448
Lies opposite the greater angle
4:5
.0004809 X 10^11

10. 1/2 divided by 3/7 is the same as
1/2 times 7/3
1.7
3 - -3
Two angles whose sum is 180.

11. 4.809 X 10^7 =
3
The set of elements found in both A and B.
.0004809 X 10^11
(a - b)(a + b)

12. (-1)^3 =
500
1
Pi is the ratio of a circle'S circumference to its diameter.
Factors are few - multiples are many.

13. 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?
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...
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
$3 -500 in the 9% and $2 -500 in the 7%.
The interesection of A and B.

14. Factor a^2 + 2ab + b^2
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
(a + b)^2
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
83.333%

15. a^2 - b^2
(a - b)(a + b)
A tangent is a line that only touches one point on the circumference of a circle.
13
I

16. What is the order of operations?
12sqrt2
4:5
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
1.0843 X 10^11

17. A company places a 6-symbol code on each product. The code consists of the letter T - followed by 3 numerical digits - and then 2 consonants (Y is a conson). How many codes are possible?
1
(amount of increase/original price) x 100%
441000 = 1 10 10 10 21 * 21
67 - 71 - 73

18. Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
The curve opens upward and the vertex is the minimal point on the graph.
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
75:11
2^9 / 2 = 256

19. What does scientific notation mean?
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
Sqrt 12
(p + q)/5
$11 -448

20. The ratio of the areas of two similar polygons is ...
IV
... the square of the ratios of the corresponding sides.
The greatest value minus the smallest.
2^9 / 2 = 256

21. What is a finite set?
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)
83.333%
C = 2(pi)r
A set with a number of elements which can be counted.

22. What is the common monomial factor in the expression 4(c^3)d - (c^2)(d^2) + 2cd?
From northeast - counterclockwise. I - II - III - IV
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
Cd
A 30-60-90 triangle.

23. What is a piecewise equation?
IV
(base*height) / 2
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
3 - -3

24. 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?
Two equal sides and two equal angles.
The union of A and B.
75:11
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.

25. Simplify the expression [(b^2 - c^2) / (b - c)]
4725
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
(b + c)

26. Which quadrant is the lower left hand?
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
2.592 kg
III

27. Write 10 -843 X 10^7 in scientific notation
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
No - only like radicals can be added.
1.0843 X 10^11

28. What is the 'union' of A and B?
The set of elements which can be found in either A or B.
Triangles with same measure and same side lengths.
Yes - like radicals can be added/subtracted.
N! / (n-k)!

29. What is the 'Solution' for a set of inequalities.
The overlapping sections.
3
N! / (n-k)!
Factors are few - multiples are many.

30. x^6 / x^3
(a - b)^2
Sector area = (n/360) X (pi)r^2
1
x^(6-3) = x^3

31. The perimeter of a square is 48 inches. The length of its diagonal is:
(a + b)^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)
The direction of the inequality is reversed.
12sqrt2

32. The four angles around a point measure y - 2y - 35 and 55 respectively. What is the value of y?
1
The direction of the inequality is reversed.
2^9 / 2 = 256
90

33. Find the surface area of a cylinder with radius 3 and height 12.
72
90pi
Angle/360 x 2(pi)r
x(x - y + 1)

34. Formula of rectangle where l increases by 20% and w decreases by 20%
The empty set - denoted by a circle with a diagonal through it.
Pi is the ratio of a circle'S circumference to its diameter.
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
x= (1.2)(.8)lw

35. 20<all primes<30
3
23 - 29
No - only like radicals can be added.
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)

36. What is the 'Range' of a function?
1
IV
The set of output values for a function.
...multiply by 100.

37. 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?
N! / (k!)(n-k)!
The empty set - denoted by a circle with a diagonal through it.
All numbers multiples of 1.
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.

38. What is a chord of a circle?
The union of A and B.
A chord is a line segment joining two points on a circle.
(a + b)^2
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.

39. Define an 'expression'.
C = (pi)d
The set of output values for a function.
The union of A and B.
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)

40. Evaluate (4^3)^2
... the square of the ratios of the corresponding sides.
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
The curve opens downward and the vertex is the maximum point on the graph.
4096

41. A number is divisible by 6 if...
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.
28. n = 8 - k = 2. n! / k!(n-k)!
10! / (10-3)! = 720
Its divisible by 2 and by 3.

42. 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)
72
4.25 - 6 - 22
When the function is not defined for all real numbers -; only a subset of the real numbers.
An arc is a portion of a circumference of a circle.

43. What is the name for a grouping of the members within a set based on a shared characteristic?
Two angles whose sum is 90.
The longest arc between points A and B on a circle'S diameter.
A subset.
A chord is a line segment joining two points on a circle.

44. Factor x^2 - xy + x.
x^(6-3) = x^3
The overlapping sections.
$11 -448
x(x - y + 1)

45. How many digits are there between the decimal point and the first even digit in the decimal equivalent of 1/[(2^8)(5^3)]
23 - 29
0
The shortest arc between points A and B on a circle'S diameter.
180

46. 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)]?
52
1
0
True

47. What is the 'Restricted domain of a function'?
When the function is not defined for all real numbers -; only a subset of the real numbers.
C = (pi)d
90pi
The direction of the inequality is reversed.

48. What is it called when a point is reflected to the quadrant opposite it (i.e. I to III or II to IV)?
2(pi)r^2 + 2(pi)rh
A reflection about the origin.
12sqrt2
2

49. What is the name of set with a number of elements which cannot be counted?
(p + q)/5
A grouping of the members within a set based on a shared characteristic.
An infinite set.
5

50. a^2 - 2ab + b^2
II
3sqrt4
(a - b)^2
12! / 5!7! = 792

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GRE Math: Common Errors

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