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Problem 94. In Jefferson School, 300
students study French or Spanish or both. OK. And they have to do
one of those two. If 100 of these students do
not study French-- so this sounds like a Venn Diagram. Let's see. So let's say that's French. And I'll do Spanish in
a different color. Let's say that is Spanish. And we have 300 students,
and they study either French or Spanish. If 100 of these students
do not study French-- so what did I say? This was French and
this is Spanish. So 100 of these students
do not study French. So this area right
here is 100. Right? Those are people who study
Spanish but no French at all. How many of these students study
both French and Spanish? So what they want to know is
the intersection of who studies French and Spanish. So that's this blue
area right here. So statement number one tells
us, of the 300 students, 60 do not study Spanish. So people who study French but
no Spanish-- and I didn't mean they know Spanish. People who study French and do
not study Spanish, that's this right here. And that's 60. Right? And let's see if we can use this
information to figure out what the intersection is. So if you think about it,
what we want to do is the whole universe. So the whole universe is going
to be equal to the people who study-- so this 60 people plus--
we'll call that the intersection, or we could call
that French and Spanish-- plus this blue area, plus
this tan area. Right? That's the whole universe. And that is equal to 300. So people who study French
and Spanish plus 160 is equal to 300. Subtract 160 from both sides
and you get the people who study just French and Spanish. That's what? That's 240. That's 140 people who study
both French and Spanish. So statement one
is sufficient. Let's see what statement
two gets us. Statement two tells us, a total
of 240 of the students study Spanish. So in statement two,
we don't know this. But we know that a total
of 240 students study Spanish, right? So we know that this whole
circle is 240. And if we're just trying to
figure out this blue part, we just have to subtract
out the tan part. So if we want to know French
and Spanish, French and Spanish is going to be equal to
the whole amount that study Spanish-- which they just told
us, 240-- minus just the people who study only Spanish. Right? Because you could study
Spanish and French. So 240 people who study Spanish
minus the people who just study Spanish. So that's 100. That's that tan area. That also equals 140. So both statements individually
are sufficient to answer this question. So the answer is D.