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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. (12sqrt15) / (2sqrt5) =
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
41 - 43 - 47
(b + c)
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...

2. What is the set of elements which can be found in either A or B?
Factors are few - multiples are many.
All numbers multiples of 1.
The union of A and B.
1/2 times 7/3

3. How to determine percent decrease?
(amount of decrease/original price) x 100%
... the square of the ratios of the corresponding sides.
Undefined
2

4. How many sides does a hexagon have?
Angle/360 x (pi)r^2
90pi
6
16.6666%

5. Simplify the expression (p^2 - q^2)/ -5(q - p)
4.25 - 6 - 22
(p + q)/5
An angle which is supplementary to an interior angle.
11 - 13 - 17 - 19

6. (x^2)^4
Two angles whose sum is 180.
x^(2(4)) =x^8 = (x^4)^2
3
The set of input values for a function.

7. 7/8 in percent?
Two angles whose sum is 180.
90
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)
87.5%

8. What is the graph of f(x) shifted right c units or spaces?
Its divisible by 2 and by 3.
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)
130pi
F(x-c)

9. 50 < all primes< 60
53 - 59
Two equal sides and two equal angles.
Arc length = (n/360) x pi(2r) where n is the number of degrees.
(a - b)(a + b)

10. Reduce: 4.8 : 0.8 : 1.6
A reflection about the axis.
IV
6 : 1 : 2
55%

11. How to find the area of a sector?
11 - 13 - 17 - 19
Angle/360 x (pi)r^2
True
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.

12. Define an 'expression'.
x^(4+7) = x^11
1:sqrt3:2
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)
8

13. Describe the relationship between 3x^2 and 3(x - 1)^2
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
12.5%
Angle/360 x (pi)r^2
F(x) + c

14. 10<all primes<20
11 - 13 - 17 - 19
Its last two digits are divisible by 4.
Its negative reciprocal. (-b/a)
31 - 37

15. 6w^2 - w - 15 = 0
Two angles whose sum is 180.
3/2 - 5/3
x^(6-3) = x^3
Its divisible by 2 and by 3.

16. What is the 'union' of A and B?
The set of elements which can be found in either A or B.
(base*height) / 2
N! / (n-k)!
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)

17. In a triangle where the two legs are 4 and 3 - what is the value of a line directly intersecting the middle coming from the meeting point of the two legs?
A tangent is a line that only touches one point on the circumference of a circle.
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
(a + b)^2
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.

18. Which quadrant is the upper right hand?
Members or elements
72
$11 -448
I

19. What is a parabola?
67 - 71 - 73
y = (x + 5)/2
Ax^2 + bx + c where a -b and c are constants and a /=0
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).

20. A number is divisible by 6 if...
Its divisible by 2 and by 3.
2
.0004809 X 10^11
A set with no members - denoted by a circle with a diagonal through it.

21. 413.03 x 10^(-4) =
...multiply by 100.
413.03 / 10^4 (move the decimal point 4 places to the left)
A subset.
71 - 73 - 79

22. Factor a^2 + 2ab + b^2
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
4725
Pi is the ratio of a circle'S circumference to its diameter.
(a + b)^2

23. What is a finite set?
The sum of digits is divisible by 9.
x(x - y + 1)
A set with a number of elements which can be counted.
A set with no members - denoted by a circle with a diagonal through it.

24. For what values should the domain be restricted for the function f(x) = sqrt(x + 8)
9 : 25
C = (pi)d
3
8

25. Convert 0.7% to a fraction.
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
31 - 37
413.03 / 10^4 (move the decimal point 4 places to the left)
7 / 1000

26. If r - t - s & u are distinct - consecutive prime numbers - less than 31 - which of the following could be an average of them (4 - 4.25 - 6 - 9 - 24 - 22 - 24)
4.25 - 6 - 22
2^9 / 2 = 256
F(x) + c
1:sqrt3:2

27. Which is greater? 64^5 or 16^8
The greatest value minus the smallest.
Move the decimal point to the right x places
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
I

28. Max and Min lengths for a side of a triangle?
A tangent is a line that only touches one point on the circumference of a circle.
37.5%
The third side is greater than the difference and less than the sum.
Members or elements

29. What are 'Supplementary angles?'
Two angles whose sum is 180.
1:sqrt3:2
Yes - like radicals can be added/subtracted.
The sum of its digits is divisible by 3.

30. What is a set with no members called?
The empty set - denoted by a circle with a diagonal through it.
12sqrt2
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
6 : 1 : 2

31. How to find the diagonal of a rectangular solid?
Infinite.
Angle/360 x (pi)r^2
The curve opens upward and the vertex is the minimal point on the graph.
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).

32. How to determine percent increase?
(amount of increase/original price) x 100%
5
0
83.333%

33. Legs: 3 - 4. Hypotenuse?
5
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
2.592 kg
2^9 / 2 = 256

34. a^2 + 2ab + b^2
(n-2) x 180
1 & 37/132
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
(a + b)^2

35. a^2 - 2ab + b^2
(a - b)^2
Members or elements
IV
90 degrees

36. Simplify the expression [(b^2 - c^2) / (b - c)]
7 / 1000
(b + c)
A central angle is an angle formed by 2 radii.
The set of elements found in both A and B.

37. Legs 6 - 8. Hypotenuse?
Angle/360 x 2(pi)r
10
3
(b + c)

38. What is the slope of a vertical line?

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39. 60 < all primes <70
41 - 43 - 47
A chord is a line segment joining two points on a circle.
1.7
61 - 67

40. Can you subtract 3sqrt4 from sqrt4?
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
2sqrt6
II
Yes - like radicals can be added/subtracted.

41. 1:1:sqrt2 is the ratio of the sides of what kind of triangle?
Relationship cannot be determined (what if x is negative?)
An isosceles right triangle.
(a - b)^2
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.

42. What is a minor arc?

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43. a^2 - b^2 =
The steeper the slope.
An infinite set.
(a - b)(a + b)
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.

44. 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)]?
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
90pi
An arc is a portion of a circumference of a circle.
True

45. To convert a decimal to a percent...
23 - 29
... the square of the ratios of the corresponding sides.
0
...multiply by 100.

46. Simplify (a^2 + b)^2 - (a^2 - b)^2
5
The objects within a set.
4a^2(b)
(amount of decrease/original price) x 100%

47. Factor x^2 - xy + x.
F(x) - c
The longest arc between points A and B on a circle'S diameter.
x(x - y + 1)
A = pi(r^2)

48. In similar hexagons - the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
Angle/360 x (pi)r^2
The sum of its digits is divisible by 3.
4:5
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).

49. A cylinder has surface area 22pi. If the cylinder has a height of 10 - what is its radius?
0
Even
1
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)

50. Solve the quadratic equation ax^2 + bx + c= 0
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
Angle/360 x (pi)r^2
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
The set of elements found in both A and B.