Problem Solving Assessment
Family/Last name:
UT Student number:
Birthdate:
Jan
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1
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1967
Reasoning
Four people ran a race, placing first, second, third and fourth, but only the runners know the results. After the race, they made the following statements...
Carlos said, "Raul got last place".
Tito said, "I did better than Carlos".
Raul said, "I won the race".
Edgar said, "Raul did worse than Tito".
If the only person who's telling the truth is the race winner, then who is it?
Carlos won the race
Tito won the race
Raul won the race
Edgar won the race
Planning
In the triangle below, each number is the sum of the two numbers below it. What are the values of a,b,c,d,e,f and g? Note: they are all positive integers (ie. 1,2,3,4,...).
23 / \ f 15 / \ / \ 6 c e / \ / \ / \ a d b g
a=
b=
c=
d=
e=
f=
g=
Understanding a definition
For the purposes of this and the next question, we make the following definition:
A
zork number
is any integer which is 3 more than a multiple of 19.
I
do
do not
understand what a positive integer is.
Which of the following are positive integers?
-23,
13,
0,
0.5,
79,
82.24
I
do
do not
understand what it means for a number to be a multiple of 21.
Which of the following are multiples of 21?
19,
20,
21,
22,
35,
38,
39,
40,
41,
42,
43
I
do
do not
understand the definition of a zork number.
Which of the following are zork numbers?
19,
20,
21,
22,
35,
38,
39,
40,
41,
42,
43
Which of the following are both zork numbers as well as multiples of 21?
19,
20,
21,
22,
35,
38,
39,
40,
41,
42,
43
Proofs
Consider the following proposition and proof...
Proposition: There are no zork numbers which are also multiples of 21. Proof: a) By contradiction. b) Assume that there was a zork number which is also a multiple of 21. c) Lets call that integer x. d) Then x=3+19y (because x is a zork number) e) and x=21y (because x is a multiple of 21). f) But then 3+19y=21y g) which implies 3=2y h) which implies y=3/2. j) But then x=21*3/2=63/2 (since we assumed that x=21y) k) which means that x is not an integer. l) Now we assumed that x was a zork number (and so an integer), so this is a contradiction. m) The conclusion is that there are no zork numbers which are also multiples of 21. n) QED
Which of the following statements characterizes your understanding of the above proof.
I
do
do not
understand the proposition,
There are no zork numbers which are also multiples of 21.
If the proposition were false, explain in complete sentences what this would mean.
I
do
do not
understand what it means to prove the proposition.
I understand
none of the proof
line a
lines a to b
lines a to c
lines a to d
lines a to e
lines a to f
lines a to g
lines a to h
lines a to i
lines a to j
lines a to k
lines a to l
lines a to m
all of the proof
Choose the correct statement:
The proof is correct.
The proof is incorrect the first error appears in line a
The proof is incorrect the first error appears in line b
The proof is incorrect the first error appears in line c
The proof is incorrect the first error appears in line d
The proof is incorrect the first error appears in line e
The proof is incorrect the first error appears in line f
The proof is incorrect the first error appears in line g
The proof is incorrect the first error appears in line h
The proof is incorrect the first error appears in line i
The proof is incorrect the first error appears in line j
The proof is incorrect the first error appears in line k
The proof is incorrect the first error appears in line l
The proof is incorrect the first error appears in line m
The proof is incorrect the first error appears in line n
The proof is just incorrect, there is no first error.
What's your strategy?
What does the following expression evaluate to?
1 1 1 1 1 ---- + ---- + ---- + ---- + ... + -------- 1*2 2*3 3*4 4*5 999*1000
Your answer goes below.
Describe how you came up with your answer in the space below.
There is always evidence
I just found the worn out receipt for the purchase of 72 widgits from Spacely Sprockets (there is no tax on widgits!). Unfortunately, the first and last digits for the
total price
have worn off leaving the digits
$_67.9_
The underscores represent the missing digits. How much does each widgit cost and what are the missing digits (there is no tax on widgits)?
Fill in the text boxes below:
Each widgit costs
.
The total cost for all 72 widgits (no tax!) is
.
End of diagnostic. Click the button below to ...