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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. What is the surface area of a cylinder with radius 5 and height 8?
18
1/2 times 7/3
N! / (n-k)!
130pi

2. Simplify the expression (p^2 - q^2)/ -5(q - p)
A = I (1 + rt)
1.7
441000 = 1 10 10 10 21 * 21
(p + q)/5

3. 1:sqrt3:2 is the ratio of the sides of what kind of triangle?
3 - -3
3/2 - 5/3
A 30-60-90 triangle.
71 - 73 - 79

4. 2sqrt4 + sqrt4 =
Angle/360 x (pi)r^2
When the function is not defined for all real numbers -; only a subset of the real numbers.
3sqrt4
x(x - y + 1)

5. 5 bakeries sell an average of 300 muffins per bakery per day. If 2 stop making muffins but the total muffins sold stays the same - what is the average of muffins per bakery sold among the remaining?
18
500
IV
5 OR -5

6. Whats the difference between factors and multiples?
1
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
Factors are few - multiples are many.
1/2 times 7/3

7. How to find the area of a sector?
The curve opens upward and the vertex is the minimal point on the graph.
Angle/360 x (pi)r^2
6 : 1 : 2
A = pi(r^2)

8. a^0 =
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
F(x + c)
10! / 3!(10-3)! = 120
1

9. 5x^2 - 35x -55 = 0
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
Divide by 100.
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
1

10. 60 < all primes <70
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
61 - 67
90

11. 10<all primes<20
11 - 13 - 17 - 19
1/(x^y)
N! / (k!)(n-k)!
413.03 / 10^4 (move the decimal point 4 places to the left)

12. x^4 + x^7 =
A tangent is a line that only touches one point on the circumference of a circle.
x^(4+7) = x^11
52
2^9 / 2 = 256

13. How many sides does a hexagon have?
4a^2(b)
13
6
37.5%

14. Legs 5 - 12. Hypotenuse?
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)
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
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
13

15. What is the order of operations?
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
(p + q)/5
From northeast - counterclockwise. I - II - III - IV
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.

16. What are the rational numbers?
An isosceles right triangle.
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
72
4096

17. What are the roots of the quadrinomial x^2 + 2x + 1?
4725
6
The two xes after factoring.
The longest arc between points A and B on a circle'S diameter.

18. A number is divisible by 4 is...
The set of elements which can be found in either A or B.
$3 -500 in the 9% and $2 -500 in the 7%.
Its last two digits are divisible by 4.
Sector area = (n/360) X (pi)r^2

19. Solve the quadratic equation ax^2 + bx + c= 0
An infinite set.
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
x(x - y + 1)
The third side is greater than the difference and less than the sum.

20. 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?
10! / 3!(10-3)! = 120
52
N! / (k!)(n-k)!
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)

21. The four angles around a point measure y - 2y - 35 and 55 respectively. What is the value of y?
The shortest arc between points A and B on a circle'S diameter.
0
I
90

22. What is the name of set with a number of elements which cannot be counted?
(a - b)(a + b)
An infinite set.
12sqrt2
1

23. Reduce: 4.8 : 0.8 : 1.6
1:1:sqrt2
Divide by 100.
6 : 1 : 2
6

24. How to determine percent decrease?
... the square of the ratios of the corresponding sides.
No - the input value has exactly one output.
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
(amount of decrease/original price) x 100%

25. 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.
(b + c)
The empty set - denoted by a circle with a diagonal through it.
10! / (10-3)! = 720

26. A cylinder has a surface area of 22pi. If the cylinder has a height of 10 - what is the radius?
1
8
62.5%
70

27. What is the slope of a horizontal line?
0
$3 -500 in the 9% and $2 -500 in the 7%.
90pi
I

28. What is the 'Range' of a series of numbers?
Diameter(Pi)
...multiply by 100.
The greatest value minus the smallest.
12! / 5!7! = 792

29. What is the set of elements which can be found in either A or B?
1.7
The union of A and B.
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)
(12/2) x (sqrt15 / sqrt5) = 6sqrt3

30. x^6 / x^3
x^(6-3) = x^3
N! / (k!)(n-k)!
288 (8 9 4)
12sqrt2

31. What is a tangent?
A central angle is an angle formed by 2 radii.
The objects within a set.
A tangent is a line that only touches one point on the circumference of a circle.
(a + b)^2

32. 1/8 in percent?
12.5%
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
The overlapping sections.
Move the decimal point to the right x places

33. (-1)^2 =
The sum of its digits is divisible by 3.
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
70
1

34. What does the graph x^2 + y^2 = 64 look like?
A circle centered on the origin with radius 8.
71 - 73 - 79
C = 2(pi)r
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.

35. What are the smallest three prime numbers greater than 65?
x= (1.2)(.8)lw
(base*height) / 2
(b + c)
67 - 71 - 73

36. Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14
N! / (n-k)!
2 & 3/7
2sqrt6
The sum of its digits is divisible by 3.

37. In a regular polygon with n sides - the formula for the sum of interior angles
(n-2) x 180
A 30-60-90 triangle.
F(x) - c
Lies opposite the greater angle

38. If the two sides of a triangle are unequal then the longer side...
Lies opposite the greater angle
A grouping of the members within a set based on a shared characteristic.
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
4725

39. Which is greater? 64^5 or 16^8
A chord is a line segment joining two points on a circle.
1/(x^y)
1
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16

40. What is the maximum value for the function g(x) = (-2x^2) -1?
1.0843 X 10^11
Even
True
1

41. Which quandrant is the lower right hand?
IV
Ax^2 + bx + c where a -b and c are constants and a /=0
62.5%
31 - 37

42. How many digits are there between the decimal point and the first even digit in the decimal equivalent of 1/[(2^8)(5^3)]
3 - -3
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)
0
1

43. What is a chord of a circle?
A chord is a line segment joining two points on a circle.
True
Indeterminable.
The set of output values for a function.

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?
A subset.
N! / (n-k)!
C = (pi)d
10! / (10-3)! = 720

45. Surface area for a cylinder?
An infinite set.
1:sqrt3:2
A set with a number of elements which can be counted.
2(pi)r^2 + 2(pi)rh

46. 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%.
90 degrees
90pi
10! / (10-3)! = 720

47. From a box of 12 candles - you are to remove 5. How many different sets of 5 candles could you remove?
288 (8 9 4)
12! / 5!7! = 792
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
The interesection of A and B.

48. What is the ratio of the sides of an isosceles right triangle?
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...
1:1:sqrt2
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
A grouping of the members within a set based on a shared characteristic.

49. a^2 + 2ab + b^2
Yes - like radicals can be added/subtracted.
(a + b)^2
$3 -500 in the 9% and $2 -500 in the 7%.
2.592 kg

50. 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
37.5%
2.592 kg
x^(4+7) = x^11