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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. Whats the difference between factors and multiples?
Factors are few - multiples are many.
A = pi(r^2)
N! / (k!)(n-k)!
5 OR -5

2. Formula for the area of a sector of a circle?
A grouping of the members within a set based on a shared characteristic.
Sector area = (n/360) X (pi)r^2
Two angles whose sum is 180.
...multiply by 100.

3. What is it called when a point is reflected to the quadrant opposite it (i.e. I to III or II to IV)?
2
Triangles with same measure and same side lengths.
4725
A reflection about the origin.

4. Simplify 9^(1/2) X 4^3 X 2^(-6)?
3
F(x) + c
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
16.6666%

5. What is the set of elements which can be found in either A or B?
4:5
1
The union of A and B.
Even

6. 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?
27^(-4)
N! / (k!)(n-k)!
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
20.5

7. Evaluate 3& 2/7 / 1/3
83.333%
x^(6-3) = x^3
(amount of increase/original price) x 100%
9 & 6/7

8. 200 <_ x <_ 300. How many values of x are divisible by 5 & 8?
1
3
8
(a + b)^2

9. 5/6 in percent?
1
90pi
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
83.333%

10. How to determine percent decrease?
Sector area = (n/360) X (pi)r^2
(amount of decrease/original price) x 100%
II
When the function is not defined for all real numbers -; only a subset of the real numbers.

11. How to determine percent increase?
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
Pi is the ratio of a circle'S circumference to its diameter.
(a - b)(a + b)
(amount of increase/original price) x 100%

12. What is the 'domain' of a function?
The point of intersection of the systems.
3sqrt4
2(pi)r^2 + 2(pi)rh
The set of input values for a function.

13. P and r are factors of 100. What is greater - pr or 100?
x^(2(4)) =x^8 = (x^4)^2
An expression with just one term (-6x - 2a^2)
Indeterminable.
A 30-60-90 triangle.

14. What is the 'Range' of a function?
The set of output values for a function.
10! / (10-3)! = 720
(b + c)
From northeast - counterclockwise. I - II - III - IV

15. 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?
441000 = 1 10 10 10 21 * 21
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
Even
55%

16. Can you subtract 3sqrt4 from sqrt4?
1/2 times 7/3
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.
III

17. What number between 70 & 75 - inclusive - has the greatest number of factors?
75:11
72
A = pi(r^2)
1/a^6

18. Area of a triangle?
A tangent is a line that only touches one point on the circumference of a circle.
0
(base*height) / 2
Sqrt 12

19. x^4 + x^7 =
12.5%
1/(x^y)
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
x^(4+7) = x^11

20. What is the surface area of a cylinder with radius 5 and height 8?
5
130pi
10! / 3!(10-3)! = 120
The empty set - denoted by a circle with a diagonal through it.

21. 10<all primes<20
6
11 - 13 - 17 - 19
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
The point of intersection of the systems.

22. 10^6 has how many zeroes?
The interesection of A and B.
Angle/360 x (pi)r^2
Its last two digits are divisible by 4.
6

23. Pi is a ratio of what to what?

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24. What is the 'Solution' for a system of linear equations?
Pi is the ratio of a circle'S circumference to its diameter.
2sqrt6
The point of intersection of the systems.
No - the input value has exactly one output.

25. What is the common monomial factor in the expression 4(c^3)d - (c^2)(d^2) + 2cd?
Cd
The interesection of A and B.
4:5
8

26. What does the graph (x+2)^2 + (y+2)^2 = 9 look like?
1
A circle centered at -2 - -2 with radius 3.
(a - b)(a + b)
2 & 3/7

27. 413.03 x 10^(-4) =
413.03 / 10^4 (move the decimal point 4 places to the left)
2^9 / 2 = 256
1/2 times 7/3
C = 2(pi)r

28. 5x^2 - 35x -55 = 0
Factors are few - multiples are many.
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
y = (x + 5)/2
13

29. 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.
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
2sqrt6
28. n = 8 - k = 2. n! / k!(n-k)!

30. 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?
The curve opens downward and the vertex is the maximum point on the graph.
10! / (10-3)! = 720
2.592 kg
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...

31. What is the side length of an equilateral triangle with altitude 6?
Triangles with same measure and same side lengths.
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...
An isosceles right triangle.
No - only like radicals can be added.

32. What is the coefficient of the x^2 term in the product of (x + 1)(x + 2)(x -1)?
72
The sum of its digits is divisible by 3.
2
.0004809 X 10^11

33. What is the ratio of the sides of an isosceles right triangle?
5 OR -5
1/2 times 7/3
1:1:sqrt2
23 - 29

34. From a box of 12 candles - you are to remove 5. How many different sets of 5 candles could you remove?
70
1:1:sqrt2
Divide by 100.
12! / 5!7! = 792

35. 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?
A circle centered at -2 - -2 with radius 3.
II
A 30-60-90 triangle.
$3 -500 in the 9% and $2 -500 in the 7%.

36. 1/6 in percent?
Undefined - because we can'T divide by 0.
(amount of decrease/original price) x 100%
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
16.6666%

37. What is a set with no members called?
The empty set - denoted by a circle with a diagonal through it.
C = 2(pi)r
Infinite.
Its last two digits are divisible by 4.

38. 1/2 divided by 3/7 is the same as
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
1/2 times 7/3
y = 2x^2 - 3
16.6666%

39. 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?
3 - -3
500
The curve opens upward and the vertex is the minimal point on the graph.
G(x) = {x}

40. What is an isoceles triangle?
Two equal sides and two equal angles.
A 30-60-90 triangle.
4096
27^(-4)

41. a^0 =
1
I
A reflection about the axis.
IV

42. 1/8 in percent?
A set with no members - denoted by a circle with a diagonal through it.
12.5%
Lies opposite the greater angle
A 30-60-90 triangle.

43. What is a tangent?
A tangent is a line that only touches one point on the circumference of a circle.
The set of output values for a function.
The shortest arc between points A and B on a circle'S diameter.
10! / (10-3)! = 720

44. (a^-1)/a^5
8
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)
1

45. Legs 6 - 8. Hypotenuse?
y = 2x^2 - 3
10
Ax^2 + bx + c where a -b and c are constants and a /=0
A reflection about the axis.

46. What are 'Supplementary angles?'
No - only like radicals can be added.
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
Divide by 100.
Two angles whose sum is 180.

47. If the two sides of a triangle are unequal then the longer side...
F(x) - c
Lies opposite the greater angle
An expression with just one term (-6x - 2a^2)
G(x) = {x}

48. x^6 / x^3
13pi / 2
The longest arc between points A and B on a circle'S diameter.
x^(6-3) = x^3
Pi is the ratio of a circle'S circumference to its diameter.

49. What are the smallest three prime numbers greater than 65?
67 - 71 - 73
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
31 - 37
130pi

50. Solve the quadratic equation ax^2 + bx + c= 0
An infinite set.
1
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
90