Download BUS 205/BUS 305 Skill Set

BUS 205 Skill Set
These problems are typical of some of the kinds of mathematical exercises you will need to be
able to do to be successful in your business statistics classes. We suggest you reserve about an
hour, grab a pencil, some scratch paper, and your calculator, and see how you do. The answers
appear at the end.
1.
Convert .237 to a percent.
2.
Convert 37.5% to a decimal.
3.
Convert 5/7 to both a percent and a decimal.
4.
Sales in 2004 were $52.37 million and sales in 2003 were $48.09 million. Express the
2004 sales as a percent of the 2003 sales. What is the percent increase in sales from 2003 to
2004?
5.
Put these numbers in order from lowest to highest.
-5, 3, 18, |-2|, -1,
6.
-1.1, -1.01,
1,
1.1
Put these numbers in order from lowest to highest.
1/2, 1/3, 5/6, 3/8
7.
Fill in the blank in each expression with the proper symbol: either < or >
5 ___ 3
-5 ___ 3
-5 ___ -3
-1.11 ___ -1.12
-1.11 ___ -1.10
8.
Evaluate
9.
Evaluate
14.36 
2.6
(8  2.16) 2
5
3
5( 2  ) 2
2
10.
As the purchasing agent for your organization, you want to buy components at the best
price possible, as long as the quality is comparable. From which company will you get the best
price for ordering 1200 units?
The price from Supplier A is given by this table.
If the order quantity is
the price for each unit is
0 – 499
$5.00
500 – 999
$4.50
1000 or more
$4.00
The price from Supplier B is
$6.00 per unit for the first 200 units
$4.00 per unit for the next 500 units
$3.00 per unit for the next 1000 units
11.
Compute the answers for each of these expressions
a.
1 3

2 7
b.
2 *3* 4
5*8
c.
6(5 x  2)
3
d.
5 3

x 2x
e.
(5) 2
f.
(4) 1 / 2
g.
(4) 1 / 2
12.
A major research study looks at the average price of a prescription drug. Records from
5000 transactions are considered. The price per prescription ranges from $13.12 to $47.38.
Which of the following could not be the average price of the 5000 prescriptions and why?
a.
b.
c.
$5000
$8.65
$41.19
Can you tell which of these is the average price?
d.
e.
f.
$47.38
$25.25
$53.29
13.
14.
Solve each of these expressions for x:
a.
5x – 3 = 12
b.
2x + 1 > x – 5
c.
4x + 2 < 7x – 4
Calculate (18 + 2(12))(1.07)
Solutions
1.
.237 = 23.7%
2.
37.5% = .375
3.
5/7 = .7143 = 71.43%
In general, there is no need to carry your calculations beyond 4 decimal places.
Exceptions to this advice will be covered by your instructor.
4.
The percent is
52.37
 1.089  108.9%
48.09
Percent increase is
5.
(52.37  48.09) 4.28

 .089  8.9%
48.09
48.09
Values in order are
-5
-1.1 -1.01 -1
1
1.1
|-2| = 2
3
18
6.
One way to determine the arrangement is to convert all of these fractions to fractions with
the same denominator. The smallest common denominator (the smallest number that 2, 3, 6, and
8 all go into evenly) is 24.
1/2 = 12/24
1/3 = 8/24
5/6 = 20/24
3/8 = 9/24
In order, these values are 1/3, 3/8, 1/2, and 5/6.
An alternative way to determine the arrangement is to convert these all to decimals.
1/2 = .5
1/3 = .3333
5/6 = .8333
3/8 = .375
In order, these values are 1/3, 3/8, 1/2, and 5/6.
7.
5>3
-1.11 > -1.12
-5 < 3
-1.11 < -1.10
-5 < -3
8.
The order of operations is to work inside parentheses first. Do exponents, then
multiplication and division, then finally addition and subtraction.
2.6
(8  2.16) 2
5
2.6
 14.36 
(5.84) 2
5
2.6
 14.36 
(34.1056)
5
 14.36  .52(34.1056)
14.36 
 14.36  17.7349
 3.3749
9.
3
5(2  ) 2  5(3.5) 2  5(12.25)  61.25
2
10.
Price from Supplier A:
(1200 units)($4.00 / unit) = $4800.
Price from Supplier B:
(200 units)($6.00 / unit) + (500 units)($4.00 / unit) + (500 units)($3.00 / unit)
= $1200 + $2000 + $1500 = $4700.
Supplier B has the better price for 1200 units.
11.
a.
1/2 + 3/7 = 7/14 + 6/14 = 13/14
b.
(2)(3)( 4) 3

(5)(8)
5
c.
6(5 x  2)
 2(5 x  2)  10 x  4
3
d.
5 3 10 3 13




x 2x 2x 2x 2x
e.
(-5)2 = 25
f.
41 / 2  4  2
g.
4 1 / 2 
1
4
1/ 2

1
4

1
 .5
2
12.
The average is found by adding up all of the prices and dividing by 5000. The result will
always be a number somewhere between the largest and smallest values.
a.
5000 is the number of prices in the sample; it cannot be the average because it is too large
b.
8.65 cannot be the average; it is smaller than the smallest value
c.
41.19 could be the average
d.
47.38 could only be the average if all 5000 prices were equal to this value; at least one
prescription was priced at $13.12.
e.
25.25 could be the average
f.
53.29 cannot be the average; it is larger than the largest value
Although 25.25 could be the average, its position midway between the largest and smallest
values doesn’t indicate that it should be the average.
13.
14.
a.
5x – 3 = 12
5x = 15
x=3
b.
2x + 1 > x – 5
x + 1 > -5
x > -6
c.
4x + 2 < 7x – 4
2 < 3x – 4
6 < 3x
2<x
(18 + 2(12))(1.07) = (18 + 24)(1.07) = 41(1.07) = 44.94