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Q
uantitative
R
easoning &
P
roblem
S
olving
172
© 2014 Pacific Crest
S
trategies
T
ips
for
S
olving
Q
uantitative
P
roblems
1. Narrow the definition of the problem to one that you can solve in the time available to you.
2. Identify the key issues by determining what qualities the solution should demonstrate.
3. Make a list of what you know, what you don’t know, what information you need to find, and
what information is irrelevant.
4. Identify assumptions that you have made that may not be true. By taking the different perspectives
of those who are affected by or interested in the problem solution, you can identify what they
could potentially challenge with respect to your problem solving work. In doing this, you can
ensure that key assumptions are known and dealt with. This also gives you the confidence that
they will hold up under scrutiny.
5. Break a problem into smaller problems by looking for problems you have solved before or know
that you can solve.
6. Model a solution using mathematics: Use mathematical structures, models, and tools to model
sub-problems (the advantage is that you know themathematical content is reliable and understood,
thus making your work with the sub-problem that much stronger).
O
ops
! A
voiding
C
ommon
E
rrors
●
Failing to break the problem into manageable sub-problems
Example
: Joan and Jeff wanted to host a dinner party for their friends. They made the guest list
and planned the menu. After they sent out invitations, the phone started ringing. Cleo
was deathly allergic to peanuts so would prefer not to attend since peanuts would
feature in the appetizer. Joaquin and his partner were committed vegetarians; could
they bring their own main dish so they could still participate? Melwin and Abeda
would prefer not to eat veal (the planned main dish) but were not vegetarians. Was
there another option? Kathleen regretfully reminded them that her lactose intolerance
made the sauce on both side dishes and the dessert problematic. With only a week to
go, Joan suggested they cancel. “This is just too much and there’s no way to solve the
problem of feeding our friends.” Jeff agreed..
Why?
After failing to consider things like food allergies when they initially created the
menu, Jeff & Joan were faced with a more complex problem, given the feedback
they received. They could have broken the problem down into sub-problems such
as, “Find a meat-free alternative main dish” and “Find an alternative appetizer that
is peanut-free”. There are many menu possibilities that could have met everyone’s
needs, but finding those solutions required solving many smaller problems and then
integrating them into a general solution (in this case, a completed menu). Breaking
down the problem into manageable units makes the main problem easier to solve.
●
Failing to identify key issues
Example
: Determining what would be the best celebration for graduation by asking the graduate
what he or she would like to do.