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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. If the two sides of a triangle are unequal then the longer side...
6
2.592 kg
The sum of digits is divisible by 9.
Lies opposite the greater angle

2. 6w^2 - w - 15 = 0
1
C = 2(pi)r
3/2 - 5/3
A circle centered on the origin with radius 8.

3. If 10800 is invested at a simple interest rate of 4% - what is the value of the investment after 18 months?
10! / (10-3)! = 720
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
$11 -448
0

4. 20<all primes<30
When the function is not defined for all real numbers -; only a subset of the real numbers.
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
23 - 29
An angle which is supplementary to an interior angle.

5. Solve the quadratic equation ax^2 + bx + c= 0
Ax^2 + bx + c where a -b and c are constants and a /=0
The empty set - denoted by a circle with a diagonal through it.
Diameter(Pi)
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a

6. Suppose that the graph of f(x) is the result of stretching y=x + 5 away from the x-axis by a factor of 2. What is the new equation for the graph f(x)?
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
y = (x + 5)/2
An isosceles right triangle.
An expression with just one term (-6x - 2a^2)

7. 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.
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
Undefined
28. n = 8 - k = 2. n! / k!(n-k)!

8. In a triangle inscribed inside a circle - where the diameter is one side of the triangle - which angle is largest?
61 - 67
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
12! / 5!7! = 792
16.6666%

9. What are the irrational numbers?

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10. 1:1:sqrt2 is the ratio of the sides of what kind of triangle?
An infinite set.
(a + b)^2
Its divisible by 2 and by 3.
An isosceles right triangle.

11. 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?
67 - 71 - 73
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
N! / (n-k)!
A central angle is an angle formed by 2 radii.

12. How to find the area of a sector?
Triangles with same measure and same side lengths.
4.25 - 6 - 22
Relationship cannot be determined (what if x is negative?)
Angle/360 x (pi)r^2

13. A number is divisible by 9 if...
18
62.5%
The empty set - denoted by a circle with a diagonal through it.
The sum of digits is divisible by 9.

14. What is a subset?
(a + b)^2
A grouping of the members within a set based on a shared characteristic.
55%
An arc is a portion of a circumference of a circle.

15. a^2 - b^2
A circle centered at -2 - -2 with radius 3.
The shortest arc between points A and B on a circle'S diameter.
(a - b)(a + b)
Move the decimal point to the right x places

16. If Madagascar'S exports totaled 1.3 billion in 2009 - and 4% came from China - what was the value in millions of the country'S exports to China?
52
288 (8 9 4)
1/a^6
y = 2x^2 - 3

17. What is a finite set?
41 - 43 - 47
A tangent is a line that only touches one point on the circumference of a circle.
90
A set with a number of elements which can be counted.

18. 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
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 point of intersection of the systems.
When the function is not defined for all real numbers -; only a subset of the real numbers.

19. x^4 + x^7 =
10
A set with a number of elements which can be counted.
x^(4+7) = x^11
(12/2) x (sqrt15 / sqrt5) = 6sqrt3

20. A number is divisible by 3 if ...
2sqrt6
The sum of its digits is divisible by 3.
1 & 37/132
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.

21. The four angles around a point measure y - 2y - 35 and 55 respectively. What is the value of y?
90
16.6666%
9 & 6/7
1 & 37/132

22. What is the percent formula?
III
Part = Percent X Whole
A central angle is an angle formed by 2 radii.
.0004809 X 10^11

23. Simplify the expression (p^2 - q^2)/ -5(q - p)
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
61 - 67
Sector area = (n/360) X (pi)r^2
(p + q)/5

24. Which is greater? 27^(-4) or 9^(-8)
II
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
3sqrt4
27^(-4)

25. What is the maximum value for the function g(x) = (-2x^2) -1?
41 - 43 - 47
IV
1
12! / 5!7! = 792

26. How to find the diagonal of a rectangular solid?
The set of elements which can be found in either A or B.
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
3
Two angles whose sum is 180.

27. What are congruent triangles?
Triangles with same measure and same side lengths.
$11 -448
The third side is greater than the difference and less than the sum.
Its last two digits are divisible by 4.

28. What is an exterior angle?
An angle which is supplementary to an interior angle.
Its negative reciprocal. (-b/a)
130pi
Factors are few - multiples are many.

29. 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)]?
True
1/a^6
Even
A grouping of the members within a set based on a shared characteristic.

30. What is the graph of f(x) shifted downward c units or spaces?
F(x) - c
y = 2x^2 - 3
The set of input values for a function.
A tangent is a line that only touches one point on the circumference of a circle.

31. x^(-y)=
Two angles whose sum is 180.
1/(x^y)
The direction of the inequality is reversed.
(a - b)(a + b)

32. 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?
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/(x^y)
N! / (k!)(n-k)!
A = pi(r^2)

33. a^0 =
1
1:1:sqrt2
2
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.

34. If an inequality is multiplied or divided by a negative number....
Undefined - because we can'T divide by 0.
N! / (n-k)!
The direction of the inequality is reversed.
3 - -3

35. x^2 = 9. What is the value of x?
3 - -3
1/(x^y)
An infinite set.
$3 -500 in the 9% and $2 -500 in the 7%.

36. What is the graph of f(x) shifted left c units or spaces?
F(x + c)
F(x-c)
The empty set - denoted by a circle with a diagonal through it.
500

37. What transformation occurs if point C is reflected over the x-axis and then the y-axis?
A reflection about the axis.
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)
F(x) + c
83.333%

38. Surface area for a cylinder?
2(pi)r^2 + 2(pi)rh
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...
61 - 67
A 30-60-90 triangle.

39. The objects in a set are called two names:
12! / 5!7! = 792
Members or elements
All numbers multiples of 1.
x^(6-3) = x^3

40. Which quandrant is the lower right hand?
IV
From northeast - counterclockwise. I - II - III - IV
1:sqrt3:2
The curve opens downward and the vertex is the maximum point on the graph.

41. What is the side length of an equilateral triangle with altitude 6?
Diameter(Pi)
Divide by 100.
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...
The steeper the slope.

42. 30< all primes<40
Pi is the ratio of a circle'S circumference to its diameter.
31 - 37
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
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

43. What are 'Supplementary angles?'
Two angles whose sum is 180.
An infinite set.
180
87.5%

44. When the 'a' in a parabola is positive....
1
The curve opens upward and the vertex is the minimal point on the graph.
37.5%
4a^2(b)

45. What percent of 40 is 22?
55%
1:sqrt3:2
x^(2(4)) =x^8 = (x^4)^2
31 - 37

46. Formula for the area of a circle?
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 = pi(r^2)
1
The point of intersection of the systems.

47. Formula of rectangle where l increases by 20% and w decreases by 20%
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
288 (8 9 4)
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
x= (1.2)(.8)lw

48. There are 10 finalists for the school spelling bee. A first - second - and third place trophy will be awarded. How many different people can get the three prizes?
A subset.
10! / 3!(10-3)! = 120
Yes - like radicals can be added/subtracted.
130pi

49. 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
An expression with just one term (-6x - 2a^2)
Angle/360 x 2(pi)r

50. What is the 'Range' of a series of numbers?
The greatest value minus the smallest.
Indeterminable.
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
Area of the base X height = (pi)hr^2