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Current time:0:00Total duration:10:02

Problem 33 asks: What distance
did Jane travel? What distance did she travel? So, one. Bill traveled 40 miles in 40
minutes, or essentially a mile a minute, which is 60 miles an
hour, whatever, 1 mile a minute, right? That's what we can figure out. 1 mile per minute. That has no information about
how far did Jane travel. It's useless. Two. Jane traveled at the same
average rate as Bill. So that tells that Jane, if she
went at the same average rate as Bill, that means
that she also went 1 mile per minute. But we're not asking for how
fast did Jane travel or what was her average rate. We're asking for how
far did she travel? So with statements one and two
combined, all we know is Jane's rate, but we don't know
how long she traveled for. So we don't know the distance. So the answer is e, that both
statements together are not sufficient. If statement two told us that
Jane traveled at the same rate as Bill and she traveled at that
rate for 10 minutes, then we would be able to solve
this problem. But it didn't, so even with both
pieces of information, we still don't know how far
Jane traveled, only how fast she traveled. 34. What number is 15% of x? So what we want to
know is 0.15x. That's what we're trying
to solve for. Statement one tells
us, 18 is 6% of x. So you normally wouldn't even
have to solve for it. All you know is, by looking
at this statement, you can solve for x. And if you can solve for x,
then you can just multiply that times 0.15, and you'll
have the answer to the original statement. So you immediately know that
statement one is sufficient. If you don't believe
me, you can just write this as a equation. 18 is equal to 6% of x. And then you just solve for x. So 18 divided by 0.06, and then
multiply it times 0.15, and you've got your answer. Statement number two. 2/3 of x is 200. Once again, you look at
this, and you say, this is a simple equation. I could solve for x. If I solve for x here, then I
just substitute it back here, and I will know what 15% of
x is, and I would be done. So each of these statements
individually are sufficient to answer our question
what is 15% of x. I don't think I've got to go
through the exercise of actually solving for that,
because I think you understand what I'm talking about. 35. Oh, I like these. So they say 3.2 rectangle
triangle, or delta, 6. And they say, if rectangle and
delta, or triangle, soon. each represent single digits
in the decimal above. OK. So this is a decimal. I thought they might
be operations. So this is a decimal. So it's four digits behind
the decimal spot. What does rectangle represent? So we want to know what does
this decimal-- what's the digit right here? Statement number one tells us,
when the decimal is rounded to the nearest tenth, 3.2
is the result. The nearest tenth. So when you round, what you do
is you look at-- if we're rounding to the nearest tenth,
we look at this number, right? We look at the rectangle. And if the rectangle is 5 or
greater, we would round up, so we would get to 3.3. If the rectangle is less
than 5, then we would round down to 2. So statement number one tells
us that rectangle is less than 5. And we know it's greater
than or equal to 0, because it's a digit. It's 0, 1, 2, 3, or 4, right? So we can say it's
0, 1, 2, 3, or 4. That's rectangle. But that by itself does not
allow to figure out what rectangle is. Now statement number two tells
us, when the decimal is rounded to the nearest
hundredth, 3.24 is the result. 3.24 is the result
when you round to the nearest hundredth. OK. So this is interesting. So this number here is either
going to be-- so when you're rounding to something, it's
either going to be either rounding down or rounding up. So this tells us-- so this
number right here can either be 3-- so we already know, it
can be 0, 1, 2, 3, or 4. But which of these numbers when
you round them could be rounded up or down to 4? Well, this could be
2, 3, 5, right? Let me give you one scenario. We could have 3.2356, where this
is the rectangle and this is triangle. So this would round to 3.24. You could also have 3.2416. where this is the rectangle
and this is the triangle. And either of these would
round to 3.24. So this tells us essentially
that the rectangle has to be either 3 or 4. And this tells us that it's
either 0, 1, 2, 3, or 4. But even when you use them
individually, they don't tell you exactly what the
rectangle is. And when you use them together,
you can just narrow down to 3 or 4, which just
statement two alone tells you. So this actually turns out
that when you use both statements together, you still
can't get the answer. You'd either need a third term
there, or we would have to have a little bit more
information about what the triangle is. If they told us that the
triangle rounds you up or is greater than 5 or less than 5
or something like that, then we could figure out what
the rectangle is. So they answer here is E, if
I haven't missed something. That together, both statements
are not sufficient to answer the question. 36. A profit from the sale of a
certain appliance increases, though not proportionally with
the number of units sold. So it's not-- you know, the
profits do not equal just some constant times units. It equals maybe some constant
times units squared or something like that. Did the profit exceed
4 million on sales of 380,000 units? So is profit greater than
4 million-- this one is interesting-- when units
is equal to 380,000? Let's see if we can
figure this out. So they say that the
profit exceeds 2 million on sales of 200,000. So statement one says profit is
greater than 2 million when units is equal to 200,000. Now, if they told us that profit
was proportional to units, then we could say, oh,
well, if we increase the units from 200,000 to 380,000, then
we're not doubling the units. So then we can't be-- well, it
still would be ambiguous because they're not saying
profit equals 2. They're saying that profit is
greater than 2, so this actually still doesn't give
me a lot of information. Statement number two. I'll do it in a different
color. Statement number two says the
profit exceeds 5 million on sales of 350,000 units. OK. So this is interesting. So this tells us that when units
are 350,000, our profit is already greater than 5
million, so they're definitely greater than 4 million. And notice, they told us that
the profit from the sale of an appliance increases, but not
proportionally, with the number of units sold. So if we made more than 5
million when there are 350,000 units, we know that when you go
from 350,000 to 380,000, we know from the statement of
the problem that the profit has to increase. We don't know by how much, but
it's going to increase. So the profit was already
greater than 5 million. It's going to increase
above 5 million. So statement two tells us that
the profit is definitely going to be above 5 million, so
it's definitely going to be above 4 million. So statement two alone
is enough. And statement one actually
tells us very little information because we don't
know how does the profit change as you incrementally
add units. Maybe every other unit-- maybe
every unit above 200,000 that you add, you get, a millionth
of a penny. And then it doesn't
tell you anything. Or maybe you get a
million pennies. So it's very hard to tell. Problem number-- actually, I'm
already at 10 minutes. Let me do that in
the next video. See