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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. Which quadrant is the upper right hand?
(amount of increase/original price) x 100%
F(x) - c
(b + c)
I

2. What are the rational numbers?
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
Diameter(Pi)
(a - b)^2

3. Describe the relationship between 3x^2 and 3(x - 1)^2
The sum of digits is divisible by 9.
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
A subset.
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.

4. 1/2 divided by 3/7 is the same as
The union of A and B.
1/2 times 7/3
x= (1.2)(.8)lw
(a + b)^2

5. 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?
$3 -500 in the 9% and $2 -500 in the 7%.
2sqrt6
90
53 - 59

6. What is the ratio of the sides of an isosceles right triangle?
90
1.7
The sum of digits is divisible by 9.
1:1:sqrt2

7. What is the intersection of A and B?
$11 -448
x= (1.2)(.8)lw
The set of elements found in both A and B.
The overlapping sections.

8. 1/6 in percent?
From northeast - counterclockwise. I - II - III - IV
(base*height) / 2
31 - 37
16.6666%

9. To convert a decimal to a percent...
The point of intersection of the systems.
(n-2) x 180
...multiply by 100.
1

10. What are 'Supplementary angles?'
A set with a number of elements which can be counted.
Divide by 100.
When the function is not defined for all real numbers -; only a subset of the real numbers.
Two angles whose sum is 180.

11. Length of an arc of a circle?
Angle/360 x (pi)r^2
Angle/360 x 2(pi)r
True
13

12. 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?
x^(2(4)) =x^8 = (x^4)^2
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
N! / (n-k)!
12! / 5!7! = 792

13. Order of quadrants:
Two angles whose sum is 180.
A chord is a line segment joining two points on a circle.
From northeast - counterclockwise. I - II - III - IV
6 : 1 : 2

14. What is the 'union' of A and B?
1 & 37/132
7 / 1000
Yes. [i.e. f(x) = x^2 - 1
The set of elements which can be found in either A or B.

15. What are complementary angles?
The sum of its digits is divisible by 3.
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...
(a - b)(a + b)
Two angles whose sum is 90.

16. A triangle is inscribed in a semi circle with legs 5 and 12. What is the circumfermence of the semicircle?
13pi / 2
Infinite.
Ax^2 + bx + c where a -b and c are constants and a /=0
$3 -500 in the 9% and $2 -500 in the 7%.

17. What are the smallest three prime numbers greater than 65?
A circle centered at -2 - -2 with radius 3.
67 - 71 - 73
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
(amount of increase/original price) x 100%

18. In similar hexagons - the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
4:5
Its divisible by 2 and by 3.
180 degrees
Indeterminable.

19. If an inequality is multiplied or divided by a negative number....
x^(4+7) = x^11
11 - 13 - 17 - 19
3
The direction of the inequality is reversed.

20. Formula to find a circle'S circumference from its radius?
C = (pi)d
Part = Percent X Whole
Arc length = (n/360) x pi(2r) where n is the number of degrees.
C = 2(pi)r

21. Legs 5 - 12. Hypotenuse?
13
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
(base*height) / 2
Divide by 100.

22. What is the order of operations?
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
2.592 kg
72
413.03 / 10^4 (move the decimal point 4 places to the left)

23. 1:sqrt3:2 is the ratio of the sides of what kind of triangle?
1
27^(-4)
A 30-60-90 triangle.
1

24. Simplify the expression [(b^2 - c^2) / (b - c)]
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
1/a^6
(b + c)
4725

25. 70 < all primes< 80
x^(2(4)) =x^8 = (x^4)^2
...multiply by 100.
(b + c)
71 - 73 - 79

26. Which is greater? 200x^295 or 10x^294?
Diameter(Pi)
18
Relationship cannot be determined (what if x is negative?)
A chord is a line segment joining two points on a circle.

27. The larger the absolute value of the slope...
The steeper the slope.
72
4a^2(b)
12sqrt2

28. 1/8 in percent?
2.592 kg
Infinite.
12.5%
4.25 - 6 - 22

29. What does scientific notation mean?
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
6 : 1 : 2
(amount of increase/original price) x 100%
Area of the base X height = (pi)hr^2

30. 10<all primes<20
11 - 13 - 17 - 19
x^(4+7) = x^11
10
The set of elements found in both A and B.

31. 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.
87.5%
0
Two angles whose sum is 180.

32. a^2 - b^2 =
1
1/2 times 7/3
... the square of the ratios of the corresponding sides.
(a - b)(a + b)

33. (-1)^3 =
An isosceles right triangle.
C = 2(pi)r
1
11 - 13 - 17 - 19

34. If a=-1 and b=3 - what is the value of (4(a^3)(b^2) - 12(a^2)(b^5)) / (16(a^3)(b^2))?
$3 -500 in the 9% and $2 -500 in the 7%.
6 : 1 : 2
(a - b)^2
20.5

35. Is 0 even or odd?
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
(base*height) / 2
.0004809 X 10^11
Even

36. What is a set with no members called?
The empty set - denoted by a circle with a diagonal through it.
6
3 - -3
71 - 73 - 79

37. 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?
An angle which is supplementary to an interior angle.
C = (pi)d
2 & 3/7
441000 = 1 10 10 10 21 * 21

38. What is the side length of an equilateral triangle with altitude 6?
(base*height) / 2
Move the decimal point to the right x places
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...
A circle centered at -2 - -2 with radius 3.

39. What is the 'Restricted domain of a function'?
The set of input values for a function.
When the function is not defined for all real numbers -; only a subset of the real numbers.
1/(x^y)
An infinite set.

40. What is the formula for compounded interest?
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.
The union of A and B.
An angle which is supplementary to an interior angle.
5 OR -5

41. Define an 'expression'.
The objects within a set.
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)
Its last two digits are divisible by 4.
1:1:sqrt2

42. Which is greater? 64^5 or 16^8
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
Pi is the ratio of a circle'S circumference to its diameter.
II
1

43. How many multiples does a given number have?
Infinite.
(p + q)/5
The sum of its digits is divisible by 3.
5

44. How to find the circumference of a circle which circumscribes a square?
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
...multiply by 100.
10! / (10-3)! = 720

45. What transformation occurs if point C is reflected over the x-axis and then the y-axis?
Sector area = (n/360) X (pi)r^2
A reflection about the axis.
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
The set of elements which can be found in either A or B.

46. What is the graph of f(x) shifted left c units or spaces?
F(x + c)
62.5%
10! / (10-3)! = 720
All numbers multiples of 1.

47. 200 <_ x <_ 300. How many values of x are divisible by 5 & 8?
3
180
F(x + c)
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.

48. Volume for a cylinder?
12! / 5!7! = 792
Area of the base X height = (pi)hr^2
1/2 times 7/3
5

49. sqrt 2(sqrt 6)=
Sqrt 12
1/a^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)
Arc length = (n/360) x pi(2r) where n is the number of degrees.

50. What is it called when a point is reflected to the quadrant opposite it (i.e. I to III or II to IV)?
Arc length = (n/360) x pi(2r) where n is the number of degrees.
500
A reflection about the origin.
12sqrt2