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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. Define a 'Term' -
No - only like radicals can be added.
75:11
1 & 37/132
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)

2. Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
87.5%
2^9 / 2 = 256
Yes - like radicals can be added/subtracted.
12sqrt2

3. What is the order of operations?
1/2 times 7/3
1
x^(2(4)) =x^8 = (x^4)^2
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)

4. What is the side length of an equilateral triangle with altitude 6?
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...
I
A tangent is a line that only touches one point on the circumference of a circle.
13

5. What transformation occurs if point C is reflected over the x-axis and then the y-axis?
5 OR -5
(amount of increase/original price) x 100%
A reflection about the axis.
Lies opposite the greater angle

6. a^2 - b^2
4:5
(a - b)(a + b)
y = 2x^2 - 3
72

7. From a box of 12 candles - you are to remove 5. How many different sets of 5 candles could you remove?
12! / 5!7! = 792
Undefined - because we can'T divide by 0.
72
y = (x + 5)/2

8. What is the 'union' of A and B?
The set of elements which can be found in either A or B.
61 - 67
A set with no members - denoted by a circle with a diagonal through it.
Two angles whose sum is 90.

9. 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?
x= (1.2)(.8)lw
$3 -500 in the 9% and $2 -500 in the 7%.
(amount of decrease/original price) x 100%
180 degrees

10. How to determine percent increase?
(amount of increase/original price) x 100%
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
$3 -500 in the 9% and $2 -500 in the 7%.
II

11. For similar triangles - the ratio of their corresponding sides is 2:3. What is the ratio of their areas?
Relationship cannot be determined (what if x is negative?)
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.

12. What is the graph of f(x) shifted right c units or spaces?
The direction of the inequality is reversed.
F(x-c)
The curve opens downward and the vertex is the maximum point on the graph.
Lies opposite the greater angle

13. x^(-y)=
1/(x^y)
6
(a + b)^2
53 - 59

14. What is a chord of a circle?
Area of the base X height = (pi)hr^2
Factors are few - multiples are many.
A chord is a line segment joining two points on a circle.
A 30-60-90 triangle.

15. How many sides does a hexagon have?
90 degrees
Relationship cannot be determined (what if x is negative?)
2sqrt6
6

16. What number between 70 & 75 - inclusive - has the greatest number of factors?
67 - 71 - 73
10! / (10-3)! = 720
1
72

17. P and r are factors of 100. What is greater - pr or 100?
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
Indeterminable.
1.0843 X 10^11
53 - 59

18. Formula for the area of a sector of a circle?
Sector area = (n/360) X (pi)r^2
C = (pi)d
II
37.5%

19. Reduce: 4.8 : 0.8 : 1.6
Two angles whose sum is 90.
6 : 1 : 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.
Pi is the ratio of a circle'S circumference to its diameter.

20. x^4 + x^7 =
10
x^(4+7) = x^11
Lies opposite the greater angle
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)

21. What is the 'Solution' for a system of linear equations?
The point of intersection of the systems.
Cd
6 : 1 : 2
From northeast - counterclockwise. I - II - III - IV

22. 60 < all primes <70
1/a^6
61 - 67
N! / (n-k)!
Relationship cannot be determined (what if x is negative?)

23. Factor x^2 - xy + x.
N! / (k!)(n-k)!
x(x - y + 1)
441000 = 1 10 10 10 21 * 21
10! / (10-3)! = 720

24. How to find the area of a sector?
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
Angle/360 x (pi)r^2
4096
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)

25. Volume for a cylinder?
Divide by 100.
Area of the base X height = (pi)hr^2
1:1:sqrt2
The steeper the slope.

26. What is the formula for computing simple interest?
A central angle is an angle formed by 2 radii.
A = I (1 + rt)
9 & 6/7
3

27. A number is divisible by 9 if...
Cd
The sum of digits is divisible by 9.
4a^2(b)
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.

28. 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)]?
y = (x + 5)/2
The set of elements found in both A and B.
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
True

29. 6w^2 - w - 15 = 0
(a - b)(a + b)
3/2 - 5/3
Members or elements
Angle/360 x 2(pi)r

30. Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
The sum of digits is divisible by 9.
No - the input value has exactly one output.
2sqrt6

31. What is the set of elements found in both A and B?
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
A subset.
The interesection of A and B.
48

32. 50 < all primes< 60
Area of the base X height = (pi)hr^2
(amount of increase/original price) x 100%
Relationship cannot be determined (what if x is negative?)
53 - 59

33. Can you simplify sqrt72?
Undefined
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
A reflection about the origin.

34. 70 < all primes< 80
x^(4+7) = x^11
130pi
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
71 - 73 - 79

35. Evaluate 4/11 + 11/12
An isosceles right triangle.
1 & 37/132
No - only like radicals can be added.
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.

36. The slope of a line perpendicular to (a/b)?
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 chord is a line segment joining two points on a circle.
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
Its negative reciprocal. (-b/a)

37. What is the maximum value for the function g(x) = (-2x^2) -1?
10! / (10-3)! = 720
1
71 - 73 - 79
Triangles with same measure and same side lengths.

38. Surface area for a cylinder?
(b + c)
12! / 5!7! = 792
2(pi)r^2 + 2(pi)rh
1

39. 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))?
20.5
500
(amount of increase/original price) x 100%
3

40. What is the slope of a horizontal line?
A = I (1 + rt)
0
3 - -3
The objects within a set.

41. Number of degrees in a triangle
500
180
The curve opens downward and the vertex is the maximum point on the graph.
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.

42. 10<all primes<20
11 - 13 - 17 - 19
F(x) - c
(b + c)
18

43. Which quadrant is the upper right hand?
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)
6
I
The greatest value minus the smallest.

44. 40 < all primes<50
1/2 times 7/3
41 - 43 - 47
288 (8 9 4)
Angle/360 x 2(pi)r

45. A cylinder has a surface area of 22pi. If the cylinder has a height of 10 - what is the radius?
1
Cd
True
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)

46. a^2 - b^2 =
8
(a - b)(a + b)
90pi
(n-2) x 180

47. What is the surface area of a cylinder with radius 5 and height 8?
An arc is a portion of a circumference of a circle.
130pi
4:5
441000 = 1 10 10 10 21 * 21

48. (x^2)^4
I
x^(2(4)) =x^8 = (x^4)^2
75:11
No - only like radicals can be added.

49. What are the smallest three prime numbers greater than 65?
67 - 71 - 73
Arc length = (n/360) x pi(2r) where n is the number of degrees.
(a - b)(a + 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)

50. Suppose that the graph of f(x) is the result of sliding the graph of y=2x^2 down 3 units of spaces. What is the new equation?
True
Infinite.
y = 2x^2 - 3
55%