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Exam 1 with Resolutions - Introduction to Quantitative Reasoning | MATH 1030, Exams of Mathematics

Material Type: Exam; Class: Intro Quant Reasoning; Subject: Mathematics; University: University of Utah; Term: Spring 2008;

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Exam 1 Solutions
MATH 1030-008 Spring 2008
1. (5 Points) You invest $1000 into a mutual fund. In 5 years, this investment is worth $2500.
Describe your profit in both relative and absolute terms.
Absolute Change = N V RV = 2500 1000 = 1500
Relative Change = NV RV
RV =1500
1000 = 1.5 or 150 %
2. (5 points) The number of students at a local high school decreased by 15% one year and
increased 8% the following year. By what percent, did the number of students change over the two
year period?
Let Sbe the original number of students, S1be the number of students after year 1, and S2be the
number of students after year 2. We have
S1= (100 15)% of S= 0.85 ×Sand S2= (100 + 8)% of S1= 1.08 ×S1.
Therefore,
S2= 1.08 ×S1= 1.08 ×(0.85 ×S) = 0.918 ×S.
This tells us that the percentage change is
(0.918 1) ×100 = 8.2 %
3. (5 points) On Monday, the average temperature was reported to be 101F. On Tuesday, the
average temperature was reported to be 40C. Which was the hotter of the two days?
We need to compare the two temperatures. So, we need to either convert the Monday temperature
to Celsius or the Tuesday temperature to Fahrenheit.
C1=F132
1.8=101 32
1.838.3C
F2= 1.8C2+ 32 = 1.8(40) + 32 = 104F
From the above calculations, we can see that it was hotter on Tuesday.
4. (5 points) Draw a Venn diagram that represents the following scenario and answer the questions
that follow. A group of 120 people were polled to see whether they had a dog, a cat, or a tarantula
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Exam 1 Solutions

MATH 1030-008 Spring 2008

  1. (5 Points) You invest $1000 into a mutual fund. In 5 years, this investment is worth $2500. Describe your profit in both relative and absolute terms.

Absolute Change = N V − RV = 2500 − 1000 = 1500

Relative Change =

N V − RV

RV

= 1.5 or 150 %

  1. (5 points) The number of students at a local high school decreased by 15% one year and increased 8% the following year. By what percent, did the number of students change over the two year period?

Let S be the original number of students, S 1 be the number of students after year 1, and S 2 be the number of students after year 2. We have

S 1 = (100 − 15)% of S = 0. 85 × S and S 2 = (100 + 8)% of S 1 = 1. 08 × S 1.

Therefore, S 2 = 1. 08 × S 1 = 1. 08 × (0. 85 × S) = 0. 918 × S.

This tells us that the percentage change is

(0. 918 − 1) × 100 = − 8 .2 %

  1. (5 points) On Monday, the average temperature was reported to be 101◦^ F. On Tuesday, the average temperature was reported to be 40◦^ C. Which was the hotter of the two days?

We need to compare the two temperatures. So, we need to either convert the Monday temperature to Celsius or the Tuesday temperature to Fahrenheit.

C 1 =

F 1 − 32

≈ 38. 3 ◦C

F 2 = 1. 8 C 2 + 32 = 1.8(40) + 32 = 104◦F

From the above calculations, we can see that it was hotter on Tuesday.

  1. (5 points) Draw a Venn diagram that represents the following scenario and answer the questions that follow. A group of 120 people were polled to see whether they had a dog, a cat, or a tarantula

as a pet. The following results were obtained.

15 have a cat, but not a dog or a tarantula. 22 have a dog, but not a cat or a tarantula. 13 have a tarantula, but not a cat or a dog. 8 have a cat and dog, but not a tarantula. 45 have a dog and a tarantula, but not a cat. 5 have a tarantula and a cat, but not a dog. 8 have none of the three pets.

How many people have all three pets? How many people have a dog or a tarantula?

See Handout.

  1. (5 points) Determine whether the following deductive arguement is valid by using a Venn diagram. Is the arguement sound?

Premise: Everyone who gets their flu shot does not get the flu. Premise: Jackie got her flu shot. Conclusion: Jackie did not get the flu.

See Handout.

  1. (5 points) You are riding your bicycle at a speed of 5 miles per hour.

a) What is your speed in feet per minute? b) How long will it take you (in minutes) to travel 1000 feet?

a) First, recall that 5280 ft = 1 mile and 60 min = 1 hr. From these conversion factors, we can convert the 5 miles per hour as follows.

Speed = 5 miles hr

×

5280 ft 1 mile

×

1 hr 60 min

440 ft min

b) For this part, recall that distance = speed × time. This tells us that time = distance/speed. Therefore,

Time = distance speed

1000 ft 440 ft per min ≈ 2 .273 min

  1. (5 Points) At a market place in Brazil, you want to buy some apples. The apples are priced at 4.25 Brazilian Reals per kilogram. If you have 12 Canadian Dollars with you, can you buy 4 pounds of apples? Note that 1.745 Brazil Real = 1Canadian Dollar.