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10 > Arithmetic reasoning > Flashcards

Arithmetic reasoning Flashcards

0
Q

Average

Standard deviation

A

Arithmetic mean
Take the sum of n numbers and divide by n
1
[Population] Standard deviation = sqrt (— sum(xi - xbar)^2)
N

                                                     1 Sample Standard deviation = sqrt(——  sum(xi - xbar)^2)
                                                   (N-1)
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1
Q

1 mi = ? ft

A

1mi = 5,280 ft

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2
Q

Median of odd # of Data

A

The middle # if the data is listed in increasing order.

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3
Q

Median of an even # of data

A

Arithmetic mean (average) of the two middle numbers when the data is listed in increasing order.

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4
Q

Mode

A

Most frequently occurring # in the list. There may be more than one mode for a list of data

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5
Q

Range

A

Greatest # in the list - least #

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6
Q

Interquartile range

A 
3rd quartile - 1st quartile
To divide data into quartiles:
1) arrange in increasing order
2)find median M. M = Q2
3) divide data into 2 equal groups, find their median, it is Q1 and Q3
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10
Q

x + y = -1

Quantity A QuantityB
x y

A

One equation, 2 unknowns,
D) the relationship cannot be determined from the information given.

Can also plug in
x = 0
Then
y = 0

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11
Q

A certain store sells two types of pens: one type for $2 per pen and the other type for $3 per pen. If a customer can spend up to $25 to buy pens at the store and there is no sales tax, what is the greatest # of pens the customer can buy?

A

Start by looking at how many of the lesser value, $2, pens the customer can buy if the customer doesn’t buy any $3 pens.
25/2 = 12.5 .
So 12 pens for $2, 0 pens for $3.

Next consider $3 pens
11 $2 pens ($22) and 1 $3 pen = 12 pens total
10 $2 pens ($20) and 1 $3 pen = 11 pens total
9 $2 pens ($18) and 2 $3 pen= 11 pens total.

As the # of $2 pens decreases the total # of pens decreases.
Therefore max amount = 12 pens

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12
Q

A list of numbers has a mean of 8 and standard deviation of 2.5. If x is a # in the list that is 2 standard deviations above the mean, what is the value of x?

A 
x = 2(2.5) + 8
x = 13
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13
Q

The following table shows the distribution of 200,000 physicians by specialty. Which of the following sectors represent more than 40,000 physicians?

A. Pediatrics - 21%
B. Internal Medicine - 25%
C. Surgery - 24%
D. Anesthesiology - 3%
E. Psychiatry - 6%
A

Find what percent of 200,000 is 40,000

40,000/200,000 = 0.2 = 20%

choices over 20% are A, B, C.

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16
Q

Profit

A

Profit, or gross profit = sales revenue - cost of production

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17
Q

If n is the integer, what is the sum of first two consecutive integers greater than n + 6?

A

(n+7)+(n+8)

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18
Q

In 2009 the property tax on each home in Town X was p percent of the assessed value of the home, where p is a constant. The property tax in 2009 on a home in Town X that had an assessed value of $125, 000 was $2, 500
Quantity A QuantityB
The property tax in 2009 on $3,000
a home in Town X that had
an assessed value of
$160, 000

A 
$125,000p = $2,500
P = 125000/2500
P = 0.02 or 2%

2% of $160,000 is
160,000 * 0.02 = 3,200

3,200 > 3000
A>B

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19
Q

Congruent angles

A

Angles that have equal measures. Opposite angles

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20
Q

Acute angle

A

Less than 90 degrees

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21
Q

Obtuse angle

A

Angle b/w 90 and 180 degrees

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22
Q

Convex polygon

A

A polygon in which the measure of each interior angle is less than 180 degrees

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23
Q

Sum of interior angles of a polygon

A

(n-2)*180

Sum of hexagon (6-2)180=720

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24
Q

Regular polygon

A

A polygon in which all sides are congruent and all interior angles are congruent.

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25
Q

Quadrilateral

A

4 sided polygon

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26
Q

Equilateral triangle

A

Triangle with three congruent sides

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27
Q

Isosceles triangle

A

A triangle with at least two congruent sides

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28
Q

Congruent triangles

A

Two triangles that have the same shape and size

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29
Q

Similar triangles

A

Two triangles that have the same shape but not the same size

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30
Q

Area of a parallelogram

A

Same as area of a square or rectangle or any quadrilateral.

Area = base* height

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31
Q

Area of trapezoid

A

Area of the trapezoid equals alf the product of the sum of the lengths of the two parallel sides b1 and b2 and the corresponding height h; that is,
A=1/2(b1+b2)*h

32
Q

Congruent circles

A

Circles with equal radii

33
Q

Chord

A

Any line segment joining two points on the circle

34
Q

Pi

A

Ratio of circumference of a circle to it’s diameter
C 22
– = pi = 3.14 = —–
d 7

35
Q

Circumference of a circle

A

C= 2pi*r

36
Q

Arc length of a circle

A

Ratio of length of an arc to the circumference
Is equal to the
Ratio of the degree measure of the arc to 360.

37
Q

Area of a circle

A

A = pi*r^2

38
Q

Area of a sector S of a circle

A

The ratio of the area of a sector of a circle to the area of the entire circle
Is equal to
The ratio of the degree measure of it’s arc to 360.

39
Q

Concentric circles

A

Two or more circles with the same center.

40
Q

Surface area of a right circular cylinder

A

Acyl = 2pir^2 + 2pir*h

41
Q

Frequency

A

Count # of times the category or value appears

42
Q

Relative frequency

A

The associated frequency divided by total # of data.
Example:
Number of children Frequency Relative frequency
0 3 3/25 = 12%
1 5 3/25 = 20%
2 7 7/25 = 28%
3 6 6/25 = 24%
4 3 3/25 = 12%
5 1 1/25 = 4%
——————————————————————————–
Total: 25

43
Q

Histogram

A

Histograms are graphs of frequency distributions that are similar to bar graphs, but they have a number line for the horizontal axis. Any spaces between bars on a histogram indicate that there are no data in the intervals represented by the spaces

44
Q

Weighted mean

A

Ex: 2,4,4,5,7,7,7,7,7,7,8,8,9,9,9,9

2(1) + 4(2) + 5(1) + 7(6) + 8(2) + 9(4) 109
————————————————— = —— = 6.8125
1 + 2 + 1 + 6 + 2 + 4 16

45
Q

Standardization

A

Subtract the mean from each value, then divide result by standard deviation

46
Q

Intersection of S and T (sets)

A

S () T is the set of all elements that are in both S and T

47
Q

Union of S and T

A

The set of all elements that are that are in S or T or both, denoted by S U T

48
Q

Disjoint or mutually exclusive elements

A

Sets S and T that have no elements in common

49
Q

Venn diagram

A

A useful way to represent two or three sets and their possible intersections and unions.

50
Q

Inclusion-exclusion principle for two sets

A

This principle relates the numbers of elements in the union and intersection of two finite sets:
1) number of elements in the union of two sets =
Sum of individual numbers of elements - # of elements in the intersection.
|A U B| = |A| + |B| - |A ^ B|

2) For the union of B and C that are mutually exclusive and have no intersection
|B U C| = |B| + |C|

51
Q

Multiplication principle
Two choices to be made sequentially one after another and independent of one another. If # of possibilities for first choice is ‘k’ and # of possibilities for the 2 nd choice is ‘m’, then there are ______ different possibilities for the pair of choices.

A

Km

52
Q

A meal consists of 1 entree and 1 dessert. If there are 5 entrees and 3 desserts on the menu, how many different meals can be ordered from the menu?

A

(5)(3) = 15 different meals can be ordered from the menu

53
Q

A computer password consists of four characters such that the first character is one of the 10 digits from 0 to 9 and each of the next 3 characters is any one of the uppercase letters from the 26 of English alphabet. How many different passwords are possible?

A

(10)(26)(26)(26) = 175, 760

54
Q

A computer password consists of four characters such that the first character is one of the digits from 0 to 9 and each of the next 3 characters is any of the non repeating uppercase letters from English alphabet. How many different passwords are possible?

A

— — — —

(10)(26)(25)(24) = 156,000

55
Q

If a coin is tossed 8 times, how many outcomes are there?

A

— — — — — — ——

(2)(2)(2)(2)(2)(2)(2)(2) = (2)^8 = 256 possible outcomes

56
Q

Permutations and factorials

To order 4 letters in order we use the formula

A 
n(n-1)(n-2)(n-3)
Or n!
So, to order 4 letters,
(4)(3)(2)(1) or 4! = 24
 Four letters can be arranged 24 different ways.
57
Q

10 students are going on a bus trip, and each of the students will be assigned to one of the 10 available seats. What’s the number of different possible seating arrangements?

A

10! = 3, 628, 800

58
Q

Determine the # of ways in which you can select 3 of the 5 letters A, B, C, D, E and place them in order from 1st to 3rd.

A

— — —
(5)(4)(3)= 60
There are 60 ways to select 3 of 5 letters

59
Q

Permutations of ‘n’ objects taken ‘k’ at a time

Or
The # of ways to select and order ‘k’ objects out of ‘n’ objects.

A

n
= ——
(n-k)!

60
Q

How many different five-digit positive integers can be formed using the digits 1, 2, 3, 4, 5, 6, 7 if none of the digits can occur more than once in the integer?

A 
This question asks how many ways there are to order 5 integers chosen from a set of 7 integers.
According to the counting principle, 
n= set, k= how mamy objects are chosen
    n!            7!          7!
——— = ——— = —— = 2,520
(n-k)!       (7-5)!      (2)!

There are 2,520 different five-digit positive integers that can be formed using 1,2,3,4,5,6,7 and none of the digits repeat in the integer.

61
Q

Probability

A

For a random experiment with a finite # of possible outcomes, if each outcome is equally likely to occur, then the probability that an event E occurs is defined by the ratio

               The # of outcomes in the event E P(E) = ——————————————————————
       The # of all possible outcomes in the experiment
62
Q

Probability that event E will not occur

A

1-P(E)

63
Q

For events E and F,

What is the probability of E and F occuring (rolling a die to get a 4 or an even # or both)

A

P(E or F or both) = P(E) + P(F) - P(E and F)

64
Q

If E and F are mutually exclusive events, what is the probability of both of them occuring?
Rolling a die to get a 4 and an odd #?

A

0

65
Q

If E and F are mutually exclusive, what is the probability to get either E or F?
Probability of rolling a 2 or an odd # or both?

A

P(E or F or both) = P(E) + P(F)

66
Q

If two events are independent, what is the probability of both E and F occuring?
If a 6-sided die is rolled twice, what is the probability of pf rolling a 3 on the first roll and 3 on the second roll?

A

P(E and F) = P(E) * P(F)

P(rolling a 3 and then rolling a 3) = (1/6)(1/6) = 1/36

67
Q

P(E or F)

A

P(E or F) = P(E) + P(F) - P(E and F)

68
Q

P(E or F) if they are mutually exclusive

A

P(E or F mut. Excl.) = P(E) + P(F)

69
Q

P(E and F) independent

A

P(E and F) = P(E)*P(F)

70
Q

If a fair 6-sided die is rolled once, what is the probability of getting a 3 and an odd #?

A

1) independent or dependent events?
Dependent. Rolling a 3 makes certain that the event of rolling an odd # occurs. Therefore

P(E and F) = P(E) = 1/6

71
Q

Suppose that there is a 6-sided die that is weighted in such a way that each time the die is rolled, the probabilities of rolling any of the numbers from 1 to 5 are all equal, but the probability of rolling 6 is twice the probability of rolling a 1. When you roll the die once, the outcomes are NOT equally likely. What are the probabilities of the 6 outcomes?

A 
p = P(1) = P(2) = P(3) = P(4) = P(5)
2p = P(6)
1 = P(1) + P(2) + P(3) + P(4) + P(5) + P(6)
1 = p + p + p + p + p + 2p = 7p
P(1) = 1/7
P(6) = 2/7

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