Basic HTML Version
Q
uantitative
R
easoning &
P
roblem
S
olving
200
© 2014 Pacific Crest
D
emonstrate Your Understanding
Apply it and show you know in context!
1. Validate that
4
3
x
=
is a solution to
2
3
4 0
x x
− + + =
.
2. Validate that the factored form of 2800 is 2
4
• 5
2
• 7.
3. How would you validate that
12,
2
is the solution to the system of equations
2 3
3 2 5
x y
x y
+ =
− =
other
than by substitution?
4. Validate that
x
= 1 is the solution to the equation 3
x
– (2 – 4
x
) = 1.
5. Use a technique from this section to validate whether a problem that asks for the speed at which a
person is walking could have a solution of 65 mph.
6. Validate that
2
4 21
7
x x
x
+ −
−
is equivalent to
x
+ 3 for
x
≠ 7.
7. Validate that 2
x
– 5 = 3 is equivalent to 2
x
= 8.
8. Validate that the expression 5
x
– 3(2 – 3
x
) + 7 is equivalent to 14
x
+ 1.
H
ardest Problem
How hard
can
it be? Can you still use what you’ve learned?
Based on the Models, the Techniques, and the Demonstrate Your Understanding (DYU) problems in
this activity, create the
hardest
problem you can. Start with the hardest DYU problem in this experience
and by contrasting and comparing it with the other DYU problems, play “What if” with the different
conditions and parameters in the various problems.
Can you still solve the problem? If so, solve it. If not, explain why not.
What are the conditions and parameters that make a problem involving validation a difficult problem to
solve?
T
roubleshooting
Find the error and correct it!
Identify the error and provide a correction:
Riley had decided to be a better uncle this year and the first step was to buy and plan to send birthday cards
to all his nieces and nephews. He knew he had 15 (8 nieces and 7 nephews, ages between 8 and 19) and
so bought 15 cards. At this year’s family Christmas dinner, when all 15 were present, he loaned his tablet
to each of them so they could enter their birth date in the calendar application. Later, when he printed out
a schedule of when to send each of the cards, from January 1 through December 31, 2014 only 14 sets of
“
names+dates
” showed on the schedule. Thinking that one of his nieces or nephews had neglected to
actually enter their birthday, he printed the list of “
entered names
” from the application: 15. Irritated
with the software (which had been free, after all), he bought and downloaded a new app and was able to
automatically transfer the data. Unfortunately, the printed schedule still showed exactly the same thing: 14
cards should be sent this year. Thinking that maybe the problem was that two of the birth dates were on
the same day and perhaps the apps somehow assumed that meant 1 birthday instead of 2, he searched for
“
shared birthdays
”: 0. Riley decided he’d have to upgrade his tablet PC (since it obviously wasn’t
a problem with the specific application) in order to meet his goal of being a better uncle.