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GRE Math: Common Errors

Subjects : gre, math

Instructions:

Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
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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 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?
N! / (n-k)!
23 - 29
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
True

2. There are 10 finalists for the school spelling bee. A first - second - and third place trophy will be awarded. In how many ways can the judges award the 3 prizes?
Sector area = (n/360) X (pi)r^2
10! / (10-3)! = 720
3
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16

3. What is the name for a grouping of the members within a set based on a shared characteristic?
An expression with just one term (-6x - 2a^2)
A subset.
Infinite.
A circle centered on the origin with radius 8.

4. What are the real numbers?
83.333%
II
4.25 - 6 - 22
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)

5. What is the side length of an equilateral triangle with altitude 6?
When the function is not defined for all real numbers -; only a subset of the real numbers.
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...
Members or elements
A set with a number of elements which can be counted.

6. Which quadrant is the upper left hand?
x^(4+7) = x^11
12! / 5!7! = 792
An angle which is supplementary to an interior angle.
II

7. If 10800 is invested at a simple interest rate of 4% - what is the value of the investment after 18 months?
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
A subset.
$11 -448
... the square of the ratios of the corresponding sides.

8. If 8 schools are in a conference - how many games are played if each team plays each other exactly once?
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
2.592 kg
3/2 - 5/3
28. n = 8 - k = 2. n! / k!(n-k)!

9. 7/8 in percent?
87.5%
Arc length = (n/360) x pi(2r) where n is the number of degrees.
Part = Percent X Whole
(a + b)^2

10. Whats the difference between factors and multiples?
Indeterminable.
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
Factors are few - multiples are many.
x(x - y + 1)

11. What is the surface area of a cylinder with radius 5 and height 8?
13pi / 2
x^(6-3) = x^3
130pi
G(x) = {x}

12. 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?
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
Infinite.
1
9 : 25

13. What are congruent triangles?
An angle which is supplementary to an interior angle.
C = 2(pi)r
48
Triangles with same measure and same side lengths.

14. Can the input value of a function have more than one output value (i.e. x: y - y1)?
No - the input value has exactly one output.
5 OR -5
1 & 37/132
x= (1.2)(.8)lw

15. What is the area of a regular hexagon with side 6?
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
When the function is not defined for all real numbers -; only a subset of the real numbers.
Lies opposite the greater angle
F(x) - c

16. If the 80th percentile of the measurements is 72degrees - about how many measurments are between 69 degrees and 72 degrees? Round your answer to the nearest tenth
1
Move the decimal point to the right x places
18
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.

17. To multiply a number by 10^x
Move the decimal point to the right x places
The set of output values for a function.
The steeper the slope.
Two angles whose sum is 90.

18. What is a minor arc?

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19. Evaluate 3& 2/7 / 1/3
1.7
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
9 & 6/7

20. What are the integers?
(amount of decrease/original price) x 100%
III
Sector area = (n/360) X (pi)r^2
All numbers multiples of 1.

21. 20<all primes<30
1
23 - 29
6
2

22. 1/2 divided by 3/7 is the same as
62.5%
...multiply by 100.
1/2 times 7/3
No - the input value has exactly one output.

23. Legs 6 - 8. Hypotenuse?
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.
10
Yes - like radicals can be added/subtracted.
90pi

24. (a^-1)/a^5
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
1/a^6
(b + c)
1.7

25. Evaluate 4/11 + 11/12
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
1 & 37/132
A central angle is an angle formed by 2 radii.
$11 -448

26. What is a set with no members called?
The empty set - denoted by a circle with a diagonal through it.
A central angle is an angle formed by 2 radii.
23 - 29
N! / (k!)(n-k)!

27. a^2 + 2ab + b^2
Divide by 100.
3
(base*height) / 2
(a + b)^2

28. 200 <_ x <_ 300. How many values of x are divisible by 5 & 8?
3
8
13pi / 2
A = I (1 + rt)

29. What are the irrational numbers?

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30. (-1)^2 =
0
1/a^6
x^(6-3) = x^3
1

31. 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)?
y = (x + 5)/2
(a + b)^2
A grouping of the members within a set based on a shared characteristic.
A set with no members - denoted by a circle with a diagonal through it.

32. What percent of 40 is 22?
55%
(a - b)(a + b)
Angle/360 x 2(pi)r
Two angles whose sum is 180.

33. How to find the circumference of a circle which circumscribes a square?
1/(x^y)
12sqrt2
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
x^(2(4)) =x^8 = (x^4)^2

34. 5x^2 - 35x -55 = 0
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
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)
x^(6-3) = x^3
C = (pi)d

35. Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
(b + c)
Sector area = (n/360) X (pi)r^2
1.7
2sqrt6

36. a^2 - 2ab + b^2
F(x) + c
(a - b)^2
1 & 37/132
IV

37. What is the 'domain' of a function?
Relationship cannot be determined (what if x is negative?)
The set of input values for a function.
Diameter(Pi)
When the function is not defined for all real numbers -; only a subset of the real numbers.

38. Simplify (a^2 + b)^2 - (a^2 - b)^2
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
9 & 6/7
IV
4a^2(b)

39. What is a finite set?
A set with a number of elements which can be counted.
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
10! / (10-3)! = 720
4725

40. 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?
288 (8 9 4)
True
441000 = 1 10 10 10 21 * 21
C = (pi)d

41. What is the ratio of the sides of an isosceles right triangle?
1:1:sqrt2
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
... the square of the ratios of the corresponding sides.
$11 -448

42. 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?
The greatest value minus the smallest.
130pi
x^(2(4)) =x^8 = (x^4)^2
$3 -500 in the 9% and $2 -500 in the 7%.

43. What is a chord of a circle?
A chord is a line segment joining two points on a circle.
A 30-60-90 triangle.
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
When the function is not defined for all real numbers -; only a subset of the real numbers.

44. What is the set of elements found in both A and B?
The interesection of A and B.
12sqrt2
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
(12/2) x (sqrt15 / sqrt5) = 6sqrt3

45. The perimeter of a square is 48 inches. The length of its diagonal is:
(amount of increase/original price) x 100%
12sqrt2
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
$3 -500 in the 9% and $2 -500 in the 7%.

46. In a triangle inscribed inside a circle - where the diameter is one side of the triangle - which angle is largest?
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
Two equal sides and two equal angles.
11 - 13 - 17 - 19
62.5%

47. Formula for the area of a circle?
Members or elements
180 degrees
A = pi(r^2)
Two angles whose sum is 90.

48. When does a function automatically have a restricted domain (2)?
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
The interesection of A and B.
Part = Percent X Whole
The sum of digits is divisible by 9.

49. A number is divisible by 3 if ...
y = 2x^2 - 3
The sum of digits is divisible by 9.
1/2 times 7/3
The sum of its digits is divisible by 3.

50. How many 3-digit positive integers are even and do not contain the digit 4?
23 - 29
6
288 (8 9 4)
37.5%

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GRE Math: Common Errors

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