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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. Ratio of ages of Anna and Emma is 3:5 and of Emma and Nicolas is 3:5. What is the ratio of Anna to Nicholas' ages?
10
20.5
9 : 25
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)

2. What is the formula for computing simple interest?
The direction of the inequality is reversed.
(a - b)(a + b)
A = I (1 + rt)
x= (1.2)(.8)lw

3. Can the input value of a function have more than one output value (i.e. x: y - y1)?
1.0843 X 10^11
90pi
When the function is not defined for all real numbers -; only a subset of the real numbers.
No - the input value has exactly one output.

4. 5x^2 - 35x -55 = 0
130pi
3
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
(a + b)^2

5. What is the name for a grouping of the members within a set based on a shared characteristic?
31 - 37
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
A subset.

6. What is the graph of f(x) shifted downward c units or spaces?
3 - -3
F(x) - c
(a - b)^2
2sqrt6

7. What is the ratio of the sides of an isosceles right triangle?
1:1:sqrt2
Its divisible by 2 and by 3.
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
Two angles whose sum is 180.

8. x^(-y)=
1/(x^y)
Cd
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
Members or elements

9. x^6 / x^3
An infinite set.
I
x^(6-3) = x^3
A grouping of the members within a set based on a shared characteristic.

10. Formula for the area of a circle?
The curve opens upward and the vertex is the minimal point on the graph.
Its negative reciprocal. (-b/a)
A = pi(r^2)
1/2 times 7/3

11. Can you simplify sqrt72?
1:1:sqrt2
(a + b)^2
6 : 1 : 2
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.

12. A number is divisible by 3 if ...
A circle centered at -2 - -2 with radius 3.
x^(4+7) = x^11
500
The sum of its digits is divisible by 3.

13. Write 10 -843 X 10^7 in scientific notation
Pi is the ratio of a circle'S circumference to its diameter.
12! / 5!7! = 792
6
1.0843 X 10^11

14. Evaluate 4/11 + 11/12
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
62.5%
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
1 & 37/132

15. Reduce: 4.8 : 0.8 : 1.6
The set of elements which can be found in either A or B.
1
The curve opens downward and the vertex is the maximum point on the graph.
6 : 1 : 2

16. What is it called when a point is reflected to the quadrant opposite it (i.e. I to III or II to IV)?
Area of the base X height = (pi)hr^2
A = I (1 + rt)
The direction of the inequality is reversed.
A reflection about the origin.

17. The larger the absolute value of the slope...
x= (1.2)(.8)lw
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
The steeper the slope.
y = (x + 5)/2

18. 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)
2
A subset.
90 degrees
4.25 - 6 - 22

19. Number of degrees in a triangle
(n-2) x 180
180
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
F(x) + c

20. A number is divisible by 4 is...
3
Its last two digits are divisible by 4.
The curve opens downward and the vertex is the maximum point on the graph.
1

21. Simplify 9^(1/2) X 4^3 X 2^(-6)?
53 - 59
(a - b)(a + b)
3
(a - b)(a + b)

22. What does the graph x^2 + y^2 = 64 look like?
Ax^2 + bx + c where a -b and c are constants and a /=0
A circle centered on the origin with radius 8.
... the square of the ratios of the corresponding sides.
The two xes after factoring.

23. 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?
62.5%
N! / (n-k)!
The objects within a set.
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15

24. What is the 'Range' of a function?
The set of output values for a function.
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
2 & 3/7

25. Formula to find a circle'S circumference from its radius?
Sector area = (n/360) X (pi)r^2
Members or elements
A set with no members - denoted by a circle with a diagonal through it.
C = 2(pi)r

26. 0^0
1/2 times 7/3
Pi is the ratio of a circle'S circumference to its diameter.
3 - -3
Undefined

27. 1/6 in percent?
An expression with just one term (-6x - 2a^2)
Members or elements
16.6666%
.0004809 X 10^11

28. What is the 'union' of A and B?
An arc is a portion of a circumference of a circle.
y = 2x^2 - 3
A central angle is an angle formed by 2 radii.
The set of elements which can be found in either A or B.

29. What is the ratio of the sides of a 30-60-90 triangle?
1:sqrt3:2
1.7
An infinite set.
10! / 3!(10-3)! = 120

30. Solve the quadratic equation ax^2 + bx + c= 0
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
Area of the base X height = (pi)hr^2
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
(a + b)^2

31. Simplify the expression [(b^2 - c^2) / (b - c)]
A circle centered at -2 - -2 with radius 3.
(b + c)
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
71 - 73 - 79

32. Define an 'expression'.
Sector area = (n/360) X (pi)r^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)
The set of output values for a function.
180

33. If 4500 is invested at a simple interest rate of 6% - what is the value of the investment after 10 months?
4725
87.5%
70
130pi

34. A number is divisible by 9 if...
The sum of digits is divisible by 9.
Its last two digits are divisible by 4.
Sqrt 12
2 & 3/7

35. What is the graph of f(x) shifted left c units or spaces?
F(x + c)
90
4a^2(b)
Pi is the ratio of a circle'S circumference to its diameter.

36. Length of an arc of a circle?
27^(-4)
70
Angle/360 x 2(pi)r
All numbers multiples of 1.

37. If the two sides of a triangle are unequal then the longer side...
18
Lies opposite the greater angle
23 - 29
Area of the base X height = (pi)hr^2

38. How to find the circumference of a circle which circumscribes a square?
x^(4+7) = x^11
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
90pi
x= (1.2)(.8)lw

39. The ratio of the areas of two similar polygons is ...
Relationship cannot be determined (what if x is negative?)
... the square of the ratios of the corresponding sides.
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

40. How to find the area of a sector?
Angle/360 x (pi)r^2
Yes. [i.e. f(x) = x^2 - 1
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
72

41. 4.809 X 10^7 =
.0004809 X 10^11
6 : 1 : 2
75:11
2

42. Which is greater? 27^(-4) or 9^(-8)
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
F(x) - c
2sqrt6
27^(-4)

43. Evaluate 3& 2/7 / 1/3
The greatest value minus the smallest.
9 & 6/7
1.7
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.

44. 6w^2 - w - 15 = 0
3/2 - 5/3
A tangent is a line that only touches one point on the circumference of a circle.
No - only like radicals can be added.
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)

45. Whats the difference between factors and multiples?
The empty set - denoted by a circle with a diagonal through it.
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
Factors are few - multiples are many.
x^(4+7) = x^11

46. The perimeter of a square is 48 inches. The length of its diagonal is:
12.5%
12sqrt2
From northeast - counterclockwise. I - II - III - IV
The curve opens upward and the vertex is the minimal point on the graph.

47. 60 < all primes <70
12.5%
10! / 3!(10-3)! = 120
61 - 67
10

48. 1:1:sqrt2 is the ratio of the sides of what kind of triangle?
180
The set of input values for a function.
An isosceles right triangle.
Angle/360 x (pi)r^2

49. 20<all primes<30
A tangent is a line that only touches one point on the circumference of a circle.
16.6666%
23 - 29
Move the decimal point to the right x places

50. What is the order of operations?
10
Members or elements
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)