jurafumo wrote:Hi All,
As I see it the wording of the question stem is misleading...
Hi jurafumo!
I can TOTALLY see the thought process here and can see why it might feel confusing! So let's look at your math and make sure that we're clear on the definitions of variables:
jurafumo wrote:it says that 100 of these students do not study French; therefore it refers to students studying Spanish only, meaning S=100.
Okay, so since we're starting to define stuff, let's clarify: you are saying that S=Spanish Only (not French).
jurafumo wrote:
being S- Spanish students // F - French students // x- both
S + F - x = 300
Uh-oh! The definition of S just changed. Before you said that S was Spanish ONLY, but if we say that S+F-x=30 (total of each group minus the overlap), then we are assuming that S=anyone who takes Spanish, NOT just those taking ONLY Spanish!
This is why it is SO important to clearly define your variables and even make a legend:
S = Spanish (might take French, might not)
F = French (might take Spanish, might not)
B = Both
Where, S + F
- B = 300.
--OR--
S = Spanish ONLY
F = French ONLY
B = Both
Where, S + F
+ B = 300.
Once you decide which definition of S and F you want to use, then you can build the correct set of equations!
CHOICE (A)
S = Spanish (might take French, might not)
F = French (might take Spanish, might not)
B = Both
Where, S + F
- B = 300.
S+F-B=300 (300 students)
S-B=100 (100 study NOT French, so we have to eliminate the "Both" from the Spanish group)
F=200 (if 100 don't study French, then 200 do!)
And that is all we know - if we try to combine these equations we see that they are all linearly DEPENDENT (meaning that they aren't actually different equations - you add the 2nd and 3rd together to get the 1st!)
STM(1):
If 60 do NOT study Spanish, then
F-B=60 (Study French without studying both)
Now I can plug this into the 1st equation S + (60) = 300, S = 240. And if S=240, then 240-B=100, B=140.
STM(2):
If 240 study Spanish, then S=240, so 240-B=100, or B=140.
CHOICE (B)
S = Spanish ONLY
F = French ONLY
B = Both
Where, S + F
+ B = 300.
S+F+B=300
S=100
F+B=200
STM(1):
If 60 do NOT study Spanish, then they study French only:
F=60, so 60+B=200, B=140.
STM(2):
If 240 study Spanish (Spanish Only + Both)
S+B=240,
and since S=100,
100+B=240 , B=140.
So we could have solved this in 2 different ways algebraically (depending on how we defined the variables) or we could use a Matrix or a Venn diagram! Lots of options!!
Hope this helps!
Whit
