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Current time:0:00Total duration:10:01

We're on problem 73. How much did a certain
telephone call cost? All right. Well, we know nothing so far. Statement one. The call lasted 53 minutes. Well, unless they tell us how
much it costs per minute, that still doesn't tell us how
much the call costs. Statement two tells us the cost
for the first 3 minutes was 5 times the cost for
each additional minute. But that still doesn't
help us. The cost for the first 3 minutes
might have been $0.05 a minute, and then we might
have been $0.01 a minute after that. Or it could have been $0.10 a
minute, and then-- or let me make it a multiple of 3-- $0.12
a minute, and then $0.04 after that. Both of these satisfy
that statement. And actually, if I have to be
honest, this statement is slightly ambiguous. Because they're saying the cost
for the first 3 minutes. Do they mean that the total cost
for the first 3 minutes was 5 times each additional
minute? Or was it the cost per minute
of the first 3 minutes was 5 times additional minutes? Well, either way, both
statements combined don't help us, because we're not able to
figure out the cost per minute, so that we could
apply it to this. So they are both useless. 74. In a certain office, 50% of the employees are college graduates. So let's say 50% college. I'll call it C. Or I could say 50% of the
employees are college graduate, right? 60% of the employees are
over 40 years old. So it says 60% of the employees
equal, we'll call it O for over 40. I don't know where this
is going, I'm just making up numbers. And it said if 30% of those over
40 have Master's degrees, how many of the employees over
40 have Master's degrees? OK. So 30% of the over 40 have
Master's degrees. I don't know, I'm just trying
to make up some notation. How many of the employees over
40 have Master's degrees? So we're actually trying to
come up with this number. So if we knew how many employees
over 40 there were, we would be set, because we'd
just multiply 30% times that. If we knew how many employees
there were, we would be all set, because we could figure
out the number over 40 and then multiply 30 times that. So let's see what
they give us. Statement one. Exactly 100 of the employees
are college graduates. So essentially, C is equal
to 100, right? And they told us
that 50% of the employees are college graduates. So that means how many total
employees are there? That means that there
are 200 employees. 100 is 50% of 200. So that told us there
are 200 employees. If there are 200 employees,
how many employees over 40 are there? Well, that's O, right? O for over 40. Well, that's just 60% of 200. That's 120. And then how many over 40
with Master's degrees? Let's that OMD. How many of these are there? Over 40 with Master's degrees. Well, that's 30% of over 40, so
that's 30%-- this is an O-- this is 30% of this, which is
equal to-- so over 40 with Master's degrees
is equal to 36. And we would be done. So statement one alone
is sufficient. I should call it over
40 instead of a 0. Don't want to get confused. Over 40 with Mater's degrees. So statement two. Of the employees 40 years
old or less, 25% have Master's degrees. So that doesn't tell us
anything, really. It doesn't tell us how many
employees there are over 40, which was one of the things that
we realized we have to figure out. It doesn't help us figure out
how many total employees there are, so we really can't
do this type of logic. So it seems fairly useless. So yeah, employees 40
years old or less. 25% of-- no. This is a useless piece
of information. So the answer is--
what is that? I always forget. A. Statement alone is sufficient
and statement 2 is useless. 75. They ask is rst equal to 1? Statement one tells us that
rs is equal to 1. This by itself doesn't
help us, right? If rs is equal to 1, the only
way that this whole thing is going to be equal to 1 is
if t is also equal 1. But we don't know that, so-- I
mean, t could be equal to 10. So statement one alone
doesn't help us. Statement two tells us,
st is equal to 1. Well, I can show that even
if we have both of these statements, that we still
can't prove this. For example, I can come up with
a scenario that meets both statements where
this is true. Because I can say what if r is
equal to 1, s is equal to 1, and t is equal to 1? Then we can make both of
these statements true. So then, definitely,
rst is equal to 1. But let me see if I can
construct something where this doesn't hold up. So what if r is equal to 6. s is equal to 1/6, and
then t is equal to 6. So then r times s would still
be equal to 1, right? s times t would still
be equal to 1. But what is rst now? It's 6 times 1/6, times 6,
which is equal to 6. So I can satisfy both of these,
but still end up not knowing whether it equals 1
or something different. I just picked this
arbitrarily. You can actually kind of pick
an arbitrary number here and set this up. So anyway, this is E. I think that's E, right? Both statements combined
are useless. Right. They're not sufficient. Next problem. Turn the page. It's problem 76. And they've drawn a
nice pie chart for us, which I'll reproduce. 76. Total expenses for the 5
divisions of company h. Let me draw this pie chart. OK. And then they have a bunch
of-- let's see, how many pies are there? There are 5 pies. I'll try to draw it the
way they do it. So that's one. Two. Three. And they have one more. There we go. So that looks pretty close
to what they've drawn. And then they write, this
is Q, R, S, T, and P. O is the center. They call this angle, x. Fair enough. So this is the total expenses
for the 5 divisions. So each of these are divisions
for company h. 76. The figure above represents a
circle graph of company h's totally expenses broken down
by the expenses for each of it's 5 divisions. If O is the center of the
circle-- fair enough, so this is the center, although I didn't
draw it quite at the center-- if O is the center of
the circle, and if company h's total expenses are $5.4 million,
what are the expenses for division R? So the whole thing
is $5.4 million. So the whole pie is
$5.4 million. And we need to figure out
what R is equal to. So the whole expenses
are 360 degrees. So whatever fraction x is of 360
degrees, that's going to be the fraction that R is
of the total expenses. So let's see if they
give us that. If we can figure out
what angle x is. One, x is equal to 94. Well, we're done. Because x over the total degrees
in the circle-- so 94 over 360 degrees-- that's
going to be equal to the expenses of division R
divided by the total expenses, $5.4 million. And this is a trivial
equation to solve. So one alone is sufficient. Let's see what they give us
for statement number two. The total expenses for divisions
S and T are twice as much as the expenses
for division R. So they're saying that this
right here is twice as much as what we're trying
to figure out. It's this right here. Well, that doesn't help us much,
because P and Q could be arbitrarily small or large. These two combined could be $2
and this could be $1, right? In which case, P and Q
are the bulk of the expenses for the company. Or maybe these two are
$4 and R is $2, which are all possible. And these would represent the
rest of the-- whatever. It gets you to $5.4 million. So statement two is useless. So statement one alone is
sufficient and statement two does us no good. And I'm out of time. I'll see you in the
next video.