SAT Prep: Test 5 Section 3 Part 4

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Kind: captions
Language: en

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We are on problem 12.

00:00:02.240 --> 00:00:04.890
I had to take a pause because I
had a hunger pang, but I had

00:00:04.890 --> 00:00:08.160
to resist. Because I do this
thing called the Warrior Diet,

00:00:08.160 --> 00:00:09.525
which is more of a
way of life-- but

00:00:09.525 --> 00:00:10.775
anyway, back to the SAT.

00:00:16.650 --> 00:00:18.380
But you shouldn't starve
yourself because you have to

00:00:18.380 --> 00:00:20.240
feed your brain for the SAT.

00:00:20.240 --> 00:00:21.580
OK, let me draw the
x- and y-axis.

00:00:28.410 --> 00:00:31.740
Whenever I'm hungry, I just go
outside and do some sprints

00:00:31.740 --> 00:00:32.990
because that's the
warrior way.

00:00:35.450 --> 00:00:36.410
That's the y-axis.

00:00:36.410 --> 00:00:37.500
But you shouldn't do
that because you're

00:00:37.500 --> 00:00:39.220
probably still growing.

00:00:39.220 --> 00:00:42.100
I, unfortunately, have
stabilized at 5'9".

00:00:47.540 --> 00:00:49.490
All right, so let's see, they
drew something that looks like

00:00:49.490 --> 00:00:52.750
a parabola, so I'm going to
assume it is without better

00:00:52.750 --> 00:00:53.320
information.

00:00:53.320 --> 00:00:56.290
So let me draw it.

00:00:56.290 --> 00:00:59.500
My thing does not look like
a parabola, but I

00:00:59.500 --> 00:01:00.690
think you get the point.

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And then they draw this
rectangle-looking thing.

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I'll draw it in another color.

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Something like that.

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Let's see, let me label
these points.

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Points q, r, s, this is t.

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And they say that this
is-- oh, p, p not t.

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And this is point
negative 1, 0.

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So obviously the y is 0 because
we're on the x-axis

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and that's negative
1 and that's 1.

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They tell us in the figure
above p, q, r, s is a

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rectangle and points q and r lie
on the graph of y equals

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ax squared.

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And that's this thing,
this yellow thing.

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Where a is a constant.

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If the perimeter of pqrs is 10,
what is the value of a?

00:02:06.150 --> 00:02:08.410
If we can figure out one ordered
pair, if we can figure

00:02:08.410 --> 00:02:12.800
out one x-y pair that lie on
this curve, we can figure out

00:02:12.800 --> 00:02:15.690
what the curve is because we
can substitute that y and x

00:02:15.690 --> 00:02:18.770
into this equation
and solve for a.

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Well, do we know any points
that are on that?

00:02:20.660 --> 00:02:23.440
Well, both r and q are on it,
so if we can figure out the

00:02:23.440 --> 00:02:27.420
coordinates of r and q,
then we will be set.

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So what can we do?

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Well, they told us
a perimeter.

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They told us the perimeter
of this rectangle.

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So what do we know about
the rectangle already?

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How long is this side
right here?

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Well, it goes 1 unit to the left
on the x-axis and it goes

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1 to the right and it's flat.

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So that has a width
of 2, right?

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It's a rectangle, so if that
has a width of 2, this also

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has a width of 2, right?

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Let's call this height.

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That's the height of
the rectangle.

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If that's the height, that's
also the height.

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So what's the perimeter?

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The perimeter is 2 plus 2, which
is 4, plus h plus h.

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And that equals what?

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They told us that equals 10.

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So we can add those
h's together.

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We get 4 plus 2h
is equal to 10.

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Or subtract 4 from both sides.

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2h is equal to 6.

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Divide both sides by 2.

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h is equal to 3.

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So we know that h equals 3.

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So if h equals 3, what
is the point r?

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Well we know that its
x-coordinate is 1 out, so it's

00:03:34.830 --> 00:03:38.020
1, and then what's
the y-coordinate?

00:03:38.020 --> 00:03:40.430
Well, this height right
here is 3, right?

00:03:40.430 --> 00:03:42.530
And we're starting at 0,
so we go 3 up from 0.

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So this is going to
be 3 right here.

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So the r's coordinate is 1, 3.

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And r is on the yellow parabola,
so now we are set.

00:03:54.070 --> 00:03:57.780
We can take this and substitute
x and y here.

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We know y is equal to 3
when x is equal to 1.

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So 1 squared, right?
x squared.

00:04:07.440 --> 00:04:11.630
So 3 is equal to a times
1 squared is 1.

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So a is equal to 3 because
that one doesn't matter,

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right? a is equal to
3 so we just write

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down 3 inside there.

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Next problem.

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Problem 13.

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If a times b plus b is equal
to a plus 2c, what is the

00:04:40.650 --> 00:04:50.880
value of b when a is equal
to 2 and c is equal to 3?

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So a real quick thing that we
can do just to maybe simplify

00:04:55.270 --> 00:04:58.600
things for us is we can factor
out the b out of this side.

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What do I mean by factoring
out a b?

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Well, divide both of these terms
by b and you get b times

00:05:04.630 --> 00:05:09.410
a plus 1 is equal
to a plus 2c.

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All right, let me box this out
so you don't get confused.

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All I did is I undistribute
the b, right?

00:05:14.290 --> 00:05:16.450
You can multiply this back
out and you'd get

00:05:16.450 --> 00:05:18.610
ab is equal to b.

00:05:18.610 --> 00:05:21.340
And then if you want to solve
for b, divide both sides by a

00:05:21.340 --> 00:05:28.680
plus 1 and you get b is equal
to a plus 2c over a plus 1.

00:05:28.680 --> 00:05:31.010
And then you substitute.

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So a is 2, so it's 2 plus 2
times c, c is 3, 2 times 3

00:05:38.100 --> 00:05:45.790
over 2 plus 1, which is equal
to 2 plus 6 over 3, which is

00:05:45.790 --> 00:05:46.340
equal to what?

00:05:46.340 --> 00:05:48.330
8/3.

00:05:48.330 --> 00:05:50.200
Another way you could have done
it-- and it might have

00:05:50.200 --> 00:05:51.610
been even faster, actually--
is just to

00:05:51.610 --> 00:05:53.150
substitute from the beginning.

00:05:53.150 --> 00:05:59.650
So you say a is 2, so that would
give us 2b plus b right?

00:05:59.650 --> 00:06:06.650
I just, a is 2 is equal to 2
plus 2 times c, 2 plus 6.

00:06:06.650 --> 00:06:09.790
So you get 2b plus b,
so what's 2b plus b?

00:06:09.790 --> 00:06:11.160
That's 3b.

00:06:11.160 --> 00:06:14.200
3b is equal to 2 plus 6, 8.

00:06:14.200 --> 00:06:15.950
Actually this would
have been faster.

00:06:15.950 --> 00:06:18.220
8 divided by 3.

00:06:18.220 --> 00:06:19.940
So those are two ways you
could have done it, and

00:06:19.940 --> 00:06:22.460
hopefully you'll do them
one of the two ways.

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Hopefully you'll do
it the faster way.

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Next problem.

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14.

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Bunch of lines for me to draw.

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I do so much for you guys.

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The only thing I get in return
is the satisfaction of you

00:06:41.630 --> 00:06:42.980
guys getting a perfect
score on the SAT.

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I'm going to take these videos
down before I have kids,

00:06:48.170 --> 00:06:50.460
though, so they don't
have competition.

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Let's see, OK.

00:06:52.070 --> 00:06:53.632
I'm kidding.

00:06:53.632 --> 00:06:55.610
The competition will only
make them stronger.

00:06:55.610 --> 00:06:58.682
I don't have kids yet, by the
way, but one day I will.

00:06:58.682 --> 00:07:03.800
And they'll have to compete
against you guys, who I've

00:07:03.800 --> 00:07:06.200
given this edge to.

00:07:06.200 --> 00:07:08.130
That's how selfless I am.

00:07:08.130 --> 00:07:10.090
And anyway, back
to the problem.

00:07:10.090 --> 00:07:15.720
So we have this-- I'm only
partially serious.

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OK, this is l, this
is a, b, c.

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This is angle y, y degrees.

00:07:32.670 --> 00:07:37.750
This out here is angle
x, x degrees.

00:07:37.750 --> 00:07:41.630
In the figure above, m is
parallel to n, so this is m,

00:07:41.630 --> 00:07:44.540
this is n, they are parallel.

00:07:44.540 --> 00:07:46.000
Fair enough?

00:07:46.000 --> 00:07:49.700
And l bisects angle abc.

00:07:53.280 --> 00:07:55.320
So what does bisect mean?

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That means that it splits the
angle perfectly, so that tells

00:07:59.190 --> 00:08:03.840
us that angle is equivalent
to this angle.

00:08:03.840 --> 00:08:04.650
OK?

00:08:04.650 --> 00:08:13.580
If y is between 45 and
55, what is one

00:08:13.580 --> 00:08:16.590
possible value for x?

00:08:16.590 --> 00:08:22.420
So let's just say that y is 50
and see what we can do here.

00:08:22.420 --> 00:08:26.940
So if y is 50, right?

00:08:26.940 --> 00:08:31.320
That satisfies, this is
between 45 and 55.

00:08:31.320 --> 00:08:33.214
What is this larger angle
here that I'm

00:08:33.214 --> 00:08:36.039
going to do in magenta?

00:08:36.039 --> 00:08:37.750
Well, it's a corresponding
angle, right?

00:08:37.750 --> 00:08:41.230
Because it's a parallel line,
k is a transversal, so this

00:08:41.230 --> 00:08:43.010
magenta angle corresponds
to y.

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So it will also be
equal to 50.

00:08:45.750 --> 00:08:50.990
And we know l bisects this
angle, so both of these

00:08:50.990 --> 00:08:55.640
smaller angles are going
to be 25 and 25.

00:08:55.640 --> 00:08:58.500
And now l is a transversal
as well.

00:08:58.500 --> 00:09:02.400
So if l is 25, this angle
right here is 25.

00:09:02.400 --> 00:09:05.360
Let me do that in
another color.

00:09:05.360 --> 00:09:07.040
No, that color was
too similar.

00:09:07.040 --> 00:09:08.500
I'll do it in red.

00:09:08.500 --> 00:09:12.900
If this right here is 25, what
angle is this going to be?

00:09:12.900 --> 00:09:16.203
Well once again, corresponding
angles of a transversal, so

00:09:16.203 --> 00:09:18.180
this is also going to be 25.

00:09:18.180 --> 00:09:20.370
And now what could x be?

00:09:20.370 --> 00:09:23.320
Well, x is opposite to this
angle, so it's also going to

00:09:23.320 --> 00:09:25.300
be 25 degrees.

00:09:25.300 --> 00:09:29.250
So this is just the angle
game on steroids.

00:09:29.250 --> 00:09:30.970
And you really didn't have to do
the range, you just pick a

00:09:30.970 --> 00:09:33.980
number. y is 50, corresponding
angle is also 50.

00:09:33.980 --> 00:09:37.740
That corresponding angle is
bisected, so each of these

00:09:37.740 --> 00:09:38.950
smaller angles is 25.

00:09:38.950 --> 00:09:42.540
And then l is a transversal
again, so if this is 25, this

00:09:42.540 --> 00:09:44.420
is 25, and x is opposite.

00:09:44.420 --> 00:09:46.560
So it's also 25.

00:09:46.560 --> 00:09:48.460
I'll see you in the
next video.


SAT Prep: Test 4 Section 8 Part 1

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Language: en

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Welcome back.

00:00:01.410 --> 00:00:03.960
We're now going to start section
eight in test four.

00:00:03.960 --> 00:00:06.210
Let's start with problem
number one.

00:00:06.210 --> 00:00:13.530
Problem number one-- if 3 times
n minus 4 is equal to

00:00:13.530 --> 00:00:17.230
18, what is n?

00:00:17.230 --> 00:00:18.820
n is equal to what?

00:00:18.820 --> 00:00:20.590
Let's divide both sides by 3.

00:00:20.590 --> 00:00:23.940
You get n minus 4
is equal to 6.

00:00:23.940 --> 00:00:28.210
Add 4 to both sides and
you get n equals 10.

00:00:28.210 --> 00:00:30.300
And that is choice D.

00:00:30.300 --> 00:00:31.545
Problem number two.

00:00:31.545 --> 00:00:31.850
Right?

00:00:31.850 --> 00:00:34.000
It was divided by-- well
you know what I did.

00:00:34.000 --> 00:00:35.550
Hopefully you know what I did.

00:00:35.550 --> 00:00:39.470
Two, for a class ring, each
senior can choose from 4 types

00:00:39.470 --> 00:00:41.500
of stones and 3 types
of metal.

00:00:46.470 --> 00:00:50.230
How many combinations of a stone
and metal are there?

00:00:50.230 --> 00:00:52.100
Well, for each stone
they can pick 3

00:00:52.100 --> 00:00:53.810
different metals, right?

00:00:53.810 --> 00:00:57.200
So there's 4-- because there's
4 different types of stones--

00:00:57.200 --> 00:00:59.305
and each of them can have
3 different metals.

00:00:59.305 --> 00:01:06.870
So it's 4 times 3 combinations
which is choice D.

00:01:10.710 --> 00:01:12.370
Next problem.

00:01:12.370 --> 00:01:12.910
Problem three.

00:01:12.910 --> 00:01:15.490
If you ever doubt yourself on
the first one or two problems

00:01:15.490 --> 00:01:18.020
because it seems too easy, you
probably shouldn't doubt

00:01:18.020 --> 00:01:20.860
yourself, because the first
couple of problems tend to be

00:01:20.860 --> 00:01:22.520
reasonably straightforward.

00:01:22.520 --> 00:01:24.430
I was just doubting myself
because I was like, was I

00:01:24.430 --> 00:01:25.630
missing something?

00:01:25.630 --> 00:01:26.100
All right.

00:01:26.100 --> 00:01:27.140
Problem number three.

00:01:27.140 --> 00:01:40.310
The sum of 3a and the square
root of b is equal to the

00:01:40.310 --> 00:01:42.270
square of the sum of a and b.

00:01:48.710 --> 00:01:50.700
Which of the following
is an expression for

00:01:50.700 --> 00:01:51.950
the statement above?

00:01:51.950 --> 00:01:53.870
Well, I just wrote it out.

00:01:53.870 --> 00:01:55.470
It's choice B.

00:01:55.470 --> 00:01:59.510
But hopefully, as I talked it
out, you saw what I was doing.

00:01:59.510 --> 00:02:05.830
I said the sum of 3a and the
square root of b-- this is the

00:02:05.830 --> 00:02:09.090
sum of 3a and the square root of
b-- is equal to the sum of

00:02:09.090 --> 00:02:11.380
a plus b squared.

00:02:11.380 --> 00:02:14.490
Or they said, equal to the
square of the sum of a plus b.

00:02:17.350 --> 00:02:18.550
Next problem.

00:02:18.550 --> 00:02:20.690
Problem four.

00:02:20.690 --> 00:02:23.620
Carrie has a cordless telephone
receiver that can

00:02:23.620 --> 00:02:26.710
operate within a range
of 1,000 feet.

00:02:26.710 --> 00:02:30.470
1,000 foot range from the
telephone's base.

00:02:30.470 --> 00:02:33.330
Carrie takes the receiver
from the base and walks

00:02:33.330 --> 00:02:34.760
800 feet due north.

00:02:34.760 --> 00:02:38.390
So this is the base and-- I
don't know if Carrie is a boy

00:02:38.390 --> 00:02:43.490
or girl's name-- but Carrie
walked 800 feet due north.

00:02:43.490 --> 00:02:47.510
From that point she walks due
east and stops at the maximum

00:02:47.510 --> 00:02:48.760
range of the receiver.

00:02:55.420 --> 00:02:58.380
In which of the following
directions can Carrie walk and

00:02:58.380 --> 00:03:00.490
still be within range
of the receiver?

00:03:00.490 --> 00:03:03.660
So the range is essentially
that you can go 1,000 feet

00:03:03.660 --> 00:03:05.950
from this point b.

00:03:05.950 --> 00:03:06.470
Right?

00:03:06.470 --> 00:03:09.190
And actually, let me draw
it as a circle.

00:03:09.190 --> 00:03:16.080
So I can go, at most-- so let
me draw the circle here-- so

00:03:16.080 --> 00:03:22.610
let's say that this is the
point b, that's the base.

00:03:22.610 --> 00:03:25.230
Let's say Carrie's a guy.

00:03:25.230 --> 00:03:27.810
Carrie can get at most 1,000
feet away from the receiver.

00:03:27.810 --> 00:03:30.390
So the furthest distance that
Carrie can get from the

00:03:30.390 --> 00:03:32.460
receiver is 1,000 feet.

00:03:32.460 --> 00:03:36.350
So this radius right
here is 1,000 feet.

00:03:36.350 --> 00:03:40.510
And in the problem, Carrie
walks 800 feet due north.

00:03:40.510 --> 00:03:42.760
So maybe right there.

00:03:42.760 --> 00:03:44.160
That's 800.

00:03:44.160 --> 00:03:50.290
And then he walks due east to
the range of the receiver.

00:03:50.290 --> 00:03:54.190
So then walks east, which is
this direction, to the range

00:03:54.190 --> 00:03:55.580
of the receiver, which
is right there.

00:03:55.580 --> 00:03:57.780
And what they want to know is,
in which of the following

00:03:57.780 --> 00:03:59.470
directions can Carrie
walk and still be in

00:03:59.470 --> 00:04:00.930
range of the receiver?

00:04:00.930 --> 00:04:04.900
Well, we know Carrie can't walk
north because then he or

00:04:04.900 --> 00:04:06.120
she will be out of range
of the receiver.

00:04:06.120 --> 00:04:08.260
Can't walk east. It would
be out of the

00:04:08.260 --> 00:04:08.920
range of the receiver.

00:04:08.920 --> 00:04:13.720
But he or she can walk south or
can walk back west, right?

00:04:13.720 --> 00:04:17.209
So they can walk south or west.
And those are choices 2

00:04:17.209 --> 00:04:21.079
and 3, which is choice E.

00:04:21.079 --> 00:04:24.890
Choice E is 2 and 3, which is
due south or due west. They

00:04:24.890 --> 00:04:28.730
can walk this way, south,
or west, that way.

00:04:28.730 --> 00:04:29.980
Next problem.

00:04:32.670 --> 00:04:33.920
Whoops.

00:04:36.680 --> 00:04:37.930
Problem five.

00:04:41.270 --> 00:04:49.640
If x over 4 is equal to 2x over
a, and x does not equal

00:04:49.640 --> 00:04:52.900
0, what is the value of a?

00:04:52.900 --> 00:04:55.910
Well, we can divide both sides
by x because we know x doesn't

00:04:55.910 --> 00:04:57.610
equal 0, because you
can't divide by 0.

00:04:57.610 --> 00:04:59.980
So this and this would
cancel out, right?

00:04:59.980 --> 00:05:02.240
We're dividing both
sides by x.

00:05:02.240 --> 00:05:06.050
So you get 1/4 is equal
to 2 over a.

00:05:06.050 --> 00:05:09.150
And you could eyeball this,
but if you want to do it

00:05:09.150 --> 00:05:12.750
mathematically, you could say 1
times a is equal to 4 times

00:05:12.750 --> 00:05:14.970
2, which is 8.

00:05:14.970 --> 00:05:19.100
And you could have said, well
2 is 1/4 of what number?

00:05:19.100 --> 00:05:20.040
Well it's 8.

00:05:20.040 --> 00:05:22.590
So a is equal to 8.

00:05:22.590 --> 00:05:24.520
Choice A.

00:05:24.520 --> 00:05:26.340
Problem number six.

00:05:26.340 --> 00:05:29.086
And we have a little
drawing here to do.

00:05:29.086 --> 00:05:30.750
Let's see, problem number six.

00:05:30.750 --> 00:05:34.037
So we have a parallel line like
that, actually I don't

00:05:34.037 --> 00:05:35.810
know if they're parallel yet,
because they haven't told me.

00:05:35.810 --> 00:05:37.300
But it kind of looks like that,

00:05:37.300 --> 00:05:38.710
although I shouldn't assume.

00:05:38.710 --> 00:05:41.560
We have a transversal, if
those are parallel.

00:05:41.560 --> 00:05:43.590
Let me switch colors.

00:05:43.590 --> 00:05:44.100
OK.

00:05:44.100 --> 00:05:48.010
So they're saying that this
angle right here is r.

00:05:48.010 --> 00:05:53.340
This is u, s, t.

00:05:53.340 --> 00:05:54.640
And this is line l.

00:05:54.640 --> 00:05:56.150
This is line m.

00:05:56.150 --> 00:05:58.360
In the figure above,
l is parallel to m.

00:05:58.360 --> 00:06:00.640
So l and m are parallel.

00:06:00.640 --> 00:06:01.710
I was right.

00:06:01.710 --> 00:06:03.075
And r is 50 degrees.

00:06:03.075 --> 00:06:06.030
So r is equal to 50 degrees.

00:06:06.030 --> 00:06:09.890
What is the value of
s plus t plus u?

00:06:09.890 --> 00:06:12.260
Well, what are the angles that
are corresponding to r?

00:06:12.260 --> 00:06:15.170
If r is 50, the corresponding
angle here is, so this is kind

00:06:15.170 --> 00:06:17.140
of the same-- if you don't
remember this, you might want

00:06:17.140 --> 00:06:19.800
to review the geometry module
where I do this-- the

00:06:19.800 --> 00:06:21.150
corresponding angle here is u.

00:06:21.150 --> 00:06:22.540
And so this angle
is also going to

00:06:22.540 --> 00:06:24.800
be equal to 50 degrees.

00:06:24.800 --> 00:06:26.330
Let me do a different color.

00:06:26.330 --> 00:06:28.120
So that equals 50, and that's
because they kind of take the

00:06:28.120 --> 00:06:31.220
same role where the transversal
intersects the

00:06:31.220 --> 00:06:32.240
parallel lines.

00:06:32.240 --> 00:06:35.510
And if this is 50, this is the
opposite angle, right?

00:06:35.510 --> 00:06:39.910
So that angle is also
going to be 50.

00:06:39.910 --> 00:06:43.760
And t and u are supplementary,
right?

00:06:43.760 --> 00:06:46.040
So t plus u is going
to be 180.

00:06:46.040 --> 00:06:50.850
Or you could say that
this is 130, right?

00:06:50.850 --> 00:06:53.320
So what's 50 plus 50 plus 130?

00:06:53.320 --> 00:06:54.540
It's 100 plus 130.

00:06:54.540 --> 00:06:59.210
It's 230 degrees, which
is choice A.

00:06:59.210 --> 00:07:00.460
Next problem.

00:07:03.290 --> 00:07:04.690
Invert colors.

00:07:04.690 --> 00:07:06.960
Problem number seven.

00:07:06.960 --> 00:07:10.830
In the x-y coordinate plane,
line l is perpendicular to the

00:07:10.830 --> 00:07:16.770
y-axis and passes through
the point 5, negative 3.

00:07:16.770 --> 00:07:21.690
So let me-- those are my axes.

00:07:25.870 --> 00:07:29.140
y. x.

00:07:29.140 --> 00:07:32.910
And this line-- I'll draw it in
green-- it passes through

00:07:32.910 --> 00:07:34.320
the point 5, negative 3.

00:07:34.320 --> 00:07:36.710
So that's like here someplace.

00:07:36.710 --> 00:07:38.975
And it's perpendicular
to the y-axis.

00:07:38.975 --> 00:07:41.000
This is the y-axis, so
perpendicular to it.

00:07:41.000 --> 00:07:45.540
So it forms a 90 degree angle.

00:07:45.540 --> 00:07:47.775
And we know this is
a 90 degree angle.

00:07:47.775 --> 00:07:56.050
And it passes through the point
5, and then minus 3.

00:07:56.050 --> 00:07:57.240
So this is the point
right here.

00:07:57.240 --> 00:08:02.040
This is 5 comma minus 3.

00:08:02.040 --> 00:08:05.500
Which of the following is an
equation of the line l?

00:08:05.500 --> 00:08:08.540
OK, well what is the
slope of this?

00:08:08.540 --> 00:08:11.570
It's a flat line.

00:08:11.570 --> 00:08:14.170
As much as you run-- as much
as you have a change in x--

00:08:14.170 --> 00:08:15.850
there's no change in y, right?

00:08:15.850 --> 00:08:18.420
So the slope is 0.

00:08:18.420 --> 00:08:19.910
And what's the y-intercept?

00:08:19.910 --> 00:08:22.900
The y-intercept is where you
intersect the y-axis.

00:08:22.900 --> 00:08:24.700
Well, you're going to intersect
it at y equals

00:08:24.700 --> 00:08:25.380
negative 3.

00:08:25.380 --> 00:08:27.580
So b is minus 3.

00:08:27.580 --> 00:08:30.630
And if you don't-- I'm saying
this from the form-- y equals

00:08:30.630 --> 00:08:32.730
mx plus b is the slope
of a line.

00:08:32.730 --> 00:08:37.640
m is 0, b is 3, so we know the
slope is y equals negative 3.

00:08:37.640 --> 00:08:39.190
That's the equation.

00:08:39.190 --> 00:08:42.110
y equals negative 3,
that's choice C.

00:08:42.110 --> 00:08:44.420
And in general, if you just drew
this line, you're like,

00:08:44.420 --> 00:08:47.900
well, no matter what x is,
y is equal to negative 3.

00:08:47.900 --> 00:08:49.200
And you could say, well
that's the equation.

00:08:49.200 --> 00:08:52.130
y is equal to negative 3.

00:08:52.130 --> 00:08:53.610
I have a minute left.

00:08:53.610 --> 00:08:55.110
I don't think that's enough
time to do a problem.

00:08:55.110 --> 00:08:56.880
It might be, but I don't
want to rush things.

00:08:56.880 --> 00:08:58.660
So I'll do the next problem
in the next video.

00:08:58.660 --> 00:09:00.140
I'll see you soon.


SAT Prep: Test 4 Section 8 Part 2

WEBVTT
Kind: captions
Language: en

00:00:00.730 --> 00:00:02.603
Here we are on problem
number 8.

00:00:05.210 --> 00:00:08.600
The total daily profit, p in
dollars, from producing and

00:00:08.600 --> 00:00:11.070
selling x units of a certain
product is given by the

00:00:11.070 --> 00:00:13.240
function p of x.

00:00:13.240 --> 00:00:24.170
So the profit as a function of
x is equal to 17x minus 10x

00:00:24.170 --> 00:00:27.880
plus b where b is a constant.

00:00:27.880 --> 00:00:31.370
If 300 units were produced and
sold yesterday for a profit of

00:00:31.370 --> 00:00:34.620
$1,900, what is the
value of b?

00:00:34.620 --> 00:00:41.470
So we know that p of 300-- 300
units-- the profit when we did

00:00:41.470 --> 00:00:45.710
300 units is $1,900.

00:00:45.710 --> 00:00:47.580
And we want to figure out b.

00:00:47.580 --> 00:00:49.260
So what is p of 300?

00:00:49.260 --> 00:00:50.520
So let's put 300 in here.

00:00:50.520 --> 00:00:53.320
We know it also equals 1,900
but let's put it here.

00:00:53.320 --> 00:01:03.200
So it's 17 times 300 minus
10 times 300 plus b.

00:01:03.200 --> 00:01:05.290
I just put 300 in for x.

00:01:05.290 --> 00:01:07.170
So we're trying to find the
profit for 300 and we know

00:01:07.170 --> 00:01:12.610
already that equals 1,900.

00:01:12.610 --> 00:01:14.480
So what's 17 times 300?

00:01:14.480 --> 00:01:18.160
17 times 3 is 51.

00:01:18.160 --> 00:01:20.320
Let's add those two 0s.

00:01:20.320 --> 00:01:27.800
Minus-- and what's 10 times 300,
that's 3,000-- 3,000 plus

00:01:27.800 --> 00:01:31.940
b is equal to 1,900.

00:01:31.940 --> 00:01:37.620
And then we get 5,100
minus 3,000 minus

00:01:37.620 --> 00:01:40.670
b is equal to 1,900.

00:01:40.670 --> 00:01:42.140
What's 5,100 minus 3,000?

00:01:42.140 --> 00:01:42.440
2,100.

00:01:42.440 --> 00:01:47.350
And 2,100 minus b is
equal to 1,900.

00:01:47.350 --> 00:01:51.170
Minus b is equal to, subtract
2,100 from both sides, and you

00:01:51.170 --> 00:01:53.060
get minus 200.

00:01:53.060 --> 00:01:55.510
b is equal to 200.

00:01:55.510 --> 00:01:56.760
And that is choice E.

00:01:59.530 --> 00:02:00.780
Next problem.

00:02:03.810 --> 00:02:05.780
Problem number 9.

00:02:05.780 --> 00:02:08.080
I will switch colors.

00:02:08.080 --> 00:02:11.009
The number that results when
an integer is multiplied by

00:02:11.009 --> 00:02:15.280
itself cannot end in which
of the following digits?

00:02:15.280 --> 00:02:16.160
Interesting.

00:02:16.160 --> 00:02:18.650
Well, what's a number when it's
multiplied by itself?

00:02:18.650 --> 00:02:19.880
That's like squaring a number.

00:02:19.880 --> 00:02:21.840
So let's kind of study
what all the perfect

00:02:21.840 --> 00:02:22.580
squares look like.

00:02:22.580 --> 00:02:24.640
So when I square 1, I get 1.

00:02:24.640 --> 00:02:26.680
When I square 2 I get 4.

00:02:26.680 --> 00:02:28.760
When I square 3 I get 9.

00:02:28.760 --> 00:02:31.710
Square 4 I get 16.

00:02:31.710 --> 00:02:33.060
5 is 25.

00:02:33.060 --> 00:02:34.900
6 is 36.

00:02:34.900 --> 00:02:37.460
7 is 49.

00:02:37.460 --> 00:02:38.930
8 is 64.

00:02:38.930 --> 00:02:42.130
So let's look at the numbers
that it can be.

00:02:42.130 --> 00:02:44.520
OK, we could go 9 is 81.

00:02:44.520 --> 00:02:48.060
Looks like it can be a 1, a
4, a 9-- and we could keep

00:02:48.060 --> 00:02:55.980
going-- 1, 4, 9, a 6, a 5, and
actually if we went to, 8 is

00:02:55.980 --> 00:02:57.840
64 so it's a 4.

00:02:57.840 --> 00:03:00.250
9 is-- oh we already
did that-- and

00:03:00.250 --> 00:03:01.480
then 10 is a 0, right?

00:03:01.480 --> 00:03:03.660
It can also end in a 0.

00:03:03.660 --> 00:03:06.460
The choices, A, sure a
number can end in 1.

00:03:06.460 --> 00:03:07.430
We just figured that out.

00:03:07.430 --> 00:03:10.010
Choice B, sure a number
can end in 4.

00:03:10.010 --> 00:03:12.470
Choice C, sure a number
can end in 5.

00:03:12.470 --> 00:03:14.550
Thus 25 as an example.

00:03:14.550 --> 00:03:17.470
Choice D, a number
can end in 6.

00:03:17.470 --> 00:03:19.560
Choice E, well none of
the numbers we looked

00:03:19.560 --> 00:03:21.170
at end in an 8.

00:03:21.170 --> 00:03:23.970
And it seems like there's a bit
of a pattern here, that it

00:03:23.970 --> 00:03:26.760
tends to be just a set-- a
subset-- of these numbers.

00:03:26.760 --> 00:03:28.880
And also we know that the other
choices-- choices A

00:03:28.880 --> 00:03:31.280
through D-- we can figure out
perfect squares that end in

00:03:31.280 --> 00:03:32.960
those numbers.

00:03:32.960 --> 00:03:37.640
So we know that the
answer is E.

00:03:37.640 --> 00:03:38.890
Next problem.

00:03:41.260 --> 00:03:43.540
Problem number 10.

00:03:43.540 --> 00:03:46.190
A bag contains only red marbles,
blue marbles, and

00:03:46.190 --> 00:03:47.310
yellow marbles.

00:03:47.310 --> 00:03:50.620
The probability of randomly
selecting a red marble from

00:03:50.620 --> 00:03:53.380
this bag is 1/4.

00:03:53.380 --> 00:03:57.630
So I can say the probability
of red is equal to 1/4.

00:03:57.630 --> 00:03:58.750
The probability of randomly
selecting a

00:03:58.750 --> 00:04:00.000
blue marble is 1/6.

00:04:04.120 --> 00:04:07.970
Which of the following could be
the total number of marbles

00:04:07.970 --> 00:04:10.000
in the bag?

00:04:10.000 --> 00:04:10.820
Fascinating.

00:04:10.820 --> 00:04:13.090
So what we need to do is we need
to essentially figure out

00:04:13.090 --> 00:04:18.140
the ratio of red to blue
to yellow marbles.

00:04:18.140 --> 00:04:20.600
So first of all, what's the
probability of getting a

00:04:20.600 --> 00:04:22.440
yellow marble?

00:04:22.440 --> 00:04:24.580
The probability of getting a
yellow marble is going to be 1

00:04:24.580 --> 00:04:25.670
minus these, right?

00:04:25.670 --> 00:04:29.410
So probability of yellow
is going to be 1

00:04:29.410 --> 00:04:32.750
minus 1/6 minus 1/4.

00:04:32.750 --> 00:04:36.670
Let's see, we could put
all of that over 12.

00:04:36.670 --> 00:04:45.120
12 minus 2/6 minus 3/12--
3/12 is 1/4.

00:04:45.120 --> 00:04:47.240
So that equals-- what's
12 minus 10?

00:04:47.240 --> 00:04:51.220
That equals 7/12.

00:04:51.220 --> 00:04:57.580
So the probability I get a
yellow marble is 7/12.

00:04:57.580 --> 00:05:02.510
So that means for every 7
marbles-- so let's write it

00:05:02.510 --> 00:05:03.900
all is a denominator of 12.

00:05:03.900 --> 00:05:05.120
That makes it actually
a lot easier.

00:05:05.120 --> 00:05:08.330
1/6 is the same thing as 2/12.

00:05:08.330 --> 00:05:10.345
And 1/4 is the same
thing as 3/12.

00:05:10.345 --> 00:05:13.210
And they all add up to 12/12.

00:05:13.210 --> 00:05:19.580
So for every 3 red marbles,
there are 2 blue marbles and

00:05:19.580 --> 00:05:21.350
there are 7 yellow marbles.

00:05:21.350 --> 00:05:28.606
The ratio of red to blue to
yellow is equal to 3:2:7.

00:05:33.370 --> 00:05:36.970
And we know we can only get
this type of a ratio when

00:05:36.970 --> 00:05:39.480
there's a total of 12
marbles, right?

00:05:39.480 --> 00:05:44.000
There has to be at least 12
marbles or any multiple of 12

00:05:44.000 --> 00:05:44.930
marbles, right?

00:05:44.930 --> 00:05:50.100
If there's exactly 2 blue
marbles, then there'll be 3

00:05:50.100 --> 00:05:52.870
red and 7 yellow.

00:05:52.870 --> 00:05:55.910
And there has to be at least
2 of the blue marbles.

00:05:55.910 --> 00:05:59.410
So any multiple of 12 marbles
will work for

00:05:59.410 --> 00:06:01.130
this type of ratio.

00:06:01.130 --> 00:06:05.590
So if we look at the choices,
which of the following could

00:06:05.590 --> 00:06:08.770
be the total number of
marbles in the bag?

00:06:08.770 --> 00:06:10.305
So out of all those choices,
which of them are

00:06:10.305 --> 00:06:11.960
a multiple of 12?

00:06:11.960 --> 00:06:13.360
Well, choice A isn't.

00:06:13.360 --> 00:06:14.430
10 isn't a multiple of 12.

00:06:14.430 --> 00:06:15.460
Choice C isn't.

00:06:15.460 --> 00:06:16.720
18, 20, 30.

00:06:16.720 --> 00:06:20.530
Well 12 is a multiple of 12,
so choice B is our answer.

00:06:20.530 --> 00:06:21.490
And we just figured out.

00:06:21.490 --> 00:06:26.800
If there were 3 red, 2 blue and
7 yellow, then we get the

00:06:26.800 --> 00:06:29.160
correct probabilities.

00:06:29.160 --> 00:06:30.630
The key is just to try to
figure out what the

00:06:30.630 --> 00:06:33.680
probability of getting a yellow
is and then realizing

00:06:33.680 --> 00:06:35.900
the ratios between the two.

00:06:35.900 --> 00:06:38.800
Next problem.

00:06:38.800 --> 00:06:42.000
Problem 11.

00:06:42.000 --> 00:06:46.420
When the sum of a list of
prices is divided by the

00:06:46.420 --> 00:06:50.060
average of the prices
the result is k.

00:06:50.060 --> 00:06:53.120
What does k represent?

00:06:53.120 --> 00:06:56.510
So if I take the sum divided
by the average.

00:06:56.510 --> 00:07:01.160
So let's say I'm taking the
sum of three numbers.

00:07:01.160 --> 00:07:08.230
So let's say, n1 plus
n2 plus n3.

00:07:08.230 --> 00:07:11.940
I could do it n times, but
just for simplicity.

00:07:11.940 --> 00:07:16.220
And I'm dividing that
by the average.

00:07:16.220 --> 00:07:17.040
What's the average?

00:07:17.040 --> 00:07:24.720
It's n1 plus n2 plus n3
divided by 3, right?

00:07:24.720 --> 00:07:26.840
And if you divide by a fraction,
that's the same

00:07:26.840 --> 00:07:29.170
thing as multiplying
by the reciprocal.

00:07:29.170 --> 00:07:34.970
So that's n1 plus n2 plus
n3 times 3 over n1

00:07:34.970 --> 00:07:37.580
plus n2 plus n3.

00:07:37.580 --> 00:07:40.700
So this cancels out, and all
we're left with is 3, which is

00:07:40.700 --> 00:07:44.460
the number of numbers we had.

00:07:44.460 --> 00:07:47.790
And you could have done this
with 16 or 20 or whatever.

00:07:47.790 --> 00:07:50.790
I mean you could have
said n1 plus n2 plus

00:07:50.790 --> 00:07:53.280
da, da, da, da, da.

00:07:53.280 --> 00:07:57.830
Where I have, let's say, n
sub-- let's say I have m

00:07:57.830 --> 00:08:03.250
digits-- and then divide that by
n1 plus n2 plus blah, blah,

00:08:03.250 --> 00:08:03.880
blah, blah.

00:08:03.880 --> 00:08:07.080
n over m.

00:08:07.080 --> 00:08:08.050
Sub m digits.

00:08:08.050 --> 00:08:09.700
And say, well I'm
dividing by m.

00:08:09.700 --> 00:08:12.205
This would have also simplified
to m digits.

00:08:15.200 --> 00:08:18.600
When you do what they said in
the problem, the result is

00:08:18.600 --> 00:08:22.840
just the number of prices
that you are summing.

00:08:22.840 --> 00:08:26.290
So that is choice D, the
number of prices.

00:08:26.290 --> 00:08:28.810
And it works out because
this sum and this

00:08:28.810 --> 00:08:31.190
sum will cancel out.

00:08:31.190 --> 00:08:32.340
Next problem.

00:08:32.340 --> 00:08:36.829
Let's see how fast-- if
I can fit this one in.

00:08:36.829 --> 00:08:38.220
So I have a drawing.

00:08:38.220 --> 00:08:39.020
It looks like this.

00:08:39.020 --> 00:08:44.220
Let's see, triangle, triangle,
triangle, triangle, and then

00:08:44.220 --> 00:08:47.940
dotted lines, dotted lines,
dotted lines, dotted lines.

00:08:47.940 --> 00:08:50.770
It says, if the area of the
square in the figure above is

00:08:50.770 --> 00:08:54.120
81-- so they're saying this is
a square, and if the area is

00:08:54.120 --> 00:08:56.480
81-- then we know that this side
is 9 and this side is 9.

00:08:56.480 --> 00:08:57.150
Right?

00:08:57.150 --> 00:08:59.930
This is 9 times 9.

00:08:59.930 --> 00:09:07.480
And the perimeter of each of
the four triangles is 30.

00:09:07.480 --> 00:09:10.500
So the perimeter is 30
of each of those.

00:09:10.500 --> 00:09:13.920
What is the perimeter of
the figure outlined

00:09:13.920 --> 00:09:16.170
by the solid line?

00:09:16.170 --> 00:09:17.670
Well think about it.

00:09:17.670 --> 00:09:19.880
The perimeter of the solid
line, that would be this.

00:09:23.160 --> 00:09:25.080
That's what we want
to figure out.

00:09:25.080 --> 00:09:28.690
Well wouldn't that just be
the perimeter of the four

00:09:28.690 --> 00:09:33.110
triangles, and then we want to
subtract out this side, this

00:09:33.110 --> 00:09:36.200
side, this side and
this side, right?

00:09:36.200 --> 00:09:40.190
The perimeter of the red part
is the perimeter of each of

00:09:40.190 --> 00:09:43.840
the triangles-- added up, all
four of them-- minus the

00:09:43.840 --> 00:09:46.260
perimeter of the
square inside.

00:09:46.260 --> 00:09:51.230
So the perimeter of the four
triangles is 30 times 4, minus

00:09:51.230 --> 00:09:54.090
the perimeter of this,
which is minus 27.

00:09:54.090 --> 00:09:56.090
No whoops, minus 36.

00:09:56.090 --> 00:10:01.190
So it's 120 minus
36 and that is--


SAT Prep: Test 4 Section 8 Part 3

WEBVTT
Kind: captions
Language: en

00:00:00.780 --> 00:00:01.410
Welcome back.

00:00:01.410 --> 00:00:02.560
I think I was rushing
that problem.

00:00:02.560 --> 00:00:06.160
So let me just make it clear
again, just so you don't get

00:00:06.160 --> 00:00:07.270
confused, because I was
trying to get under

00:00:07.270 --> 00:00:08.930
that 10-minute limit.

00:00:08.930 --> 00:00:10.800
But they want to know what
the perimeter of

00:00:10.800 --> 00:00:12.860
this red is, right?

00:00:12.860 --> 00:00:14.980
That's kind of the outside of
this thing that looks like a

00:00:14.980 --> 00:00:16.570
flower or something.

00:00:16.570 --> 00:00:19.370
And what I'm saying is that the
perimeter of the red part

00:00:19.370 --> 00:00:22.000
is equivalent to the sum of
the perimeters of the

00:00:22.000 --> 00:00:24.490
rectangle-- of the triangle,
sorry-- the sum of the

00:00:24.490 --> 00:00:25.620
perimeters of the triangles.

00:00:25.620 --> 00:00:27.550
But if I were just to take the
sum of the perimeters of the

00:00:27.550 --> 00:00:31.230
triangle, I wouldn't just
be getting the red part.

00:00:31.230 --> 00:00:33.780
I'd also be getting in
these parts, right?

00:00:33.780 --> 00:00:36.630
Because those are parts of the
perimeters of the triangles.

00:00:36.630 --> 00:00:40.020
So if I want just the red part,
I subtract out this,

00:00:40.020 --> 00:00:43.170
what I just drew in blue, and
the blue is the perimeter of

00:00:43.170 --> 00:00:44.450
that inside square.

00:00:44.450 --> 00:00:46.350
And the perimeter of that inside
square is 9 plus 9 plus

00:00:46.350 --> 00:00:48.340
9 plus 9, or 36.

00:00:48.340 --> 00:00:52.490
So I just take the perimeter
of all four triangles.

00:00:52.490 --> 00:00:55.110
Each of them has a perimeter of
30, so together they have a

00:00:55.110 --> 00:00:59.660
perimeter of 120, and then
subtract out the perimeter of

00:00:59.660 --> 00:01:02.630
the square inside, which
has a perimeter of 36.

00:01:02.630 --> 00:01:05.450
So 120 minus 36 is what?

00:01:05.450 --> 00:01:06.690
84.

00:01:06.690 --> 00:01:07.900
Right, 84.

00:01:07.900 --> 00:01:10.740
That's choice D.

00:01:10.740 --> 00:01:11.385
Next problem.

00:01:11.385 --> 00:01:13.910
Let me remember that this is
where I ended the last one.

00:01:13.910 --> 00:01:14.830
OK, next problem.

00:01:14.830 --> 00:01:20.210
Problem number 13.

00:01:20.210 --> 00:01:24.340
The graph of g of x
is shown above.

00:01:24.340 --> 00:01:27.600
OK, I'd better draw it because
they want us to essentially

00:01:27.600 --> 00:01:29.305
look at the graph and
figure out a value.

00:01:34.810 --> 00:01:40.810
Well, let's see, it starts at
roughly-- so if I were to--

00:01:40.810 --> 00:01:47.405
let's see, 2, 4, 6, 8.

00:01:47.405 --> 00:01:54.770
And we have 2, 4, 6, 8, 10.

00:01:54.770 --> 00:01:57.010
I'll try my best to draw it like
they have. So the line

00:01:57.010 --> 00:02:03.750
starts roughly a little bit
above 6, not even up to 7.

00:02:03.750 --> 00:02:04.970
And then, where does it go?

00:02:04.970 --> 00:02:06.150
It goes to like 4.

00:02:06.150 --> 00:02:09.940
Oh my God, I thought I was
using the line tool.

00:02:09.940 --> 00:02:12.360
It starts a little bit above
6, not even up to 7.

00:02:12.360 --> 00:02:14.640
It looks like about at 1.

00:02:14.640 --> 00:02:18.140
It starts here, then it goes
to the point 4 comma 2, it

00:02:18.140 --> 00:02:19.390
looks like.

00:02:22.050 --> 00:02:26.124
And then it goes from 4 comma
2 to 6 comma 3, roughly.

00:02:26.124 --> 00:02:28.060
Or maybe even exactly.

00:02:28.060 --> 00:02:29.390
6 comma 3.

00:02:29.390 --> 00:02:32.570
And then it looks like
it goes to 8 comma 8.

00:02:32.570 --> 00:02:35.646
8 comma 8 is like
there, roughly.

00:02:35.646 --> 00:02:37.390
That's about right.

00:02:37.390 --> 00:02:40.280
And then it goes down to like--
I don't know-- almost

00:02:40.280 --> 00:02:45.020
11 comma 2.

00:02:45.020 --> 00:02:50.565
It goes to someplace like that,
and they're saying this

00:02:50.565 --> 00:02:53.040
is the graph of g of x.

00:02:53.040 --> 00:02:57.540
And they're saying, if g of 2
is equal to k, which of the

00:02:57.540 --> 00:03:00.790
following could be the
value of g of k?

00:03:00.790 --> 00:03:03.110
g of k is what?

00:03:03.110 --> 00:03:04.290
So what could k equal?

00:03:04.290 --> 00:03:06.880
Let's figure out g of 2.

00:03:06.880 --> 00:03:12.100
So when x is 2, bum, bum, bum,
bum, bum, bum, bum, bum, bum.

00:03:12.100 --> 00:03:13.780
what is y equal to?

00:03:13.780 --> 00:03:18.290
Well, it looks pretty darn close
to 5, if not exactly 5.

00:03:18.290 --> 00:03:21.010
So k is equal to 5, right?

00:03:21.010 --> 00:03:26.060
g of 2 is equal to 5, right?

00:03:26.060 --> 00:03:27.880
And they want to know
what g of k is.

00:03:27.880 --> 00:03:30.310
Well, we figured out that k is
equal 5, so now we want to

00:03:30.310 --> 00:03:32.870
know what g of 5 is.

00:03:32.870 --> 00:03:34.370
So we go to 5.

00:03:34.370 --> 00:03:36.940
We go, bup, bup,
bup, bup, bup.

00:03:36.940 --> 00:03:37.860
This is 5.

00:03:37.860 --> 00:03:40.310
And then we go bup, bup, bup,
bup, bup, bup, bup, bup, bup.

00:03:40.310 --> 00:03:42.200
Looks pretty close to 3.

00:03:42.200 --> 00:03:46.340
g of 5-- and actually the way
they drew it, it doesn't look

00:03:46.340 --> 00:03:47.370
close to 3.

00:03:47.370 --> 00:03:50.310
The way they drew it, if you
look at where 5 is, it looks

00:03:50.310 --> 00:03:51.270
actually less than 3.

00:03:51.270 --> 00:03:54.010
It looks like 2 and
1/2, actually, the

00:03:54.010 --> 00:03:55.150
way they drew it.

00:03:55.150 --> 00:03:57.000
My drawing is a little off.

00:03:57.000 --> 00:04:00.280
So if you look down, look
at the x value.

00:04:00.280 --> 00:04:03.770
When x is equal to 5, you go up
to the graph, it looks like

00:04:03.770 --> 00:04:06.630
the graph value there is
right around 2 and 1/2.

00:04:06.630 --> 00:04:08.790
So I should say this
is 2 and 1/2.

00:04:08.790 --> 00:04:12.880
And that is one of
the choices, B.

00:04:12.880 --> 00:04:14.130
Next problem.

00:04:19.829 --> 00:04:23.690
Problem 14.

00:04:23.690 --> 00:04:28.290
If 0 is less than or equal to x,
which is less than or equal

00:04:28.290 --> 00:04:34.920
to 8, and negative 1 is less
than equal to y, which is less

00:04:34.920 --> 00:04:39.460
than or equal to 3, which of the
following gives the set of

00:04:39.460 --> 00:04:44.830
all possible values
of x times y?

00:04:44.830 --> 00:04:48.240
OK, so we really just want to
figure out how low can x times

00:04:48.240 --> 00:04:52.590
y be and how high can
x times y be?

00:04:52.590 --> 00:04:55.743
Well, what's the lowest possible
value for x times y?

00:04:59.190 --> 00:05:04.560
Well, if we make y negative, and
we make x really big, or

00:05:04.560 --> 00:05:09.420
as big as it can be, if x is 8
and y is negative 1, then that

00:05:09.420 --> 00:05:15.140
is the lowest value for x
times y I can think of.

00:05:15.140 --> 00:05:21.410
So xy is going to be greater
than or equal to negative 8

00:05:21.410 --> 00:05:23.850
because when you take a negative
number, you want the

00:05:23.850 --> 00:05:26.100
other number to be as big as
possible so you get a large

00:05:26.100 --> 00:05:27.260
negative number.

00:05:27.260 --> 00:05:35.170
And it's going to be less than
or equal to-- well, what's the

00:05:35.170 --> 00:05:38.970
largest number that
I can think of?

00:05:38.970 --> 00:05:41.670
Well, if I take 8 and I multiply
it times the large

00:05:41.670 --> 00:05:44.175
value of y and this is a
positive value, then I get 24.

00:05:44.175 --> 00:05:46.890
So xy is going to be greater
than or equal to negative 8

00:05:46.890 --> 00:05:49.200
and less than or equal to 24.

00:05:49.200 --> 00:05:50.640
And that is choice E.

00:05:53.690 --> 00:05:55.270
And once again, how did
I get negative 8?

00:05:55.270 --> 00:05:58.160
This is probably the part that's
not intuitive for you.

00:05:58.160 --> 00:06:01.570
It's because-- I mean, your
instinct might have said the

00:06:01.570 --> 00:06:03.260
minimum x is 0, right?

00:06:03.260 --> 00:06:05.500
So I'll take 0 times any
of these, so this

00:06:05.500 --> 00:06:06.930
is going to be 0.

00:06:06.930 --> 00:06:09.740
But, you can actually get a
smaller value for xy by using

00:06:09.740 --> 00:06:12.180
negative 1 and 8, so
that's where we got

00:06:12.180 --> 00:06:13.760
the negative 8 from.

00:06:13.760 --> 00:06:14.920
Next question.

00:06:14.920 --> 00:06:19.590
15.

00:06:19.590 --> 00:06:20.640
Switch colors.

00:06:20.640 --> 00:06:22.352
15.

00:06:22.352 --> 00:06:23.340
Let me draw that.

00:06:23.340 --> 00:06:30.100
It looks like a line there, line
there, line there, then

00:06:30.100 --> 00:06:33.310
there's another line that
goes like that.

00:06:33.310 --> 00:06:38.330
And they write that this is
n degrees right there.

00:06:38.330 --> 00:06:42.350
In the figure above, what is
this sum in terms of n of the

00:06:42.350 --> 00:06:45.660
degree measures of the four
angles marked with arrows?

00:06:45.660 --> 00:06:46.940
Fascinating.

00:06:46.940 --> 00:06:52.600
So they want to know that plus
that plus that plus that.

00:06:52.600 --> 00:06:54.450
Well, let's just do
the angle game.

00:06:54.450 --> 00:07:00.520
If this angle as n, well, then
this angle is n, right?

00:07:00.520 --> 00:07:01.630
Let me switch colors.

00:07:01.630 --> 00:07:03.470
What is this angle here?

00:07:03.470 --> 00:07:10.770
Well, it's supplementary to
n, so this is 180 minus n.

00:07:10.770 --> 00:07:11.490
And so is this.

00:07:11.490 --> 00:07:15.360
This is also 180 minus n.

00:07:15.360 --> 00:07:17.620
And so what are these?

00:07:17.620 --> 00:07:20.316
What's the sum of these
two angles?

00:07:20.316 --> 00:07:24.380
Let me call this a, b.

00:07:24.380 --> 00:07:26.140
What's the sum of a plus b?

00:07:26.140 --> 00:07:31.590
Well, we know that a plus b
plus this angle, plus 180

00:07:31.590 --> 00:07:37.110
minus n is equal
to 180, right?

00:07:37.110 --> 00:07:38.810
Because they're all in
the same triangle.

00:07:38.810 --> 00:07:47.860
So a plus b is equal to
180 minus 180 plus n.

00:07:47.860 --> 00:07:51.150
I just took this and subtracted
180 and added n to

00:07:51.150 --> 00:07:51.685
both sides.

00:07:51.685 --> 00:07:56.300
This cancels out so you get
a plus b is equal to n.

00:07:56.300 --> 00:07:59.340
And similarly, if you had c,
if this were c and d, you

00:07:59.340 --> 00:08:00.460
could do the same thing.

00:08:00.460 --> 00:08:07.090
c plus d plus this angle, 180
minus n is equal to 180

00:08:07.090 --> 00:08:09.830
because they're all in
the same triangle.

00:08:09.830 --> 00:08:13.120
Subtract 180 from both sides and
then add n to both sides.

00:08:13.120 --> 00:08:16.070
You get c plus d
is equal to n.

00:08:16.070 --> 00:08:23.740
So if you want to know what a
plus b plus c plus d is, a

00:08:23.740 --> 00:08:28.130
plus b is n, c plus d is n, so
the whole thing is going to be

00:08:28.130 --> 00:08:30.760
n plus n or 2n.

00:08:30.760 --> 00:08:34.404
And that is choice B.

00:08:34.404 --> 00:08:38.110
Let's see if I have time to do
problem 16, considering I have

00:08:38.110 --> 00:08:41.400
a little under a minute left.

00:08:41.400 --> 00:08:43.580
Problem 16.

00:08:43.580 --> 00:08:46.650
After the first term, each term
in a sequence-- actually,

00:08:46.650 --> 00:08:48.480
this is going to be-- I think
this will take some

00:08:48.480 --> 00:08:51.080
explanation, so I'll do 16
in a video by itself.

00:08:51.080 --> 00:08:52.990
I'll see you in the
next video.


SAT Prep: Test 4 Section 8 Part 4

WEBVTT
Kind: captions
Language: en

00:00:00.690 --> 00:00:02.215
One last problem in
this section.

00:00:02.215 --> 00:00:03.940
Let's see, problem number 16.

00:00:03.940 --> 00:00:07.400
After the first term, each
term in a sequence is 3

00:00:07.400 --> 00:00:10.130
greater than 1/3 the
preceding term.

00:00:10.130 --> 00:00:15.190
So if I were to write that--
so if I were to say n of i

00:00:15.190 --> 00:00:20.940
plus 1 is equal to the
preceding term

00:00:20.940 --> 00:00:26.190
times 1/3 plus 3.

00:00:26.190 --> 00:00:28.900
And all I'm saying is, if
I have a term, right?

00:00:28.900 --> 00:00:33.720
Say the ith term is n, n sub i--
I take 1/3 of it and add 3

00:00:33.720 --> 00:00:34.670
to get the next term.

00:00:34.670 --> 00:00:35.030
That's all.

00:00:35.030 --> 00:00:37.710
This is just fancy notation
for that.

00:00:37.710 --> 00:00:40.490
If t is the first term of the
sequence and t does not equal

00:00:40.490 --> 00:00:42.920
0-- so this is t.

00:00:42.920 --> 00:00:44.390
I probably didn't even
have to write this.

00:00:44.390 --> 00:00:46.550
Ignore this if this
confuses you.

00:00:46.550 --> 00:00:47.890
So t is the first term.

00:00:47.890 --> 00:00:49.110
What's the next term
going to be?

00:00:49.110 --> 00:00:51.840
It's going to be 1/3
times t plus 3.

00:00:51.840 --> 00:00:57.000
So it's going to
be t/3 plus 3.

00:00:57.000 --> 00:00:59.320
And they're going to say-- and
then we could keep going-- but

00:00:59.320 --> 00:01:01.100
they just want to know, what
is the ratio of the second

00:01:01.100 --> 00:01:02.095
term to the first term?

00:01:02.095 --> 00:01:04.269
So what is the ratio
of this to this?

00:01:04.269 --> 00:01:10.520
Well the ratio is t/3
plus 3, to t.

00:01:10.520 --> 00:01:11.260
Right?

00:01:11.260 --> 00:01:24.320
And that's the same thing
as t/3 plus 3 times 1/t.

00:01:24.320 --> 00:01:31.560
That's the same thing as t/3
times 1/t plus 3 times 1/t.

00:01:31.560 --> 00:01:33.760
I just distributed the 1/t.

00:01:33.760 --> 00:01:35.450
These cancel out.

00:01:35.450 --> 00:01:41.480
So that equals 1/3
plus 3 over t.

00:01:41.480 --> 00:01:45.050
And that doesn't look like any
of the choices I see, so we

00:01:45.050 --> 00:01:46.540
probably have to find a
common denominator.

00:01:46.540 --> 00:01:48.710
So let's say the common
denominator is 3t.

00:01:48.710 --> 00:01:50.290
Just multiply the two.

00:01:50.290 --> 00:01:55.820
1/3 is the same thing as t over
3t, and 3/t is the same

00:01:55.820 --> 00:02:00.930
thing as 9/3 t, right?

00:02:00.930 --> 00:02:04.070
I just multiplied the top
and the bottom by 3.

00:02:04.070 --> 00:02:06.495
So t plus 9/3 t.

00:02:06.495 --> 00:02:10.350
t plus 9/3 t is choice C.

00:02:10.350 --> 00:02:12.170
And you could even
ignore this.

00:02:12.170 --> 00:02:16.550
Really, the hard part
isn't even this.

00:02:16.550 --> 00:02:19.100
The hard part is actually just,
you might end up with

00:02:19.100 --> 00:02:20.050
something like this.

00:02:20.050 --> 00:02:21.775
And then you're like, well I
don't see that choice, and

00:02:21.775 --> 00:02:23.170
then you have to realize, oh
I have to find a common

00:02:23.170 --> 00:02:25.690
denominator to get to this.

00:02:25.690 --> 00:02:28.110
The common denominator is 3t.

00:02:28.110 --> 00:02:28.680
Well that's it.

00:02:28.680 --> 00:02:29.780
That's a very short video.

00:02:29.780 --> 00:02:35.320
I'll see you in the next SAT
test, or on the next SAT test.


SAT Prep: Test 4 Section 4 Part 2

WEBVTT
Kind: captions
Language: en

00:00:01.030 --> 00:00:01.450
Welcome back.

00:00:01.450 --> 00:00:03.400
We're on problem number 7.

00:00:03.400 --> 00:00:06.010
And let's see, they drew a
triangle here, let me draw a

00:00:06.010 --> 00:00:07.260
triangle here as well.

00:00:20.585 --> 00:00:25.390
It's got altitude like that,
this is the height h, this is

00:00:25.390 --> 00:00:30.670
perpendicular, xyz.

00:00:30.670 --> 00:00:35.190
They say, in the triangle
above xz is 6/7 of h.

00:00:35.190 --> 00:00:42.420
So this right here is 6/7h, h is
the length of the altitude.

00:00:42.420 --> 00:00:44.630
What is area in terms of h?

00:00:44.630 --> 00:00:50.100
Well area is equal to 1/2
base times height.

00:00:50.100 --> 00:00:51.340
And what's the base?

00:00:51.340 --> 00:00:52.650
1/2 times the base.

00:00:52.650 --> 00:00:57.065
Well the base is 6/7h, and
then the height is h.

00:01:01.910 --> 00:01:06.700
This 2 becomes a 1, this becomes
a 3, so I get 3/7

00:01:06.700 --> 00:01:08.990
times h squared.

00:01:08.990 --> 00:01:11.840
Which is choice B.

00:01:11.840 --> 00:01:14.590
Their word is 3h squared over
7, but we know that is the

00:01:14.590 --> 00:01:15.270
same thing.

00:01:15.270 --> 00:01:16.720
So that is choice B.

00:01:16.720 --> 00:01:17.970
Next problem.

00:01:20.430 --> 00:01:22.420
Problem number 8.

00:01:22.420 --> 00:01:28.380
If a and b are positive
integers, and they say a to

00:01:28.380 --> 00:01:38.460
the 1/2 power, times b to the
1/3 power, to the 6th power,

00:01:38.460 --> 00:01:41.490
is equal to 432.

00:01:41.490 --> 00:01:44.320
What is a times b?

00:01:48.270 --> 00:01:50.960
Here I just try use exponent
rules and play around with

00:01:50.960 --> 00:01:52.470
this as best as I can.

00:01:52.470 --> 00:01:56.200
So if I raise a product of two
numbers that have exponents,

00:01:56.200 --> 00:01:58.830
and I raise it to an exponent,
that's like raising each of

00:01:58.830 --> 00:01:59.940
these to the exponent.

00:01:59.940 --> 00:02:06.890
So this is the same thing is a
to the 1/2 to the 6th, times b

00:02:06.890 --> 00:02:09.490
to the 1/3 to the 6th.

00:02:09.490 --> 00:02:10.919
And then when you raise
something to an exponent, and

00:02:10.919 --> 00:02:12.300
you raise that to an
exponent, you just

00:02:12.300 --> 00:02:13.880
multiply the exponents.

00:02:13.880 --> 00:02:16.880
So that's the same thing as a
to the, what's 1/2 times 6,

00:02:16.880 --> 00:02:18.530
that's a cubed.

00:02:18.530 --> 00:02:20.650
And what's 1/3 times 6?

00:02:20.650 --> 00:02:22.310
That's 2.

00:02:22.310 --> 00:02:23.695
1/3 times 6 is 2.

00:02:23.695 --> 00:02:36.420
That's a cubed times b squared
is equal to 432.

00:02:36.420 --> 00:02:42.220
And then we could even write
this as, a times a squared

00:02:42.220 --> 00:02:46.550
times b squared is
equal to 432.

00:02:46.550 --> 00:02:51.280
And then this we could write
as, a times ab squared, I'm

00:02:51.280 --> 00:02:52.850
just playing around I actually
don't know if this is going to

00:02:52.850 --> 00:02:57.640
get me to the problem, is
equal to 432 So this is

00:02:57.640 --> 00:02:58.650
interesting.

00:02:58.650 --> 00:03:00.880
We want to figure
out what ab is.

00:03:00.880 --> 00:03:05.920
So if we can divide this
expression by some number,

00:03:05.920 --> 00:03:08.110
some integer, and get a perfect
square, then we're

00:03:08.110 --> 00:03:09.690
essentially done.

00:03:09.690 --> 00:03:11.930
So let's just try divide by 2.

00:03:11.930 --> 00:03:13.350
What's this divided by 2?

00:03:13.350 --> 00:03:19.970
If you divide it by
2 you get 216.

00:03:19.970 --> 00:03:24.750
Is 216 a perfect square?

00:03:24.750 --> 00:03:26.930
See, I forget.

00:03:26.930 --> 00:03:31.110
6 times 6 is 36.

00:03:31.110 --> 00:03:33.890
9 and then 160.

00:03:33.890 --> 00:03:39.610
No, that's 256.

00:03:39.610 --> 00:03:41.820
14 times 14, that might be it.

00:03:41.820 --> 00:03:44.470
14 times 14.

00:03:44.470 --> 00:03:46.890
4 times 4 is 16.

00:03:46.890 --> 00:03:52.300
1 times 4 is 4, 56, 0,
140, no that's 196.

00:03:52.300 --> 00:03:54.510
216 isn't a perfect square.

00:03:54.510 --> 00:03:55.760
Well let me erase all this.

00:03:59.126 --> 00:04:02.140
As you can see, I don't do these
problems ahead of time.

00:04:02.140 --> 00:04:06.110
I do them in real time
for your benefit.

00:04:06.110 --> 00:04:08.400
I don't even know if I'm going
down the right route, I'm just

00:04:08.400 --> 00:04:11.270
taking it cold like you
will when you're

00:04:11.270 --> 00:04:12.520
in the mix of things.

00:04:15.820 --> 00:04:17.970
What other numbers are there?

00:04:17.970 --> 00:04:20.440
Let me make sure my
pen is right.

00:04:20.440 --> 00:04:22.160
Is this divisible by 3?

00:04:22.160 --> 00:04:22.510
Yes.

00:04:22.510 --> 00:04:24.790
What happens when
3 goes into 432.

00:04:24.790 --> 00:04:26.450
432 into 3.

00:04:26.450 --> 00:04:29.780
It's 100, remainder 3.

00:04:29.780 --> 00:04:31.740
13 goes into it 4 times.

00:04:31.740 --> 00:04:35.440
4 times 3 is 12.

00:04:35.440 --> 00:04:37.760
Look at that, that's
a perfect square.

00:04:37.760 --> 00:04:42.740
So we could write this, that's
equal to 3 times 144.

00:04:42.740 --> 00:04:46.190
So ab could be 12.

00:04:46.190 --> 00:04:49.820
How do I know ab can be 12?

00:04:49.820 --> 00:04:59.310
If we said a is equal to 3,
then ab squared, then this

00:04:59.310 --> 00:05:02.320
whole term is going to
be equal to 144.

00:05:02.320 --> 00:05:05.190
And if this whole term is
144, then we know that

00:05:05.190 --> 00:05:08.050
ab is equal to 12.

00:05:08.050 --> 00:05:10.930
And that's choice B.

00:05:10.930 --> 00:05:12.370
You know, you could have done
it the other way around.

00:05:12.370 --> 00:05:14.230
You could have actually looked
at the choices and tried to

00:05:14.230 --> 00:05:15.490
work backwards.

00:05:15.490 --> 00:05:18.070
I kind of fumbled a little bit
trying to figure out, well,

00:05:18.070 --> 00:05:21.250
how can I have 432 as the
product of a perfect square

00:05:21.250 --> 00:05:22.540
and some other number?

00:05:22.540 --> 00:05:25.760
And you could have tried each of
the choices, squared them,

00:05:25.760 --> 00:05:32.410
and tried to see if they
actually went into 432.

00:05:32.410 --> 00:05:34.510
And also met the other
constraints, that a and b have

00:05:34.510 --> 00:05:36.130
to be positive integers
that are different,

00:05:36.130 --> 00:05:37.120
et cetera, et cetera.

00:05:37.120 --> 00:05:41.600
And of course if a is 3 and ab
is 12, then of course b is 4.

00:05:41.600 --> 00:05:43.150
But we didn't have
to know that.

00:05:43.150 --> 00:05:45.310
Alright, next problem.

00:05:50.000 --> 00:05:51.440
Invert colors.

00:05:51.440 --> 00:05:54.380
Problem number 9.

00:05:54.380 --> 00:05:56.910
What is the greatest three
digit number that

00:05:56.910 --> 00:06:11.350
has a factor of 10?

00:06:11.350 --> 00:06:13.750
Oh, OK, that has 10 as
one of its factors.

00:06:13.750 --> 00:06:15.180
For some reason when
I read that it just

00:06:15.180 --> 00:06:17.530
didn't register my brain.

00:06:17.530 --> 00:06:20.710
So first of all, when they say
three digit integer, we're

00:06:20.710 --> 00:06:22.260
essentially saying any number.

00:06:22.260 --> 00:06:23.860
So let's say x is our integer.

00:06:23.860 --> 00:06:27.460
So it has to be greater
than or equal to 100.

00:06:27.460 --> 00:06:30.460
It has to be less than 999.

00:06:30.460 --> 00:06:32.850
And we essentially want some
number in this range that has

00:06:32.850 --> 00:06:34.280
10 as a factor.

00:06:34.280 --> 00:06:35.570
Well, what do we know
about things that

00:06:35.570 --> 00:06:36.990
have 10 as a factor?

00:06:36.990 --> 00:06:38.580
They end in 0.

00:06:38.580 --> 00:06:42.440
10, 20, 30, 40, 50.

00:06:42.440 --> 00:06:44.050
They have to end in 0.

00:06:44.050 --> 00:06:47.050
So what's the largest number,
that's less than this number,

00:06:47.050 --> 00:06:48.470
that ends in 0?

00:06:48.470 --> 00:06:51.320
Well, 990.

00:06:51.320 --> 00:06:53.920
And that's our answer.

00:06:53.920 --> 00:06:58.120
Problem number 10.

00:06:58.120 --> 00:06:59.355
Maybe I don't have to
clear this, I can

00:06:59.355 --> 00:07:00.920
just do it right here.

00:07:00.920 --> 00:07:03.230
Problem number 10.

00:07:03.230 --> 00:07:05.380
A recipe for chili
for 20 people

00:07:05.380 --> 00:07:06.946
requires 4 pounds of beans.

00:07:15.560 --> 00:07:18.760
At this rate, how many pounds of
beans are required to make

00:07:18.760 --> 00:07:21.320
chili for 150 people?

00:07:21.320 --> 00:07:22.690
So we can make a ratio.

00:07:22.690 --> 00:07:29.270
20 is to 150, as 4
pounds is to x.

00:07:29.270 --> 00:07:33.430
I just say whatever factor I
have to multiply 20 by to get

00:07:33.430 --> 00:07:35.745
150, I have to multiply the
same factor to get to x.

00:07:35.745 --> 00:07:37.100
I just set up a ratio.

00:07:37.100 --> 00:07:41.880
And if we cross multiply,
we get 20 times x is

00:07:41.880 --> 00:07:43.560
equal to 4 times 150.

00:07:43.560 --> 00:07:45.102
What's 4 times 150?

00:07:45.102 --> 00:07:47.430
It's 600.

00:07:47.430 --> 00:07:49.300
Divide both sides by 20.

00:07:49.300 --> 00:07:51.485
600 divided by 20 is 30.

00:07:51.485 --> 00:07:54.680
We need 30 pounds of beans
if we're going to

00:07:54.680 --> 00:07:57.340
do it for 150 people.

00:07:57.340 --> 00:07:58.590
Next problem.

00:08:01.810 --> 00:08:03.210
Problem number 11.

00:08:03.210 --> 00:08:05.770
I'll switch colors.

00:08:05.770 --> 00:08:11.080
When the positive even integer
n-- n is positive and even--

00:08:11.080 --> 00:08:16.950
is increased by 50% of itself--
so plus 50% of

00:08:16.950 --> 00:08:25.390
itself-- the result is
between 10 and 20.

00:08:25.390 --> 00:08:33.270
10 is less than n plus 0.5n,
which is less than 20.

00:08:33.270 --> 00:08:34.210
That's what we know.

00:08:34.210 --> 00:08:36.409
What is one possible
value for n?

00:08:36.409 --> 00:08:37.440
So let's do a couple
of things.

00:08:37.440 --> 00:08:39.080
One, we can simplify this.

00:08:39.080 --> 00:08:40.709
What's 1n plus 0.5n?

00:08:40.709 --> 00:08:41.959
That's 1.5n.

00:08:44.300 --> 00:08:46.200
And that's -- I'm going to write
as a fraction-- that's

00:08:46.200 --> 00:08:52.570
3/2n, is greater than 10,
which is less than 20.

00:08:52.570 --> 00:08:54.300
This is an inequality, right?

00:08:54.300 --> 00:08:59.390
So we can multiply every term
of this inequality by 2/3.

00:08:59.390 --> 00:09:04.770
So 2/3 times 10 is less than 2/3
times 3/2n, which is less

00:09:04.770 --> 00:09:07.170
than 20 times 2/3.

00:09:07.170 --> 00:09:13.660
So here we get 20 over 3 is less
than-- this cancels out--

00:09:13.660 --> 00:09:18.840
n which is less than
40 over 3.

00:09:18.840 --> 00:09:24.210
And 20 over 3, this is 6 point
something something.

00:09:24.210 --> 00:09:27.170
It's a little less than 7, is
less than n, which is less

00:09:27.170 --> 00:09:28.140
than 40 over 3.

00:09:28.140 --> 00:09:30.820
This is 13 point something
something.

00:09:30.820 --> 00:09:32.780
So just have to pick
any number between,

00:09:32.780 --> 00:09:35.160
essentially, 7 and 13.

00:09:35.160 --> 00:09:39.130
So 7 is less than or equal
to n, which is less

00:09:39.130 --> 00:09:40.340
than or equal to 13.

00:09:40.340 --> 00:09:42.240
Any number you picked between
that range would work.

00:09:42.240 --> 00:09:44.910
So 10 would be a good number
to write down.

00:09:44.910 --> 00:09:47.470
And a very easy way of doing
that problem is just trying

00:09:47.470 --> 00:09:49.030
out 10 and seeing if
it worked out.

00:09:49.030 --> 00:09:51.230
And it would have worked out.

00:09:51.230 --> 00:09:52.720
Anyway I have 10 seconds
left, so I'll see

00:09:52.720 --> 00:09:53.970
you in the next video.


SAT Prep: Test 4 Section 4 Part 1

WEBVTT
Kind: captions
Language: en

00:00:00.600 --> 00:00:01.370
Welcome back.

00:00:01.370 --> 00:00:04.190
We're now going to be in the
next section, section four in

00:00:04.190 --> 00:00:08.220
our fourth test. And that's
problem one, 594.

00:00:08.220 --> 00:00:09.420
Problem one.

00:00:09.420 --> 00:00:13.540
x minus y is equal to 8.

00:00:13.540 --> 00:00:14.910
y is equal to 3z.

00:00:17.620 --> 00:00:21.150
And z is equal to 2.

00:00:21.150 --> 00:00:22.570
What is x?

00:00:22.570 --> 00:00:28.260
z is equal to 2, y is equal
to 3z, so y is equal to 6.

00:00:28.260 --> 00:00:34.470
So x minus 6 is equal to
8, or x is equal to 14.

00:00:34.470 --> 00:00:35.720
E.

00:00:37.890 --> 00:00:40.060
I already said z
is equal to 2.

00:00:40.060 --> 00:00:42.210
I sometimes forget
when I just said.

00:00:42.210 --> 00:00:43.500
Maybe I'm aging.

00:00:43.500 --> 00:00:44.980
Problem number two.

00:00:44.980 --> 00:00:50.590
Todd is older than Marta,
but younger than Susan.

00:00:50.590 --> 00:00:54.320
Let's say their first
letter is their age.

00:00:54.320 --> 00:00:57.900
Say Todd is older than
Marta, so his age is

00:00:57.900 --> 00:00:59.150
greater than Marta.

00:01:01.510 --> 00:01:04.849
But he's also younger than
Susan, for his age is less

00:01:04.849 --> 00:01:06.099
than Susan's age.

00:01:08.460 --> 00:01:10.390
Oh I think I did this problem
inadvertantly.

00:01:10.390 --> 00:01:13.440
If t, m, and s represent the
ages in years of Todd, Marta,

00:01:13.440 --> 00:01:16.450
and Susan respectively, which
of the following is true?

00:01:16.450 --> 00:01:20.700
And exactly what I
drew is choice A.

00:01:20.700 --> 00:01:22.530
And this comes straight
from their statements.

00:01:22.530 --> 00:01:24.067
I literally was just writing
this because I thought they

00:01:24.067 --> 00:01:25.690
were going to ask something
harder.

00:01:25.690 --> 00:01:28.290
But this they're saying Todd is
older than Marta, so t is

00:01:28.290 --> 00:01:29.920
greater than m.

00:01:29.920 --> 00:01:33.790
And Todd is younger than Susan,
so t is less than s, so

00:01:33.790 --> 00:01:35.100
that's just choice A.

00:01:35.100 --> 00:01:38.570
Problem number three.

00:01:38.570 --> 00:01:42.550
If the areas of two regions are
equal, and the sum of the

00:01:42.550 --> 00:01:47.670
areas of the regions is 5, what
is the average of the

00:01:47.670 --> 00:01:49.760
areas of the two regions?

00:01:49.760 --> 00:01:54.040
So area 1 equals area 2.

00:01:54.040 --> 00:01:55.730
We know that.

00:01:55.730 --> 00:02:00.420
And we also know that the
sum of the areas is 5.

00:02:00.420 --> 00:02:05.200
So area 1 plus area
2 is equal to 5.

00:02:05.200 --> 00:02:06.850
But then, of course, we know
that area 2 is the same

00:02:06.850 --> 00:02:07.800
thing as area 1.

00:02:07.800 --> 00:02:11.870
So we also know that area 1
times 2 is equal to 5, or that

00:02:11.870 --> 00:02:15.100
each of the areas is 2.5.

00:02:15.100 --> 00:02:17.630
And area 2 would also be 2.5.

00:02:17.630 --> 00:02:20.180
We know that because they're
equal to each other, and when

00:02:20.180 --> 00:02:21.460
you add them up it's 5.

00:02:21.460 --> 00:02:23.450
So they're each going to
be half of that, so

00:02:23.450 --> 00:02:24.970
they're each 2 and 1/2.

00:02:24.970 --> 00:02:28.090
And they want to know, what is
the average of the areas in

00:02:28.090 --> 00:02:28.930
the two regions?

00:02:28.930 --> 00:02:30.360
Well they're the same
number, right?

00:02:30.360 --> 00:02:32.550
So if you average two of the
same number, the average is

00:02:32.550 --> 00:02:33.620
going to be that number.

00:02:33.620 --> 00:02:35.140
You could add them and divide
by 2, but you're

00:02:35.140 --> 00:02:36.600
going to get 2.5.

00:02:36.600 --> 00:02:39.460
And if you look at the
choices, where's 2.5?

00:02:39.460 --> 00:02:44.970
2.5 is the same thing as 2 and
1/2, which is the same thing

00:02:44.970 --> 00:02:49.320
as 5/2, so it's choice D.

00:02:49.320 --> 00:02:50.570
Next problem.

00:02:52.600 --> 00:02:53.750
I'll switch colors.

00:02:53.750 --> 00:02:56.420
Problem number four.

00:02:56.420 --> 00:02:59.950
Let s be the set of all integers
that can be written

00:02:59.950 --> 00:03:06.410
as n squared plus 1, where
n is a non zero integer.

00:03:06.410 --> 00:03:09.117
N is greater than zero, and it
soon. is an integer, it is a

00:03:09.117 --> 00:03:10.160
non zero integer.

00:03:10.160 --> 00:03:12.970
Which of the following
integers is an s?

00:03:12.970 --> 00:03:14.220
So n squared plus 1.

00:03:14.220 --> 00:03:16.130
So let's get a feel
for what it is.

00:03:19.160 --> 00:03:23.280
When n is 1, 2, 3, 4, 5, 6.

00:03:23.280 --> 00:03:27.890
When n is 1, n squared,
plus 1 is 2.

00:03:27.890 --> 00:03:29.410
2 squared plus 1 is 5.

00:03:29.410 --> 00:03:31.240
3 squared plus 1 is 10.

00:03:31.240 --> 00:03:33.180
4 squared plus 1 is 17.

00:03:33.180 --> 00:03:35.390
It's always going to be one more
than a perfect square.

00:03:35.390 --> 00:03:37.980
25 plus 1 is 26.

00:03:37.980 --> 00:03:39.100
There's 37, right?

00:03:39.100 --> 00:03:41.080
So the choice is, it
has to be one more

00:03:41.080 --> 00:03:42.430
than a perfect square.

00:03:42.430 --> 00:03:46.370
So which of the following
integers is an s?

00:03:46.370 --> 00:03:48.300
So choice A is 16.

00:03:48.300 --> 00:03:50.530
16 is a perfect square, but
it's not one more than a

00:03:50.530 --> 00:03:52.120
perfect square.

00:03:52.120 --> 00:03:55.980
Similarly, choice B, 28.

00:03:55.980 --> 00:04:00.040
28 minus 1 is 27, that's
not a perfect square.

00:04:00.040 --> 00:04:02.350
35 minus 1 isn't a
perfect square.

00:04:02.350 --> 00:04:04.150
39 minus 1 isn't a
perfect square.

00:04:04.150 --> 00:04:07.290
And if you look at
choice E, 50.

00:04:07.290 --> 00:04:10.330
50 minus 1 is 49, which is,
of course, 7 squared.

00:04:10.330 --> 00:04:11.540
Actually we would have gotten
there if we had

00:04:11.540 --> 00:04:12.880
just done one more.

00:04:12.880 --> 00:04:17.529
7 squared plus 1, 49 plus
1, is equal to 50.

00:04:17.529 --> 00:04:21.600
The important thing to realize
is that, the integers in s are

00:04:21.600 --> 00:04:23.890
integers that are one more
than a perfect square.

00:04:23.890 --> 00:04:25.500
So you just have to look at the
choices and say, which of

00:04:25.500 --> 00:04:28.230
these is one more than
a perfect square?

00:04:28.230 --> 00:04:30.225
Let's do problem number five.

00:04:35.080 --> 00:04:40.140
So I have a circle here,
that's my circle.

00:04:40.140 --> 00:04:42.070
And it has a triangle
inside the circle.

00:04:42.070 --> 00:04:46.180
It looks something-- I try to
draw these as close to what

00:04:46.180 --> 00:04:48.640
they drew in the book
as possible.

00:04:48.640 --> 00:04:53.540
There's point like that, there's
point like that, and

00:04:53.540 --> 00:04:57.880
then there's a triangle
that looks like that.

00:04:57.880 --> 00:05:02.110
And they write this is the
center, of course, is o.

00:05:02.110 --> 00:05:04.850
They're saying that this
right here is x.

00:05:04.850 --> 00:05:08.700
They say that this
right here is y.

00:05:08.700 --> 00:05:11.880
And then the question reads, in
the figure above, point o

00:05:11.880 --> 00:05:13.640
is the center of the circle.

00:05:13.640 --> 00:05:21.540
If x is equal to 40 degrees,
what is the value of y?

00:05:21.540 --> 00:05:23.270
And you'll be like, how
do I figure this out?

00:05:23.270 --> 00:05:27.310
I know the angles of a triangle
add up to 180, and

00:05:27.310 --> 00:05:29.000
all that, but they've only
given me one angle.

00:05:29.000 --> 00:05:30.060
And I don't know the angle.

00:05:30.060 --> 00:05:31.360
Or so you think you don't
know this angle.

00:05:34.280 --> 00:05:36.540
One of the things that should
immediately enter your mind

00:05:36.540 --> 00:05:39.500
when you see this in the SAT is,
the sides of this triangle

00:05:39.500 --> 00:05:42.350
are the radius of the circle.

00:05:42.350 --> 00:05:43.730
It's the radius of the circle.

00:05:43.730 --> 00:05:45.820
Because every time it gets to
the end point, and they

00:05:45.820 --> 00:05:47.620
actually it draw like that.

00:05:47.620 --> 00:05:49.660
So if this is the radius, we
know that this side is going

00:05:49.660 --> 00:05:50.570
to be equal to this side.

00:05:50.570 --> 00:05:53.220
Because both of these sides are
the length of the radius

00:05:53.220 --> 00:05:54.140
of the circle.

00:05:54.140 --> 00:05:56.580
And they do this a
lot in the SAT.

00:05:56.580 --> 00:05:58.840
If something is a radius of a
circle, it never changes.

00:05:58.840 --> 00:06:00.150
Anywhere you draw it.

00:06:00.150 --> 00:06:02.660
The radius is constant as you
go around the circle.

00:06:02.660 --> 00:06:04.880
So if this side is equal
to this side,

00:06:04.880 --> 00:06:06.020
what do we know happens?

00:06:06.020 --> 00:06:09.550
It's an isosceles triangle, and
the base angles are equal.

00:06:09.550 --> 00:06:13.390
So this is y, we also
know that this is y.

00:06:13.390 --> 00:06:14.873
Because they're the
base angles.

00:06:14.873 --> 00:06:18.200
you They're corresponding angles
to these two sides.

00:06:18.200 --> 00:06:19.820
They're the base angles
for this triangle.

00:06:19.820 --> 00:06:21.280
Now we can solve it.

00:06:21.280 --> 00:06:28.020
We could say, x, which is 40
degrees, plus y plus y is

00:06:28.020 --> 00:06:29.730
equal to 180.

00:06:29.730 --> 00:06:34.360
Or we could say 40 plus
2y is equal to 180.

00:06:34.360 --> 00:06:37.240
2y is equal to 140.

00:06:37.240 --> 00:06:39.190
Y is equal to 70 degrees.

00:06:39.190 --> 00:06:40.720
And that is choice D.

00:06:43.250 --> 00:06:44.500
Next problem.

00:06:47.420 --> 00:06:50.510
Problem number 6.

00:06:50.510 --> 00:06:55.250
A simple square is any integer
greater than 1 that has only

00:06:55.250 --> 00:06:58.170
three positive integer
factors.

00:06:58.170 --> 00:07:01.540
Itself, its square
root, and 1.

00:07:01.540 --> 00:07:04.580
Which of the following
is a simple square?

00:07:04.580 --> 00:07:06.595
It can only have three
factors, it

00:07:06.595 --> 00:07:08.130
can't anything else.

00:07:08.130 --> 00:07:12.370
So, for example, if we wrote
all of the perfect squares.

00:07:12.370 --> 00:07:22.350
1, 4, 9, 16, 25, 36.

00:07:22.350 --> 00:07:24.330
If we write the factors,
this factor only has 1.

00:07:24.330 --> 00:07:25.630
This factor has 1, 2 and 1.

00:07:25.630 --> 00:07:26.920
This has 1, 3 and 9.

00:07:26.920 --> 00:07:30.060
I'm just writing out
all the factors.

00:07:30.060 --> 00:07:32.080
1, 2, and 4.

00:07:32.080 --> 00:07:38.160
So it would be 1, 2, 4, 8, 16.

00:07:38.160 --> 00:07:39.390
I'm just doing this
as an example.

00:07:39.390 --> 00:07:40.400
You shouldn't do this
on the SAT.

00:07:40.400 --> 00:07:42.630
But I want to explain
what they're saying.

00:07:42.630 --> 00:07:45.530
All of these numbers are
perfect squares.

00:07:45.530 --> 00:07:54.500
But notice 16 has itself, 1, and
it has some extra factors.

00:07:54.500 --> 00:07:57.610
While these numbers only have
its square root, and

00:07:57.610 --> 00:07:59.720
themselves, and 1 as factors.

00:07:59.720 --> 00:08:02.750
So these are simple squares.

00:08:02.750 --> 00:08:08.300
So if we look at the choices,
choice A, 121.

00:08:08.300 --> 00:08:11.810
121, I know 1 is a factor,
I know that's 11 squared.

00:08:11.810 --> 00:08:13.660
I know it's 121.

00:08:13.660 --> 00:08:16.400
And I think, other than that,
there's not any other factors.

00:08:16.400 --> 00:08:18.720
It's not divisible by 3.

00:08:18.720 --> 00:08:20.900
B is 100.

00:08:20.900 --> 00:08:22.170
100's got a ton of factors.

00:08:22.170 --> 00:08:24.650
I mean it's got 1,
10, and 100.

00:08:24.650 --> 00:08:30.930
It also has 2 and 50.

00:08:30.930 --> 00:08:34.059
It has 4 and 25, it has a ton
of factors other than its

00:08:34.059 --> 00:08:36.309
square root, so it's
not choice B.

00:08:36.309 --> 00:08:39.159
Choice C, 81, same thing.

00:08:39.159 --> 00:08:43.990
It could be 1, 1 times 81,
it could be 9 times 9.

00:08:43.990 --> 00:08:47.640
Or it could be 27 times 3,
and so forth and so on.

00:08:47.640 --> 00:08:48.890
So it's not choice C.

00:08:48.890 --> 00:08:51.290
I think A is our prime
contender.

00:08:51.290 --> 00:08:52.670
Choice D, 64.

00:08:52.670 --> 00:08:55.890
Once again, tons of factors
outside of its square root.

00:08:55.890 --> 00:08:57.280
It has 1, 64, and 8.

00:08:57.280 --> 00:08:59.870
But it also has 2 times 32.

00:08:59.870 --> 00:09:03.180
It has 4 times 16, and
you could go on.

00:09:03.180 --> 00:09:04.810
64 has a ton of factors.

00:09:04.810 --> 00:09:08.010
And, finally, choice E.

00:09:08.010 --> 00:09:08.790
33.

00:09:08.790 --> 00:09:11.070
E doesn't work, because that's
not even a perfect sqaure.

00:09:11.070 --> 00:09:12.240
What squared equals 33?

00:09:12.240 --> 00:09:13.260
I don't know.

00:09:13.260 --> 00:09:14.630
So that doesn't even work.

00:09:14.630 --> 00:09:18.240
So it's definitely choice A.

00:09:18.240 --> 00:09:19.080
Next problem.

00:09:19.080 --> 00:09:20.990
Actually I only have 40 seconds
left, so I'll do it in

00:09:20.990 --> 00:09:21.860
the next video.

00:09:21.860 --> 00:09:23.110
See


SAT Prep: Test 4 Section 4 Part 3

WEBVTT
Kind: captions
Language: en

00:00:00.840 --> 00:00:01.530
Welcome back.

00:00:01.530 --> 00:00:03.140
We're on problem
number twelve.

00:00:06.570 --> 00:00:13.880
The perimeter of a rectangular
plot of land is 250 meters.

00:00:13.880 --> 00:00:17.500
If the length of one side of the
plot is 40 meters, what is

00:00:17.500 --> 00:00:19.960
the area of the plot
in square meters?

00:00:19.960 --> 00:00:21.410
So let me draw a
rectangle here.

00:00:26.960 --> 00:00:32.189
We know that one side of
the plot is 40 meters.

00:00:32.189 --> 00:00:33.050
Well it's a rectangle.

00:00:33.050 --> 00:00:35.210
So if this side is 40,
then this side is

00:00:35.210 --> 00:00:37.440
also going to be 40.

00:00:37.440 --> 00:00:40.700
And let's say we don't
know the other side.

00:00:40.700 --> 00:00:43.260
Well if this side is
x, this is also x.

00:00:43.260 --> 00:00:47.090
So what is the perimeter,
expressed in these terms?

00:00:47.090 --> 00:00:52.750
What's 40 plus 40, which
is 80, plus x plus x.

00:00:52.750 --> 00:00:55.660
So if 80 plus 2x is the
perimeter, and we know that

00:00:55.660 --> 00:00:59.850
the perimeter is 250.

00:00:59.850 --> 00:01:04.349
And so solving for x we get 2x
is equal to, what's 250 minus

00:01:04.349 --> 00:01:07.920
80, that's 170.

00:01:07.920 --> 00:01:17.220
At that x is equal to 85.

00:01:17.220 --> 00:01:19.770
And now if we want to get the
area of this, we just multiply

00:01:19.770 --> 00:01:21.350
the base times the height.

00:01:21.350 --> 00:01:30.550
So 85 times 40, put a 0 here,
and 4 times 5 is 20.

00:01:30.550 --> 00:01:34.930
4 times 8 is 32, plus 2 is 34.

00:01:34.930 --> 00:01:39.740
So the area is 3400
square meters.

00:01:39.740 --> 00:01:41.650
I hope I didn't do something
wrong with the math, but I

00:01:41.650 --> 00:01:43.700
think you get the point.

00:01:43.700 --> 00:01:44.950
Next problem.

00:01:47.170 --> 00:01:48.420
Problem thirteen.

00:01:50.810 --> 00:01:53.410
A school ordered $600 worth
of light bulbs.

00:01:57.350 --> 00:02:00.340
Some of the light bulbs cost $1
each, and others cost $2.

00:02:00.340 --> 00:02:02.910
So some were $1, some
were $2 each.

00:02:02.910 --> 00:02:10.199
If twice as many $1 bulbs as
$2 bulbs were ordered, how

00:02:10.199 --> 00:02:14.270
many light bulbs were ordered
all together?

00:02:14.270 --> 00:02:15.410
Fascinating.

00:02:15.410 --> 00:02:23.850
So let's let x equal
number of $1 bulbs.

00:02:23.850 --> 00:02:29.950
I could introduce a variable y,
but I could just say that x

00:02:29.950 --> 00:02:34.490
is the number of $1 bulbs, and
we know that twice as many $1

00:02:34.490 --> 00:02:36.730
bulbs as $2 bulbs
were ordered.

00:02:36.730 --> 00:02:39.680
So how can I express the
number of $2 bulbs?

00:02:43.850 --> 00:02:46.090
Well we know that twice
as many $1 bulbs were

00:02:46.090 --> 00:02:47.220
ordered as $2 bulbs.

00:02:47.220 --> 00:02:49.530
So this would be
x divided by 2.

00:02:49.530 --> 00:02:53.470
There are half as many
$2 bulbs as $1 bulbs.

00:02:53.470 --> 00:02:58.290
And we know that if we add up
the total number of bulbs,

00:02:58.290 --> 00:02:59.640
well actually we don't know.

00:02:59.640 --> 00:03:04.400
So what is the total cost if we
get x $1 bulbs, and if we

00:03:04.400 --> 00:03:07.150
get x divided by 2 $2 bulbs?

00:03:07.150 --> 00:03:10.120
What is going to be the
total cost of this?

00:03:10.120 --> 00:03:13.143
Well, I'm going to get x $1
bulbs, and they're each going

00:03:13.143 --> 00:03:14.800
to cost $1.

00:03:14.800 --> 00:03:18.400
Plus, I'm going to get x over
2 $2 bulbs, and they're each

00:03:18.400 --> 00:03:21.940
going to cost $2.

00:03:21.940 --> 00:03:26.040
And when I add it all up it's
going to equal $600.

00:03:26.040 --> 00:03:28.680
So x times 1 is, of course, x.

00:03:28.680 --> 00:03:32.060
And then x over 2 times 2,
that's lucky that worked out,

00:03:32.060 --> 00:03:34.990
plus x is equal to $600.

00:03:34.990 --> 00:03:39.150
So 2x is equal to 600.

00:03:39.150 --> 00:03:41.780
x is equal to 300.

00:03:41.780 --> 00:03:44.460
And they want to know
how many lightbulbs

00:03:44.460 --> 00:03:47.210
were ordered all together.

00:03:47.210 --> 00:03:54.650
So we got 300 $1 bulbs, and we
got 1/2 as many $2 bulbs, x

00:03:54.650 --> 00:03:55.450
divided by 2.

00:03:55.450 --> 00:04:01.370
So we got 150 $2 bulbs.

00:04:01.370 --> 00:04:06.490
So together we got 450 bulbs.

00:04:06.490 --> 00:04:07.740
Next problem.

00:04:10.180 --> 00:04:11.685
Image clear.

00:04:14.240 --> 00:04:18.850
I'll do it in a new color
so we don't get bored.

00:04:18.850 --> 00:04:20.550
Fourteen.

00:04:20.550 --> 00:04:32.440
If 4 times x plus y times x
minus y is equal to 40, and we

00:04:32.440 --> 00:04:36.660
also know that x minus y is
equal to 20, what is the value

00:04:36.660 --> 00:04:38.360
of x plus y?

00:04:38.360 --> 00:04:40.510
Well, we know x minus y is equal
to 20, so we can just

00:04:40.510 --> 00:04:41.540
substitute that right here.

00:04:41.540 --> 00:04:46.027
So then we get 4 times x plus y
times, instead of writing x

00:04:46.027 --> 00:04:51.510
minus y we can just write times
20, is equal to 40.

00:04:51.510 --> 00:04:57.390
Or, if we multiply 20 times 4,
we know that 80 times x plus y

00:04:57.390 --> 00:04:59.700
is equal to 40.

00:04:59.700 --> 00:05:03.240
Then we know, divide both sides
by 80, and we get x plus

00:05:03.240 --> 00:05:04.200
y is 40 over 80.

00:05:04.200 --> 00:05:06.905
Which is the same
thing as 1/2.

00:05:06.905 --> 00:05:08.060
And that's our answer.

00:05:08.060 --> 00:05:11.500
x plus y is equal to 1/2.

00:05:11.500 --> 00:05:12.750
Next problem.

00:05:16.000 --> 00:05:17.250
Fifteen.

00:05:19.260 --> 00:05:21.420
In a rectangular coordinate
system, that's what we're

00:05:21.420 --> 00:05:26.600
familiar with, the center of a
circle has coordinates 5, 12.

00:05:26.600 --> 00:05:32.590
So I draw a circle, and then the
center of the circle has

00:05:32.590 --> 00:05:35.840
the coordinates 5, 12.

00:05:35.840 --> 00:05:39.990
And the circle touches the
x-axis at one point only.

00:05:39.990 --> 00:05:41.580
What is the radius
of the circle?

00:05:41.580 --> 00:05:44.710
So it just touches the x-axis.

00:05:44.710 --> 00:05:47.190
And the only place where it can
touch the x-axis only in

00:05:47.190 --> 00:05:48.840
one point is this exact.

00:05:48.840 --> 00:05:51.690
Because the x-axis is
essentially a horizontal line.

00:05:51.690 --> 00:05:53.870
And where else can you
touch the x-axis?

00:05:53.870 --> 00:05:55.650
You could touch it
here, on top.

00:05:55.650 --> 00:05:59.870
But if the x-axis was up here,
then the y coordinate would

00:05:59.870 --> 00:06:00.940
not be positive.

00:06:00.940 --> 00:06:03.730
So this has a positive y
coordinate, so we know it has

00:06:03.730 --> 00:06:07.300
to be above the x-axis,
it's at 12.

00:06:07.300 --> 00:06:10.690
So we know the only place where
you can touch the x-axis

00:06:10.690 --> 00:06:13.850
just once is right here, just
right at the bottom.

00:06:13.850 --> 00:06:15.480
So it's gotta be like that.

00:06:18.290 --> 00:06:19.540
That's gotta be the x-axis.

00:06:22.700 --> 00:06:24.700
That could be the x-axis and
then the y-axis could be out

00:06:24.700 --> 00:06:27.010
here someplace.

00:06:27.010 --> 00:06:28.610
Just so you have a frame
of reference.

00:06:28.610 --> 00:06:30.900
And if that's the x-axis,
then what's the radius?

00:06:30.900 --> 00:06:39.920
Well, this is the point 5,
12, this is y equals 12.

00:06:39.920 --> 00:06:41.310
So what is this height?

00:06:41.310 --> 00:06:42.980
This is a radius.

00:06:42.980 --> 00:06:44.450
Well that's just the
y-coordinate, it's 12.

00:06:44.450 --> 00:06:48.440
So the radius is equal to 12.

00:06:48.440 --> 00:06:49.790
They're just saying what is
the radius of the circle,

00:06:49.790 --> 00:06:50.850
well, the radius is 12.

00:06:50.850 --> 00:06:52.890
It's the y-coordinate.

00:06:52.890 --> 00:06:54.140
Next problem.

00:06:56.710 --> 00:06:58.200
Whoops.

00:06:58.200 --> 00:07:00.840
I say whoops a lot.

00:07:00.840 --> 00:07:02.090
Problem sixteen.

00:07:04.410 --> 00:07:11.610
They have this men, women,
woman, and then they say

00:07:11.610 --> 00:07:13.480
voting age population.

00:07:13.480 --> 00:07:21.850
So population, and then
registered, and they say 1200,

00:07:21.850 --> 00:07:30.341
1000, 1300, and 1200.

00:07:30.341 --> 00:07:33.290
They say, the table above gives
the voter registration

00:07:33.290 --> 00:07:35.060
data for the town of
Bridgeton at the

00:07:35.060 --> 00:07:36.930
time of a recent election.

00:07:36.930 --> 00:07:40.280
In the election, 40%
of the voting age

00:07:40.280 --> 00:07:42.880
population actually voted.

00:07:42.880 --> 00:07:46.430
So this is the voting
age population.

00:07:46.430 --> 00:07:50.400
And we know that 40%
actually voted.

00:07:50.400 --> 00:07:53.360
If the turnout for the election
is defined by the

00:07:53.360 --> 00:08:02.990
number who actually voted,
divided by registered, what

00:08:02.990 --> 00:08:05.000
was the turnout for
this election?

00:08:05.000 --> 00:08:06.830
So what's the number
who actually voted?

00:08:06.830 --> 00:08:10.310
It's 40% of the voting
age population.

00:08:10.310 --> 00:08:11.830
So what's the voting
age population?

00:08:11.830 --> 00:08:13.310
Well the total population
is the men and

00:08:13.310 --> 00:08:15.470
women, so that's 2500.

00:08:15.470 --> 00:08:16.740
Just add these two up.

00:08:16.740 --> 00:08:19.110
And what's 40% of 2500?

00:08:19.110 --> 00:08:26.110
That's 2500 times 0.4.

00:08:26.110 --> 00:08:26.470
Let's see.

00:08:26.470 --> 00:08:29.800
4 times 25 is 100.

00:08:29.800 --> 00:08:30.590
Two more zeros.

00:08:30.590 --> 00:08:32.120
0, 0.

00:08:32.120 --> 00:08:35.710
And then, of course,
one decimal.

00:08:35.710 --> 00:08:39.370
So it's 1000.

00:08:39.370 --> 00:08:41.090
I just took 40% of 2500.

00:08:41.090 --> 00:08:42.950
1000 people voted.

00:08:42.950 --> 00:08:44.740
And if we want to know the
turnout, we just have to say

00:08:44.740 --> 00:08:47.570
the number voted, which is
1000, divided by the

00:08:47.570 --> 00:08:49.390
registered voters.

00:08:49.390 --> 00:08:52.890
Well the registered voters,
there's 1000 men, 1200 women,

00:08:52.890 --> 00:08:53.780
so you add that up.

00:08:53.780 --> 00:08:58.310
That's 2200 total registered
voters.

00:08:58.310 --> 00:09:06.670
That's the same thing
as 10/22, or 5/11.

00:09:06.670 --> 00:09:07.360
That's our answer.

00:09:07.360 --> 00:09:09.410
That's the fraction
that voted.

00:09:09.410 --> 00:09:10.560
That's what they wanted.

00:09:10.560 --> 00:09:12.525
To find to be the fraction, so
you can write it as this

00:09:12.525 --> 00:09:14.630
fraction, 5/11.

00:09:14.630 --> 00:09:16.340
I'll see you in the next video,
hopefully I didn't make

00:09:16.340 --> 00:09:17.090
them mad there.

00:09:17.090 --> 00:09:19.090
See you in the next video.