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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. a^2 - b^2 =
(a - b)(a + b)
Undefined
A reflection about the axis.
(12/2) x (sqrt15 / sqrt5) = 6sqrt3

2. Circumference of a circle?
Triangles with same measure and same side lengths.
Diameter(Pi)
An expression with just one term (-6x - 2a^2)
Lies opposite the greater angle

3. Legs: 3 - 4. Hypotenuse?
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
5
The interesection of A and B.
180 degrees

4. What is the order of operations?
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
y = 2x^2 - 3
The greatest value minus the smallest.
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)

5. Which quandrant is the lower right hand?
Angle/360 x (pi)r^2
IV
1
37.5%

6. 7/8 in percent?
87.5%
1
71 - 73 - 79
(p + q)/5

7. If an inequality is multiplied or divided by a negative number....
x(x - y + 1)
The direction of the inequality is reversed.
Triangles with same measure and same side lengths.
From northeast - counterclockwise. I - II - III - IV

8. Define an 'expression'.
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)
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
$3 -500 in the 9% and $2 -500 in the 7%.
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...

9. 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
x(x - y + 1)
18
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)
.0004809 X 10^11

10. 70 < all primes< 80
71 - 73 - 79
5
1
The union of A and B.

11. Can you simplify sqrt72?
Sqrt 12
N! / (n-k)!
The direction of the inequality is reversed.
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.

12. a^2 - b^2
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
12! / 5!7! = 792
Two equal sides and two equal angles.
(a - b)(a + b)

13. x^6 / x^3
The interesection of A and B.
28. n = 8 - k = 2. n! / k!(n-k)!
x^(6-3) = x^3
1/(x^y)

14. Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
2sqrt6
1/(x^y)
7 / 1000

15. What are the smallest three prime numbers greater than 65?
67 - 71 - 73
28. n = 8 - k = 2. n! / k!(n-k)!
III
5

16. To multiply a number by 10^x
10! / (10-3)! = 720
Move the decimal point to the right x places
9 & 6/7
180 degrees

17. In similar hexagons - the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
Divide by 100.
3
4:5
A subset.

18. 3/8 in percent?
37.5%
1/a^6
A set with a number of elements which can be counted.
2.592 kg

19. What are the irrational numbers?

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20. To convert a decimal to a percent...
x^(6-3) = x^3
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
...multiply by 100.
The third side is greater than the difference and less than the sum.

21. For similar triangles - the ratio of their corresponding sides is 2:3. What is the ratio of their areas?
413.03 / 10^4 (move the decimal point 4 places to the left)
Lies opposite the greater angle
Angle/360 x 2(pi)r
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.

22. What is an arc of a circle?
2sqrt6
7 / 1000
An arc is a portion of a circumference of a circle.
N! / (n-k)!

23. Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14
The third side is greater than the difference and less than the sum.
2 & 3/7
4096
Two equal sides and two equal angles.

24. What is the side length of an equilateral triangle with altitude 6?
A tangent is a line that only touches one point on the circumference of a circle.
The sum of digits is divisible by 9.
The union of A and B.
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...

25. Find the surface area of a cylinder with radius 3 and height 12.
90pi
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
0
4096

26. 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
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
Even
9 : 25

27. Can you add sqrt 3 and sqrt 5?
1:sqrt3:2
A 30-60-90 triangle.
72
No - only like radicals can be added.

28. What is the graph of f(x) shifted upward c units or spaces?
F(x) + c
N! / (n-k)!
The third side is greater than the difference and less than the sum.
The shortest arc between points A and B on a circle'S diameter.

29. What is the absolute value function?
y = (x + 5)/2
3sqrt4
G(x) = {x}
(base*height) / 2

30. What is the name of set with a number of elements which cannot be counted?
2^9 / 2 = 256
(a + b)^2
1/a^6
An infinite set.

31. 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?
The curve opens upward and the vertex is the minimal point on the graph.
12sqrt2
N! / (n-k)!
A tangent is a line that only touches one point on the circumference of a circle.

32. Which is greater? 64^5 or 16^8
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
From northeast - counterclockwise. I - II - III - IV
Cd
$3 -500 in the 9% and $2 -500 in the 7%.

33. A number is divisible by 6 if...
Its divisible by 2 and by 3.
A subset.
(p + q)/5
1 & 37/132

34. What are the real numbers?
x^(6-3) = x^3
62.5%
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 reflection about the axis.

35. The objects in a set are called two names:
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...
Relationship cannot be determined (what if x is negative?)
N! / (n-k)!
Members or elements

36. 30< all primes<40
31 - 37
Two angles whose sum is 180.
The two xes after factoring.
71 - 73 - 79

37. 1/2 divided by 3/7 is the same as
10! / 3!(10-3)! = 120
1/2 times 7/3
9 & 6/7
Undefined

38. Simplify (a^2 + b)^2 - (a^2 - b)^2
Angle/360 x (pi)r^2
Triangles with same measure and same side lengths.
4a^2(b)
A central angle is an angle formed by 2 radii.

39. From a box of 12 candles - you are to remove 5. How many different sets of 5 candles could you remove?
12! / 5!7! = 792
Two angles whose sum is 90.
(amount of decrease/original price) x 100%
90

40. What is it called when a point is reflected to the quadrant opposite it (i.e. I to III or II to IV)?
An expression with just one term (-6x - 2a^2)
A reflection about the origin.
The set of output values for a function.
II

41. What is the empty set?
A set with no members - denoted by a circle with a diagonal through it.
71 - 73 - 79
(amount of decrease/original price) x 100%
6

42. To convert a percent to a fraction....
The steeper the slope.
x= (1.2)(.8)lw
Divide by 100.
1/a^6

43. 50 < all primes< 60
C = (pi)d
$3 -500 in the 9% and $2 -500 in the 7%.
53 - 59
From northeast - counterclockwise. I - II - III - IV

44. Define a 'Term' -
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)
... the square of the ratios of the corresponding sides.
A subset.
The overlapping sections.

45. A number is divisible by 4 is...
Its last two digits are divisible by 4.
180
Indeterminable.
The curve opens downward and the vertex is the maximum point on the graph.

46. The perimeter of a square is 48 inches. The length of its diagonal is:
Two equal sides and two equal angles.
12sqrt2
An isosceles right triangle.
31 - 37

47. How to find the area of a sector?
Angle/360 x (pi)r^2
A reflection about the axis.
Factors are few - multiples are many.
2 & 3/7

48. The slope of a line perpendicular to (a/b)?
2sqrt6
Lies opposite the greater angle
C = (pi)d
Its negative reciprocal. (-b/a)

49. (a^-1)/a^5
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)
1/a^6
(a + b)^2
(b + c)

50. a^2 + 2ab + b^2
(a + b)^2
N! / (n-k)!
1
Pi is the ratio of a circle'S circumference to its diameter.