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We're on problem 42. And they've drawn this little,
looks like a pie graph. And they say, in the circular
region with center o shown above, the two unshaded sections
constitute 3/7 and 1/3 of the area of the
circular region. Fair enough. The shaded section constitutes
what fractional part of the area of the circular region? So the shaded section is just
the whole area minus these two fractions, right? So if you said what fraction of
the whole area is the whole area, you would say that's 1. And you would subtract out these
two areas to get the shaded area. So 1 minus 3/7 minus 1/3 is
equal to the fraction of the totally area that this
shaded area is. And let's just add or subtract
those fractions. The least common
multiple is 21. 1 is the same thing as 21/21. Minus 3/7. Let's see, 7 goes
into 21 3 times. So 3 times 3 is 9. So this is the same thing
as minus 9 over 21. And minus 1/3 is the same thing
as minus 7 over 21. So this is equal to 21
minus 16 over 21. And that's 5/21, which
is choice D. Next question. 0.3. [SNEEZES] Excuse me. My apologies. 0.3 to the 5th over
0.3 to the 3rd. Well, anything to the 5th
divided by anything to the 3rd, you could essentially say
divide the top and the bottom by 0.3 squared. Well, actually, you could divide
the top and the bottom by 0.3 cubed. You could say this is the same
thing as 0.3 to the 5th times 0.3 to the minus third. That's just another
way of doing this. And so if you're dividing these
two numbers, you would subtract the exponents. But now we're multiplying. We're adding the exponents. But either way, it becomes
0.3 squared. And that is equal to 3
times 3, which is 9. And you're going to have two
numbers behind the decimal points, right? 0.3 times 0.3. Two numbers behind the
decimal points. 1, 2. So two numbers behind
the decimal point. So 0.09. Or another way of saying it
is 30% of 0.3 is 0.09. And that is choice C. 44. In a horticultural experiment--
this is sounding interesting already-- 200 seeds
were planted in plot 1. So plot 1 got 200 seeds. And 300 were planted
in plot 2. So plot 2 got 300 seeds. If 57% of the seeds in plot 1
germinated, and 42% of the seeds in plot 2 germinated, what
percentage of the total number of planted seeds
germinated? So the total number of planted,
what percent? So how many total seeds
germinated is going to be 200 times 0.57. That's how many in plot
1 germinated. Plus 300 times 42%, or 0.42. That's how many in plot
2 germinated. All of that divided by 500. Right? And how do I know 500? Because there were a
total of 500 seeds. So just to simplify the math,
we could just divide everything by 100, right
from the get go. So if you divide the bottom by
100 and the top by 100, you have to do both terms by 100. So you get 2 times 0.57 plus
3 times 0.42 divided by 5. 2 times 0.57. That is what? Let's see, this is
1.14 plus 1.26. Is that right? 3 times 4 is 12. 3 times 2 is 6. Right? 1.26. All of that over 5. This becomes what? This is equal to 2.4
divided by 5. And so 5 goes into 2.4. Let's see, goes into
4, 4 times 5 is 20. 48. So 0.48. So the answer is 48%
or 100 times 0.48. And that's choice C. Question 45. Let's switch to a more
interesting color. 3 and 8 are the lengths of two
sides of a triangular region. Which of the following can be
the length of the third side? OK. So let's think about
it a little bit. 3 and 8 are the lengths of two
sides of a triangular region. Let me write their
choices down. Choice one is 5. I can easily imagine
a triangle that has sides 3, 8, and 5. That seems completely
reasonable. I'm just experimenting. I don't know where
this is going. 8. Well, sure, that's just
an isosceles triangle. You can easily have a triangle
that has 8, 8, and 3. Choice three. 11. Now, this is interesting. Let me ask you a question. Can I have a triangle that
looks like this? 11 and then 3 and then 8. Is this possible? Well, no, because
3 plus 8 is 11. So the only way you're going to
get 11 is if you push this side all the way flat. That's the only way you're going
to get the length of this third side to be 11. In fact, 11 is the upper
bound on what this third side could be. Because imagine this. Imagine if I made the triangle
really flat, I made this angle right here really wide, as
close to 180 as I can. And I make it really flat. Right? If this length plus this length,
or this length plus this length is equal to 11,
this length is going to be shorter than it. This length right here has to
be shorter than this length plus this length, right? Because it's kind of a
straight-line distance between this point and this point. So 11 is the upper
bound, right? The only way to get 11 is if
you completely flatten out this triangle, at which point
that's not a triangle anymore. It'll be a line. So it can't be choice three. So the only possibility. They say, which of the following
can be the length of the third side? So it's only choices
one and two. And that is choice C. Next problem. 46. How many integers n are there
such that 1 is less than 5n plus 5, which is less than 25? OK. So they say how many integers n
are there so that 5n plus 5. So they didn't say positive
integers, right? So that's an interesting
thing to keep in mind. So let's just try to simplify
this a little bit. Let's subtract 5 from all
sides of this double inequality. So if you subtract 5 from
everything you get minus 4 is less than 5n, which
is less than 20. Right? So another way you could say
it, is let's just divide everything by 5. So because 5 is positive you
don't have to change the inequalities. So you get minus 4/5 is less
than n, which is less than 20 divided by 5, is 4. So now the question becomes
a lot simpler. How many integers n are
there such that this? How many integers are there
between minus 4/5 and 4? And it's not equal
to any of those. So 0 is an integer. 1, 2, and 3. So there are 4 integers. So that is B. OK, next problem. 47. A car dealer sold x used cars
and y new cars during May. So number used is equal to x. Number new is equal to y. During May. If the number of used cars sold
was 10 greater than the number new cars, which of the
following expresses this relationship? So the number of used cars, x,
was 10 greater than the number of new cars. So it's 10 greater than y, so
it equals y plus 10, right? This says that the number of
used cars is 10 more than the number of new cars. So we just have to look for
that. x is equal to y plus 10. That's choice D. I think we have time
for one more. 48. If a 10% deposit that has been
paid toward the purchase of a certain product is $110,
how much more remains on the product? So essentially they're saying,
110 is 10% of what number? That's the first thing
you have to say. So 110 is equal to 0.1
times what number? So that's the price. Let's call that the original
price of the product. So the original price of the
product is going to be what? It's going to be 110 divided
by 0.1, which is just this times 10. Which is 1,100, right? Just add a 0. So that's original purchase
price of the product. The deposit is $110 and
they want to know what do you have left. So you're going to put
$110 deposit on it. This was the original
purchase price. You put $110 deposit. Let's see, 1,100 minus 100 would
be 1,000, but then we have another 10. So it would be 990. So that is choice B. And you could do it
the other way. You could just do a little
bit of borrowing. Anyway, you get the idea. And you would get choice
B, which is 990. And I'm out of time. See you in the next video.