SAT Prep: Test 5  Section 7 Part 1

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Language: en

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Where are we?

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So we're on page 669, and we're
going to start on test

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number five, section seven.

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Problem number one-- if k is a
positive integer divisible by

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3, and if k is less than 60,
what is the greatest possible

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value of k?

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So it's a positive integer
greater than-- it's positive,

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so it's greater than 0.

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It's divisible by 3, and
it's less than 60.

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k is less than 60.

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60 is divisible by 3, right?

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3 times 20 is 60.

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So if I subtract 3 from
60, that will also be

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divisible by 60.

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So k is equal to 57.

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Right? k can't be 60 because
it's less than 60.

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And then the next
one down is 57.

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And if you don't believe that
3 is divisible into 57-- 3

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goes into 57-- 1, 1 times 3,
27-- goes into it 19 times.

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There you go.

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So the choice is C, 57.

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And if you haven't learned this
already, the easiest way

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to figure out if the
number's divisible

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by 57, add the digits.

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So 5 plus 7 is 12,
1 plus 2 is 3.

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So if when you add the digits,
the sum you get is divisible

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by 3, then the original number
is also divisible by 3.

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So you could actually have gone
down the choices, but you

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don't want to waste too much
time on the first problem.

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Problem two-- the letter H is
symmetric with respect to two

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different lines, as shown
in the dotted line

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in the figure above.

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Which of the following is
symmetric with respect to at

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least two different lines?

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So when they talk about H,
they're saying-- if I draw an

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H, they draw this line
of symmetry here.

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And that means if I were to flip
H over this way, I get

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the same thing.

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If I were to flip it over this
line, I get the same thing.

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It's like a mirror image
on either side.

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Right?

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This green line is a mirror
image of this purple line.

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And the other way is true too.

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If I have H, this mauve part
is the mirror image of this

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brown part along the
horizontal axis.

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If I were to draw a--
if this was the axis

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of the mirror image.

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So which of the other
letters has it?

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So it should be a letter that
looks the same-- that could be

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kind of folded in half either
vertically or horizontally.

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And if we look at all
the choices, X is

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definitely the answer.

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Because if you have an X, and if
you have a vertical line of

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symmetry, notice that the
left-hand side is the mirror

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image of the right-hand side.

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Or you could flip
it over, right?

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They look the same.

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It almost looks like a
reflection of the other side.

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Similarly, if you took
it the other way.

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Also you could flip it up and
down, and they also have the

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mirror image.

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None of the other letters
have that property.

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Next problem.

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Problem number three.

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Bobby receives $2.00 for each
chore he does during the week,

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plus a weekly allowance
of $10.00.

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If Bobby receives no other
money, which of the following

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expressions represents the
total dollar amount Bobby

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receives per week in which
he does n chores?

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So if he does n chores, how much
money is he going to get

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just from doing chores?

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He does n chores, and how much
does he get per chore?

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Well, he gets $2.00.

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Times 2.

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So this is how much he gets
just from doing chores,

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2n, or n times 2.

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And then how much is he
going to get even

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if he does 0 chores?

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He gets a $10.00 allowance no
matter what, far more than I

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ever got as a child.

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So what is the formula?

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It's 2n plus 10, is the amount
of money he gets.

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And that is choice D.

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Right?

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n is the number of chores, he
gets $2.00 per chore, and he

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gets $10.00 no matter what,
even if n is 0, even if he

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does no chores.

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Next problem, four.

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The smallest squares in figure
A and figure B are

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all equal in size.

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If the area in A is 26 square
centimeters, what is the area

00:04:07.100 --> 00:04:07.900
of figure B?

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So let's see if I can
draw these figures.

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So I'll use the line tool, so a
looks like-- let's see, you

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have a line there.

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So let me draw a rectangle.

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So the rectangle looks
like that.

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Close enough.

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And then there's another
rectangle that's like this.

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Another rectangle like this--
the drawing is the hardest

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part, my shaky hands.

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OK, almost there.

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I think you get the point,
I try my best.

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Have to give me credit.

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OK, so that's figure A, and then
figure B looks like this.

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Horizontal line, and then a
vertical line like that.

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And then, let's see,
it has that.

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Connect these two.

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And then-- oh boy,
this is tiring.

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I have a line like that.

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And then it gets split roughly
in half over there.

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And then this connects
like that.

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That connects like that.

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And then I have a
line like that.

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So what they're telling us is in
figure A-- whoops, I don't

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want to do that, edit undo--
what they're saying is figure

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A, each of these squares are the
same size as each of these

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squares in figure B.

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And they also tell us that
figure A is 26 square

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centimeters.

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So the area is 26 centimeters
squared.

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So we want to figure
out the area of B.

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We have to just figure out,
how big is each of these

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little tiles?

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Right?

00:06:01.090 --> 00:06:02.360
So how many tiles are in a?

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Let's count them.

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1, 2, 3, 4, 5, 6, 7, 8,
9, 10, 11, 12, 13.

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13 tiles.

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And they're 26 centimeters
cubed total, right?

00:06:16.490 --> 00:06:21.070
So if 13 times the area of
a tile is equal to 26

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centimeters, a tile-- divide
both sides by 13-- is 2

00:06:24.310 --> 00:06:25.800
centimeters squared, right?

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Each tile is 2 centimeters
squared.

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And how many tiles
does B have?

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1, 2, 3, 4, 5, 6, 7, 8.

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It has 8.

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So its area is 8 times the
number of tiles-- or the area

00:06:38.610 --> 00:06:39.110
of the tiles.

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And we know what the area of
the tiles are-- it's 2,

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because it's the same as A.

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So area is equal to 8 times
2, which is equal to 16

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centimeters squared,
which is choice C.

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Next problem.

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More drawing for Sal.

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Oh boy, it's the drawing
that really tires me.

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OK.

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And I have to draw it pretty
accurately, because

00:07:01.970 --> 00:07:03.975
otherwise-- this is all
about reading a graph.

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All right, so let me draw.

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Let me make the first one-- so
Albert goes to like 300.

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This is 300.

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And then it's 150, which is
roughly half of that.

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And then the next guy is
like a little over 200,

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so it's like 2/3.

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I'm just trying my best,
trying my best.

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Then the next guy, I guess
at like 250, here.

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And then the last guy-- I'm
drawing the white boxes, this

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is pretty much the
same number.

00:07:49.970 --> 00:07:52.000
Like that.

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And then let me draw the other
one in here, so the

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other guy is 150.

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This guy gets to 250.

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Which I said was roughly
the same amount as

00:08:05.830 --> 00:08:07.120
these guys over here.

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Next guy looks about the same.

00:08:15.040 --> 00:08:18.300
250, that's about that.

00:08:18.300 --> 00:08:22.100
And this guy is like that.

00:08:22.100 --> 00:08:24.340
All the work I'm doing now is
just to redraw what you

00:08:24.340 --> 00:08:29.820
already have. Then this guy is
like 350, 300 or something.

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If I were to draw-- let
me mark it off.

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So this is 300, this is 150--
see those guys that are a

00:08:40.350 --> 00:08:42.796
little bit under 200.

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So this is like 200,
this is 250.

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They're asking us, according
to the graph above, which

00:08:50.530 --> 00:08:53.830
salesperson had the greatest
increase in the number of

00:08:53.830 --> 00:08:56.360
units sold from 1988 to 1999?

00:08:56.360 --> 00:09:00.860
So the 1988 ones are
the blue ones, and

00:09:00.860 --> 00:09:02.310
1999 are the red ones.

00:09:02.310 --> 00:09:05.750
So you're essentially saying,
who had the greatest increase

00:09:05.750 --> 00:09:08.160
going from the blue
to the red, right?

00:09:08.160 --> 00:09:12.400
And this is Albert, this is
Goldberg, Patel-- that's nice,

00:09:12.400 --> 00:09:14.070
they included an Indian guy.

00:09:14.070 --> 00:09:17.170
Smith, Wang.

00:09:17.170 --> 00:09:18.876
I look forward to when
they have a Khan on

00:09:18.876 --> 00:09:20.920
the SAT, but anyway.

00:09:20.920 --> 00:09:23.120
So who increased the most going
from the blue year,

00:09:23.120 --> 00:09:25.170
1998, to 1999.

00:09:25.170 --> 00:09:27.190
This guy clearly decreased,
right?

00:09:27.190 --> 00:09:30.450
He went from 300 to 150,
so it's not him.

00:09:30.450 --> 00:09:33.000
This guy decreased, he went
from something larger to

00:09:33.000 --> 00:09:34.980
something smaller,
so it's not him.

00:09:34.980 --> 00:09:36.410
So who had the largest
increase?

00:09:36.410 --> 00:09:38.150
Well, you could eyeball
it, right?

00:09:38.150 --> 00:09:38.980
Where are the increases?

00:09:38.980 --> 00:09:47.240
This guy increased this much,
compared to a small increase

00:09:47.240 --> 00:09:50.500
here, and a small
increase here.

00:09:50.500 --> 00:09:56.290
So the answer is G, or Goldberg,
which is choice B.

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See you in the next video.


SAT Prep: Test 5 Section 7 Part 3

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We're on problem number 10.

00:00:04.800 --> 00:00:15.830
Problem 10-- if 2x minus 2,
times 2 minus x, is equal to

00:00:15.830 --> 00:00:19.200
0, what are all possible
values of x?

00:00:19.200 --> 00:00:23.140
If I multiply two numbers,
right, I multiply two

00:00:23.140 --> 00:00:26.780
expressions equal to 0, that
means one or both of these

00:00:26.780 --> 00:00:28.090
expressions are going
to be equal to 0.

00:00:28.090 --> 00:00:31.960
And if you've solved for roots
of a quadratic using

00:00:31.960 --> 00:00:34.150
factoring, you'll be familiar
with this notion.

00:00:34.150 --> 00:00:41.100
So either 2x minus 2 is 0, and
or, actually, either of these

00:00:41.100 --> 00:00:42.670
could be equal to 0,
or both of them

00:00:42.670 --> 00:00:46.340
could be equal to zero.

00:00:46.340 --> 00:00:47.280
Let's just solve this.

00:00:47.280 --> 00:00:52.100
So add 2 to both sides, 2x is
equal to 2, x is equal to 1.

00:00:52.100 --> 00:00:55.475
And here, if we just add x to
both sides, we get 2 is equal

00:00:55.475 --> 00:00:58.520
to x, or x is equal to 2.

00:00:58.520 --> 00:01:02.500
So x could be 1, or
x could be 2.

00:01:02.500 --> 00:01:06.910
So choice D, 1 and 2 only.

00:01:06.910 --> 00:01:08.580
And you could try
them out, right?

00:01:08.580 --> 00:01:13.170
If x is 1, this becomes 0 times
1, which is of course 0.

00:01:13.170 --> 00:01:15.790
If x is 2, this becomes
2, right?

00:01:15.790 --> 00:01:17.560
2 times 2 minus 2 is 2.

00:01:17.560 --> 00:01:19.050
Times 0, which is 0.

00:01:19.050 --> 00:01:20.820
And 0 doesn't work.

00:01:20.820 --> 00:01:22.800
That might have been your
temptation, but if you put 0

00:01:22.800 --> 00:01:26.240
in here, you get minus 2--
because this term will go

00:01:26.240 --> 00:01:29.720
away-- you get minus 2 times 2,
which is minus 4, so that

00:01:29.720 --> 00:01:31.030
doesn't work.

00:01:31.030 --> 00:01:34.090
You just have to set each of
these expressions to 0.

00:01:34.090 --> 00:01:42.450
Next question, problem 11.

00:01:42.450 --> 00:01:50.540
If x to the third is equal to
y to the ninth, what is x in

00:01:50.540 --> 00:01:53.010
terms of y?

00:01:53.010 --> 00:01:55.470
So what we can do here is we
just want to get rid of this

00:01:55.470 --> 00:01:56.770
cubed power.

00:01:56.770 --> 00:01:58.660
So how do we get rid
of the cubed power?

00:01:58.660 --> 00:02:01.052
Well, we could take the cube
root of both sides.

00:02:01.052 --> 00:02:03.396
If that doesn't make sense to
you, I'll show you how.

00:02:03.396 --> 00:02:07.050
x to the third-- let me give
this some breathing room-- is

00:02:07.050 --> 00:02:07.990
equal to y to the ninth.

00:02:07.990 --> 00:02:10.400
I'm just writing the same thing
a little bit bigger.

00:02:10.400 --> 00:02:13.000
What we do to one side of the
equation, we can do to the

00:02:13.000 --> 00:02:14.850
other side of the equation.

00:02:14.850 --> 00:02:17.220
If I want this exponent to be
1, I just have to take it to

00:02:17.220 --> 00:02:19.800
the 1/3 power.

00:02:19.800 --> 00:02:21.650
How do I know that?

00:02:21.650 --> 00:02:25.100
Well, if I take something to an
exponent, and then take it

00:02:25.100 --> 00:02:28.300
to another exponent, I
essentially just multiply the

00:02:28.300 --> 00:02:29.220
two exponents, right?

00:02:29.220 --> 00:02:30.810
That's an exponent rule.

00:02:30.810 --> 00:02:33.380
And you can review that in
the exponent videos.

00:02:33.380 --> 00:02:37.540
If you multiply 3 and 1/3, you
get 1, so that's why I'm

00:02:37.540 --> 00:02:39.550
raising to the 1/3 power.

00:02:39.550 --> 00:02:40.840
And that, of course, is
the same thing as

00:02:40.840 --> 00:02:42.830
taking the cube root.

00:02:42.830 --> 00:02:46.200
Excuse me, I just had some
chicken, I need to drink some

00:02:46.200 --> 00:02:46.740
water or something.

00:02:46.740 --> 00:02:48.780
But of course, if I do something
to one side of the

00:02:48.780 --> 00:02:50.230
equation, I have to do
it to both sides of

00:02:50.230 --> 00:02:51.290
this equation, right?

00:02:51.290 --> 00:02:54.330
If I take the cube root of one
side, for the equation to

00:02:54.330 --> 00:02:57.330
hold, I have to take the cube
root of the other side.

00:02:57.330 --> 00:02:59.820
So x to the third to the 1/3,
well that's just x to the

00:02:59.820 --> 00:03:02.020
first, or just x, right?

00:03:02.020 --> 00:03:06.180
Because 3 times 1/3 is 1, so
x to the first is just x.

00:03:06.180 --> 00:03:07.710
And that equals what?

00:03:07.710 --> 00:03:10.590
y to the 9 times 1/3.

00:03:10.590 --> 00:03:14.520
Well what's 9 times-- 9 times
1/3 is equal to 9 divided by

00:03:14.520 --> 00:03:17.130
3, which is equal to 3.

00:03:17.130 --> 00:03:19.830
So x is equal to y to
the third power.

00:03:19.830 --> 00:03:21.730
That's just this 3.

00:03:21.730 --> 00:03:24.680
And that is choice C.

00:03:27.790 --> 00:03:29.040
Next problem.

00:03:31.870 --> 00:03:34.180
I will switch colors
for variety.

00:03:34.180 --> 00:03:37.480
And there's something
that I have to draw.

00:03:37.480 --> 00:03:40.120
OK.

00:03:40.120 --> 00:03:47.450
So they drew-- let's see if
I can pull this one off.

00:03:51.060 --> 00:03:53.580
Let's see if I can pull drawing
this figure off.

00:03:53.580 --> 00:03:57.960
So it looks like a
line like that.

00:03:57.960 --> 00:04:01.140
And a line like that.

00:04:01.140 --> 00:04:03.430
And a line like that.

00:04:03.430 --> 00:04:05.410
And then it has almost
a mirror image

00:04:05.410 --> 00:04:08.270
of a line like that.

00:04:08.270 --> 00:04:09.520
Line like that.

00:04:12.520 --> 00:04:14.920
Close enough.

00:04:14.920 --> 00:04:20.870
And they're asking us, in the
x-y coordinate system above,

00:04:20.870 --> 00:04:23.080
which of the following line
segments has a slope of

00:04:23.080 --> 00:04:24.780
negative 1?

00:04:24.780 --> 00:04:26.682
So what is a slope
of negative 1?

00:04:26.682 --> 00:04:32.720
A slope of negative 1 means that
as we move to the right

00:04:32.720 --> 00:04:37.610
1, we move down 1.

00:04:37.610 --> 00:04:38.760
That's a slope of negative 1.

00:04:38.760 --> 00:04:43.190
And if you're familiar with
slopes a lot, just intuitively

00:04:43.190 --> 00:04:46.740
you know that it looks
something like this.

00:04:46.740 --> 00:04:49.595
Slope of negative 1 looks
something like that.

00:04:49.595 --> 00:04:52.420
And if we look at the lines
that they drew, all the

00:04:52.420 --> 00:04:55.690
choices, the ones that are
moving up are definitely not

00:04:55.690 --> 00:04:56.550
our answer, right?

00:04:56.550 --> 00:04:59.230
This one is moving up, so this
one can't be the answer.

00:04:59.230 --> 00:05:01.720
This one is moving up, so this
can't be the answer.

00:05:01.720 --> 00:05:04.460
This one's moving up, so this
one can't be the answer.

00:05:04.460 --> 00:05:07.630
So all of these lines-- the
yellow ones that I haven't

00:05:07.630 --> 00:05:10.590
scratched out-- all of these
have negative slopes.

00:05:10.590 --> 00:05:13.730
And we just have to figure out
which one could be negative 1.

00:05:13.730 --> 00:05:20.530
If we look at this slope here
between point O and point A,

00:05:20.530 --> 00:05:26.330
they mark off that this is
1, 2, 3, and this is 1.

00:05:26.330 --> 00:05:30.950
So for this line, we
went over 1, right?

00:05:30.950 --> 00:05:33.630
We moved over 1, but
we went down 3.

00:05:33.630 --> 00:05:35.920
So this line has a slope
of negative 3.

00:05:38.435 --> 00:05:44.320
And similarly, they draw-- this
goes out 1, 2, 3-- this

00:05:44.320 --> 00:05:50.310
line, we have to go 3 for it to
go-- we have to move in the

00:05:50.310 --> 00:05:54.200
x-direction positive 3 for
it to move down 1.

00:05:54.200 --> 00:05:55.970
So this has a slope of 1/3.

00:05:55.970 --> 00:05:59.060
And you can kind of tell that
it goes down very gradually.

00:05:59.060 --> 00:06:00.320
Right?

00:06:00.320 --> 00:06:01.840
Actually negative 1/3, sorry.

00:06:01.840 --> 00:06:05.520
The rise is negative 1,
and the run is 3.

00:06:05.520 --> 00:06:08.640
Run is just how far you move
in the x-direction, right?

00:06:08.640 --> 00:06:13.240
The rise is negative 1,
which is right there,

00:06:13.240 --> 00:06:15.920
and the run is 3.

00:06:15.920 --> 00:06:17.970
So we know that this
isn't the answer.

00:06:17.970 --> 00:06:20.780
So just by deductive reasoning,
we know that this

00:06:20.780 --> 00:06:22.640
is probably going to
be our answer.

00:06:22.640 --> 00:06:25.720
And it also looks like it
has a slope negative 1.

00:06:25.720 --> 00:06:32.700
And if you were to actually look
at it, points D and C,

00:06:32.700 --> 00:06:39.655
this is about-- if I
just look at it by

00:06:39.655 --> 00:06:41.620
inspection-- 1 comma 3.

00:06:41.620 --> 00:06:46.830
And this looks like the point
3 comma 1, right here.

00:06:46.830 --> 00:06:51.500
So what is the change in
y over the change in x?

00:06:51.500 --> 00:06:57.670
Well, the change in y is 3 minus
1, so that equals 2.

00:06:57.670 --> 00:07:01.700
And the change in x is 1 minus
3, which is minus 2.

00:07:01.700 --> 00:07:02.760
Which is minus 1.

00:07:02.760 --> 00:07:05.490
Remember, when you calculate
slope, you always have to use

00:07:05.490 --> 00:07:08.430
the first-- if I use 3 the first
time of the numerator, I

00:07:08.430 --> 00:07:10.720
have to use 1 the first
time in the denomator.

00:07:10.720 --> 00:07:13.665
So 3, minus 1, over 1, minus
3, is the slope,

00:07:13.665 --> 00:07:15.030
and it's minus 1.

00:07:15.030 --> 00:07:16.910
But if you're really good, you
should just be able to look at

00:07:16.910 --> 00:07:19.440
it and say, well that's the
closest thing to negative 1,

00:07:19.440 --> 00:07:22.290
because it's not too steep
and not to shallow.

00:07:22.290 --> 00:07:23.540
Next problem.

00:07:26.170 --> 00:07:29.290
Oh, and so that is choice
D, C, E-- choice E.

00:07:33.090 --> 00:07:36.820
Problem 13.

00:07:36.820 --> 00:07:39.010
Kyle's lock combination
consists of

00:07:39.010 --> 00:07:41.430
three two digit numbers.

00:07:41.430 --> 00:07:47.530
The combination satisfies the
three conditions below.

00:07:47.530 --> 00:08:03.620
One number is odd, one number
is a multiple of 5, and then

00:08:03.620 --> 00:08:06.590
one month is the day of the
month of Kyle's birthday.

00:08:13.480 --> 00:08:15.950
So what do we know about
that number?

00:08:15.950 --> 00:08:18.030
Well, it's a two digit number,
so it has to be

00:08:18.030 --> 00:08:20.940
between 01 and 31, right?

00:08:20.940 --> 00:08:23.240
In order for it to be a
birthday, it can't be-- OK.

00:08:23.240 --> 00:08:26.810
If each number satisfies exactly
one of the conditions,

00:08:26.810 --> 00:08:28.360
which of the following
could be the

00:08:28.360 --> 00:08:30.280
combination to the lock?

00:08:30.280 --> 00:08:32.809
So one number can't satisfy two
of these conditions, and

00:08:32.809 --> 00:08:34.470
then you have another number
that satisfies none.

00:08:34.470 --> 00:08:36.470
Each of them has to
do one of them.

00:08:36.470 --> 00:08:37.720
So let's look at the choices.

00:08:40.190 --> 00:08:50.720
Choice A is 14, 20, 13.

00:08:50.720 --> 00:08:52.540
Let's see, which one could
satisfy the odd?

00:08:52.540 --> 00:08:54.270
Well this number is odd.

00:08:54.270 --> 00:08:58.830
So let me see, if this condition
is satisfied by this

00:08:58.830 --> 00:09:01.410
number, it's odd.

00:09:01.410 --> 00:09:02.985
What number is a
multiple of 5?

00:09:05.900 --> 00:09:07.830
So this condition-- well that's

00:09:07.830 --> 00:09:10.950
satisfied by this number.

00:09:10.950 --> 00:09:12.670
And what number is a
day of the month?

00:09:12.670 --> 00:09:15.980
Well, this looks pretty
straightforward.

00:09:15.980 --> 00:09:19.260
One number is a day
of the month.

00:09:19.260 --> 00:09:21.450
Well, 14 could be a
day of a month.

00:09:21.450 --> 00:09:24.000
And in general, in any SAT
problem, and I'm seeing this

00:09:24.000 --> 00:09:26.790
pattern more and more as I go
through all of these practice

00:09:26.790 --> 00:09:29.310
tests, is when they have a
problem where they want you to

00:09:29.310 --> 00:09:33.550
go through every choice, the
answers tend to be one of the

00:09:33.550 --> 00:09:35.750
first few choices, because they
don't want you to waste a

00:09:35.750 --> 00:09:36.890
lot of time.

00:09:36.890 --> 00:09:38.250
So you should feel pretty
comfortable if you did this

00:09:38.250 --> 00:09:39.790
and you got choice A.

00:09:39.790 --> 00:09:41.680
And if you want to see an
example of what won't work,

00:09:41.680 --> 00:09:43.220
I'm guessing B won't work.

00:09:43.220 --> 00:10:00.070
Choice B says 14, 25, 13.

00:10:00.070 --> 00:10:02.100
Actually, that doesn't look
like it could satisfy.

00:10:02.100 --> 00:10:06.380
If each number satisfies exactly
one of the conditions,

00:10:06.380 --> 00:10:08.300
which of the following
could be the

00:10:08.300 --> 00:10:09.550
combination to the lock?

00:10:12.840 --> 00:10:13.780
Oh, exactly.

00:10:13.780 --> 00:10:15.570
So why can't this one be?

00:10:15.570 --> 00:10:20.600
Because this condition that one
number is odd, it can only

00:10:20.600 --> 00:10:22.580
be satisfied by one
of the choices.

00:10:22.580 --> 00:10:24.150
Oh, I'm running over, I'll see
you in the next video.


SAT Prep: Test 5 Section 7 Part 2

WEBVTT
Kind: captions
Language: en

00:00:00.530 --> 00:00:01.240
Welcome back.

00:00:01.240 --> 00:00:06.620
We're on problem number
six, on page 670.

00:00:06.620 --> 00:00:16.980
If the average of 6, 6, 12,
16, and x-- the average is

00:00:16.980 --> 00:00:19.220
equal to x, what is
the value of x?

00:00:19.220 --> 00:00:21.420
So if I were to average all
these numbers, I get x.

00:00:21.420 --> 00:00:22.280
How do I average?

00:00:22.280 --> 00:00:27.070
I add them up, I add up the
numbers, and I divide by the

00:00:27.070 --> 00:00:28.200
number of numbers there are.

00:00:28.200 --> 00:00:31.960
So there's 1, 2, 3, 4, 5
numbers, so I divide by that.

00:00:31.960 --> 00:00:36.220
And they're saying that this
average is going to equal x.

00:00:36.220 --> 00:00:39.140
So let's multiply
both sides by 5.

00:00:39.140 --> 00:00:47.400
And I get 6 plus 6 plus 12 plus
16 plus x is equal to

00:00:47.400 --> 00:00:52.570
20-- my brain is malfunctioning,
the average is

00:00:52.570 --> 00:00:53.550
equal to x, right?

00:00:53.550 --> 00:00:55.095
So I have to multiply
both sides by 5.

00:00:57.870 --> 00:01:00.610
So I multiply both sides
by 5, I get 5x.

00:01:00.610 --> 00:01:01.110
Right?

00:01:01.110 --> 00:01:04.660
This is the average, and they
say the average is equal to x.

00:01:04.660 --> 00:01:08.050
Multiply both sides by 5, you
get rid of the 5 in the

00:01:08.050 --> 00:01:10.970
denominator here, you get 5x
on the right-hand side.

00:01:10.970 --> 00:01:11.990
And what's the sum?

00:01:11.990 --> 00:01:18.852
6 plus 6 is 12, 12 plus 12
is 24, 24 plus 16 is 40.

00:01:18.852 --> 00:01:23.300
So we get 40 plus x
is equal to 5x.

00:01:23.300 --> 00:01:27.530
Subtract x from both sides,
40 is equal to 4x.

00:01:27.530 --> 00:01:31.730
Divide both sides by 4, you
get x is equal to 10.

00:01:31.730 --> 00:01:34.200
And that is choice D.

00:01:34.200 --> 00:01:35.450
Next problem.

00:01:39.820 --> 00:01:46.020
Let me draw this triangle.

00:01:46.020 --> 00:01:47.640
Let me try my best to
draw the triangle.

00:01:50.270 --> 00:01:52.200
Looks something like that.

00:01:52.200 --> 00:01:54.372
And then there's an altitude
right here, just

00:01:54.372 --> 00:01:56.760
drop straight down.

00:01:56.760 --> 00:01:59.090
And then they tell us that
this is a 90-- or

00:01:59.090 --> 00:02:00.550
do they tell us?

00:02:00.550 --> 00:02:04.070
My cousin who used my book drew
over it, so I'm not sure.

00:02:04.070 --> 00:02:07.720
But I'm pretty sure they
tell us that this

00:02:07.720 --> 00:02:10.770
is a 90 degree angle.

00:02:10.770 --> 00:02:12.660
For the figure above, what
is the value of z?

00:02:12.660 --> 00:02:21.470
So they say this is z, this
is y, this is 2y,

00:02:21.470 --> 00:02:25.690
and this is 40 degrees.

00:02:25.690 --> 00:02:27.110
So what is z?

00:02:27.110 --> 00:02:30.280
So we know this is a 90 degree
angle, and we know that z plus

00:02:30.280 --> 00:02:33.620
y plus 90 is equal to 180.

00:02:33.620 --> 00:02:35.490
So if we know what y is,
we could figure out z.

00:02:35.490 --> 00:02:37.520
And how can we figure out y?

00:02:37.520 --> 00:02:40.760
Well we know that 2y-- if we
look at this right-hand

00:02:40.760 --> 00:02:46.600
triangle-- we know that
2y plus 40 plus

00:02:46.600 --> 00:02:59.130
90 is equal to 180.

00:02:59.130 --> 00:02:59.960
Right?

00:02:59.960 --> 00:03:06.480
So 2y plus 130 is
equal to 180.

00:03:06.480 --> 00:03:10.780
2y is equal to 50 degrees.

00:03:10.780 --> 00:03:16.020
y is equal to 25 degrees.

00:03:16.020 --> 00:03:18.970
So this is 25 degrees.

00:03:18.970 --> 00:03:21.170
I really wish I could read this
problem, I'm pretty sure

00:03:21.170 --> 00:03:23.730
they drew in a little
perpindicular-- but anyway, we

00:03:23.730 --> 00:03:24.480
might have been able
to address it

00:03:24.480 --> 00:03:25.550
even if they didn't.

00:03:25.550 --> 00:03:31.980
But if y is 25, then we know
that z plus 25 plus 90 is

00:03:31.980 --> 00:03:33.800
equal to 180.

00:03:33.800 --> 00:03:37.970
z plus 115 is equal to 180.

00:03:37.970 --> 00:03:41.310
z is equal to-- subtract
115 from both sides,

00:03:41.310 --> 00:03:42.980
what's 80 minus 15?

00:03:42.980 --> 00:03:45.140
65.

00:03:45.140 --> 00:03:49.200
The choice is C.

00:03:49.200 --> 00:03:51.750
Next problem, problem
number eight.

00:03:58.400 --> 00:04:01.400
A computer program randomly
selects a

00:04:01.400 --> 00:04:04.000
positive 2 digit integer.

00:04:04.000 --> 00:04:06.720
If the integer selected
is odd, twice

00:04:06.720 --> 00:04:07.830
that integer is printed.

00:04:07.830 --> 00:04:13.690
So odd, it prints
2 times integer.

00:04:16.959 --> 00:04:20.079
If the integer is even, the
integer itself is printed.

00:04:20.079 --> 00:04:26.350
So if it's even, it just
prints the integer.

00:04:26.350 --> 00:04:27.780
So if it's an odd and you
multiply it by 2, it's

00:04:27.780 --> 00:04:29.600
actually going to print an even
integer no matter what.

00:04:32.780 --> 00:04:35.670
If the integer printed is 26,
which of the following could

00:04:35.670 --> 00:04:39.040
have been the integer
selected?

00:04:39.040 --> 00:04:42.170
So all we see is 26.

00:04:42.170 --> 00:04:44.460
We just see 26.

00:04:44.460 --> 00:04:47.590
So 26 could've been generated
one of two ways.

00:04:47.590 --> 00:04:49.780
It could have been generated
by an even number that was

00:04:49.780 --> 00:04:51.420
just kept the same.

00:04:51.420 --> 00:04:53.290
Well, if it was an even number
that was kept the same and you

00:04:53.290 --> 00:04:55.960
got 26, then we know that
the number is 26.

00:04:55.960 --> 00:04:58.480
The number that generated
was 26.

00:04:58.480 --> 00:05:02.010
The other possibility is it
could've been an odd number

00:05:02.010 --> 00:05:04.770
that was doubled, right?

00:05:04.770 --> 00:05:08.180
If it was an odd number that
was doubled, that means 2

00:05:08.180 --> 00:05:14.620
times the odd number
is equal to 26.

00:05:14.620 --> 00:05:17.860
So that means that the number
would have to be 13, right?

00:05:17.860 --> 00:05:23.560
13 times odd-- sorry-- 2 times
odd-- these are the two

00:05:23.560 --> 00:05:26.130
situations-- 2 times odd is
going to be equal to 26, in

00:05:26.130 --> 00:05:28.350
which case odd is equal to 13.

00:05:28.350 --> 00:05:32.730
Or 1 times even is going to be
equal to 26, it which case

00:05:32.730 --> 00:05:34.870
even equals 26.

00:05:34.870 --> 00:05:37.330
So the number generated could've
been 26 or it could

00:05:37.330 --> 00:05:38.760
have been 13.

00:05:38.760 --> 00:05:43.900
And those are choices 1
and 2, and that's C.

00:05:43.900 --> 00:05:46.180
Next problem, problem
number nine.

00:05:51.730 --> 00:05:54.110
They give you choice 52 in
that last problem just to

00:05:54.110 --> 00:05:57.730
confuse you, to actually end
up doubling the 26, but we

00:05:57.730 --> 00:06:00.500
know that the odd number was
doubled to get 26, so the

00:06:00.500 --> 00:06:02.520
number generated would
have been 13.

00:06:02.520 --> 00:06:03.710
Problem number nine.

00:06:03.710 --> 00:06:07.575
How many seconds are there in
m minutes and s seconds?

00:06:17.930 --> 00:06:23.590
Well, how many seconds
are there per minute?

00:06:23.590 --> 00:06:28.500
Let's write this expression
as m minutes

00:06:28.500 --> 00:06:31.140
plus s seconds, right?

00:06:31.140 --> 00:06:34.840
Well, what does m equal
in terms of seconds?

00:06:34.840 --> 00:06:38.060
Or how many seconds are
there per minute?

00:06:38.060 --> 00:06:43.680
Well, we know that there are
60 seconds per m, right?

00:06:43.680 --> 00:06:54.260
Or we could say that 60 seconds
is equal to 1m, right?

00:06:54.260 --> 00:07:02.110
So if there's 60 seconds in 1m,
how many-- actually, I'm

00:07:02.110 --> 00:07:04.490
confusing the issue, let
me write it this way.

00:07:04.490 --> 00:07:06.090
m minutes, right?

00:07:06.090 --> 00:07:07.290
There's m minutes.

00:07:07.290 --> 00:07:11.350
How many seconds are
there per minute?

00:07:11.350 --> 00:07:12.787
Let me start over, because
I think I confused

00:07:12.787 --> 00:07:14.040
you a little bit.

00:07:14.040 --> 00:07:15.620
So I'm going to write--
actually, let me write it

00:07:15.620 --> 00:07:18.080
without m and s, that's what
confusing me as well.

00:07:18.080 --> 00:07:29.490
Let's say I have x minutes plus
y seconds, and I want to

00:07:29.490 --> 00:07:32.350
convert it all into seconds.

00:07:32.350 --> 00:07:38.090
Well, we know that there are 60
seconds per minute, right?

00:07:38.090 --> 00:07:41.490
So if we want to convert a
minute to seconds, we write x

00:07:41.490 --> 00:07:54.530
minutes times 60 seconds per
minute plus y seconds.

00:07:54.530 --> 00:07:57.880
And so the minutes will cancel
out, and so you're left with

00:07:57.880 --> 00:08:01.030
60 times x-- and this is
something that you'll learn in

00:08:01.030 --> 00:08:03.110
physics class, that you can
treat units just like you

00:08:03.110 --> 00:08:05.710
would treat variables, and
they'll cancel out similarly.

00:08:05.710 --> 00:08:10.850
So you'd get 60x-- right, the
minutes have canceled out--

00:08:10.850 --> 00:08:13.720
let me switch colors--
you'll get 60 times x

00:08:13.720 --> 00:08:17.911
seconds, plus y seconds.

00:08:17.911 --> 00:08:22.870
So your total number of
seconds is 60x plus y.

00:08:22.870 --> 00:08:25.500
And in the problem though, in
minutes they didn't say x,

00:08:25.500 --> 00:08:29.610
they said m, so x is
m, and then y is s.

00:08:32.299 --> 00:08:39.030
So 60m plus s, so
that's choice A.

00:08:39.030 --> 00:08:41.600
And this might have been a
little confusing, let me do it

00:08:41.600 --> 00:08:45.480
a simpler way, or maybe a more
intuitive way for you.

00:08:45.480 --> 00:08:48.320
There's m minutes, how many
seconds are in m minutes?

00:08:52.620 --> 00:08:53.420
Think about it.

00:08:53.420 --> 00:08:56.600
If there is-- if I'm talking
about 2 minutes, there's 60

00:08:56.600 --> 00:09:01.160
seconds per minute, so if I
said 2 minutes, I would

00:09:01.160 --> 00:09:05.260
multiply 2 times 60, and I
would get to 120 seconds.

00:09:05.260 --> 00:09:09.960
If it was 5 minutes, I would
multiply 5 times 60, and get

00:09:09.960 --> 00:09:11.760
to 300 seconds.

00:09:11.760 --> 00:09:15.620
So if I have m minutes,
I'll multiply 60 times

00:09:15.620 --> 00:09:21.070
m to get 60m seconds.

00:09:21.070 --> 00:09:26.120
And of course, they said m
minutes plus s seconds.

00:09:26.120 --> 00:09:31.390
So now I have 60m seconds,
plus these s seconds.

00:09:31.390 --> 00:09:36.080
So my total number of seconds
is 60m plus s.

00:09:36.080 --> 00:09:38.680
This is a more intuitive
way, maybe.

00:09:38.680 --> 00:09:40.560
You should always try out
numbers, and hopefully it'll

00:09:40.560 --> 00:09:41.750
make a little bit more sense.

00:09:41.750 --> 00:09:43.570
The way I did it previously is
how you would do it in physics

00:09:43.570 --> 00:09:46.230
class, where you would actually
cancel out the units

00:09:46.230 --> 00:09:47.990
and make sure you're doing
it the right way.

00:09:47.990 --> 00:09:49.780
See you in the next video.


SAT Prep: Test 5 Section 3 Part 1

WEBVTT
Kind: captions
Language: en

00:00:00.720 --> 00:00:04.030
Let's do some SAT problems.
Let's see, we're starting test

00:00:04.030 --> 00:00:07.350
5 now and it's problem
number 1.

00:00:07.350 --> 00:00:09.550
This is page 652.

00:00:09.550 --> 00:00:15.740
According to a certain recipe,
20-- I'm getting deja-vu, this

00:00:15.740 --> 00:00:17.860
looks like a question I did in
the last test, but maybe this

00:00:17.860 --> 00:00:20.160
is different-- 25 pounds
of flour are

00:00:20.160 --> 00:00:22.940
needed to make 300 rolls.

00:00:22.940 --> 00:00:29.110
So 25 pounds per 300
hundred rolls.

00:00:32.650 --> 00:00:36.070
At this rate, how many
pounds of flour are

00:00:36.070 --> 00:00:38.960
needed to make 12 rolls?

00:00:38.960 --> 00:00:41.780
Well, we can make
a ratio here.

00:00:41.780 --> 00:00:48.680
So I need 25 to do
300 rolls, right?

00:00:48.680 --> 00:00:51.500
But they're asking us well, how
much do I need if I only

00:00:51.500 --> 00:00:53.520
need to do 12 rolls?

00:00:53.520 --> 00:00:56.190
So 12 is what fraction of 300?

00:00:56.190 --> 00:01:02.090
Whatever that fraction is, the
fraction of rolls of pounds of

00:01:02.090 --> 00:01:04.690
flour I need to use will
be the same fraction.

00:01:04.690 --> 00:01:07.820
Let's say that this is
x is the pounds of

00:01:07.820 --> 00:01:09.030
flour I need to use.

00:01:09.030 --> 00:01:12.220
So x is to 25 as twelve
is to 300.

00:01:12.220 --> 00:01:16.460
And I can tell you from
inspection that 12 over 300 is

00:01:16.460 --> 00:01:19.450
the same thing as 1/25.

00:01:19.450 --> 00:01:22.400
If you don't believe me,
divide 300 by 12 and I

00:01:22.400 --> 00:01:23.000
come up with that.

00:01:23.000 --> 00:01:25.660
Well, you know 25 goes into
100 4 times and then

00:01:25.660 --> 00:01:27.360
4 times 3 is 12.

00:01:27.360 --> 00:01:29.240
If you don't believe me,
you can confirm this.

00:01:29.240 --> 00:01:30.980
And they did it on purpose
because this is the first

00:01:30.980 --> 00:01:32.880
problem, which tends
to be a quick one.

00:01:32.880 --> 00:01:37.250
So x over 25 is equal to one
over 25, so x equals 1.

00:01:37.250 --> 00:01:41.090
So you need 1 pound of flour.

00:01:41.090 --> 00:01:43.030
And you could have also set the
ratio up like this: you

00:01:43.030 --> 00:01:50.770
could have said 25 is to
300 as x is to 12.

00:01:50.770 --> 00:01:51.820
This would have also worked.

00:01:51.820 --> 00:01:56.080
Here we would have put the rolls
all on one fraction and

00:01:56.080 --> 00:01:58.850
we could've put the pounds
of flour all

00:01:58.850 --> 00:02:00.610
on the other fraction.

00:02:00.610 --> 00:02:01.860
Next problem.

00:02:07.950 --> 00:02:09.750
Switching colors.

00:02:09.750 --> 00:02:11.260
Problem number 2.

00:02:11.260 --> 00:02:21.850
If xy is equal to 10, what is
the value of 2 times x divided

00:02:21.850 --> 00:02:26.050
by y times y squared?

00:02:26.050 --> 00:02:28.790
Well the trick here is you've
got to simplify this

00:02:28.790 --> 00:02:31.040
expression before you attempt
to do anything.

00:02:31.040 --> 00:02:35.990
And simplifying, what's x
divided by y times y squared?

00:02:35.990 --> 00:02:41.390
Well this right here, this is
the same thing as xy squared

00:02:41.390 --> 00:02:43.160
divided by y, right?

00:02:43.160 --> 00:02:45.340
We could put the 2 out here.

00:02:45.340 --> 00:02:48.820
And see, we have a 2 on top and
the y on the bottom is the

00:02:48.820 --> 00:02:52.340
same thing as y to the first,
so this is the same thing.

00:02:52.340 --> 00:02:54.270
What's y squared divided by y?

00:02:54.270 --> 00:02:55.830
Well it's just y, right?

00:02:55.830 --> 00:03:01.320
So we get 2x and y squared
divided by y is just y, right?

00:03:01.320 --> 00:03:03.830
The squared cancels out
with this entire term.

00:03:03.830 --> 00:03:04.880
This just gets 1.

00:03:04.880 --> 00:03:06.770
I divide the top and
the bottom by 1.

00:03:06.770 --> 00:03:10.240
So all I'm left with is 2xy, and
we know that xy is equal

00:03:10.240 --> 00:03:14.910
to 10, so 2 times 10 is 20.

00:03:14.910 --> 00:03:16.950
That's choice e.

00:03:16.950 --> 00:03:18.750
Next problem.

00:03:18.750 --> 00:03:19.685
Problem 3.

00:03:19.685 --> 00:03:23.720
Let's see if I can fit it on
this without having to-- x

00:03:23.720 --> 00:03:30.400
plus y is equal to 30.

00:03:30.400 --> 00:03:31.370
I might be talking funny.

00:03:31.370 --> 00:03:34.140
I just came from the dentist.
And x is greater than 8.

00:03:36.980 --> 00:03:41.220
Which of the following
must be true?

00:03:41.220 --> 00:03:44.210
Well, we know x is greater than
8, and we also know that

00:03:44.210 --> 00:03:48.530
x is equal to 30
minus y, right?

00:03:48.530 --> 00:03:51.576
I just subtracted y from both
sides of that equation.

00:03:51.576 --> 00:03:53.920
x is equal to 30 minus y.

00:03:53.920 --> 00:03:57.250
Well we also know that x is
greater than 8, so 30 minus y,

00:03:57.250 --> 00:03:59.250
which is the same thing
as x, must also be

00:03:59.250 --> 00:04:01.730
greater than 8, right?

00:04:01.730 --> 00:04:05.580
30 minus y is also going
to be greater than 8.

00:04:05.580 --> 00:04:07.190
And we could play with
this a little bit.

00:04:07.190 --> 00:04:10.800
We could add y to both
sides and get 30 is

00:04:10.800 --> 00:04:13.300
greater than 8 plus y.

00:04:13.300 --> 00:04:19.890
We could subtract 8 from both
sides and then you get 22 is

00:04:19.890 --> 00:04:23.615
greater than y, or y
is less than 22.

00:04:23.615 --> 00:04:26.900
And that's choice b.

00:04:26.900 --> 00:04:27.640
Next problem.

00:04:27.640 --> 00:04:28.890
Problem 4.

00:04:32.130 --> 00:04:35.410
I'm writing in toothpaste color
in honor of my recent

00:04:35.410 --> 00:04:38.110
visit to the dentist. OK,
what do they have here?

00:04:38.110 --> 00:04:40.930
They have three points.

00:04:40.930 --> 00:04:45.320
So point p, which
is 3 comma 2.

00:04:45.320 --> 00:04:49.950
Point q, which is 7 comma 2.

00:04:49.950 --> 00:04:53.980
And point r, which
is 7 comma 4.

00:04:53.980 --> 00:04:59.450
The coordinates of points p, q,
and r and the xy plane are

00:04:59.450 --> 00:05:00.610
given above.

00:05:00.610 --> 00:05:04.410
What is the perimeter of pqr?

00:05:04.410 --> 00:05:08.830
Let's draw that real fast. I
think that'll make things make

00:05:08.830 --> 00:05:13.890
more sense, especially
if you missed it

00:05:13.890 --> 00:05:16.160
the first time around.

00:05:16.160 --> 00:05:18.110
So p is 3 comma 2.

00:05:18.110 --> 00:05:22.950
So 3 comma 2, approximately.

00:05:22.950 --> 00:05:25.005
q is 7 comma 2, so this is 3.

00:05:28.930 --> 00:05:30.640
So this is going to be
a straight line.

00:05:30.640 --> 00:05:31.950
And what's this length
going to be?

00:05:31.950 --> 00:05:35.430
Well, it's going to be 4 because
it's going from 3 to 7

00:05:35.430 --> 00:05:38.480
and we have no change in the
y, they're both at 2.

00:05:38.480 --> 00:05:41.750
Then we have r is 7 comma 4.

00:05:41.750 --> 00:05:43.845
It's going to be roughly
over here.

00:05:47.120 --> 00:05:49.760
This is q, this is r.

00:05:49.760 --> 00:05:51.290
And what's this distance?

00:05:51.290 --> 00:05:54.790
Well we had no change it x, so
the distance is just going to

00:05:54.790 --> 00:05:57.700
be the change in y,
so this is just 2.

00:05:57.700 --> 00:06:00.760
And now we have to-- and this is
r-- and now the only thing

00:06:00.760 --> 00:06:02.980
we have to do to finish
this problem is

00:06:02.980 --> 00:06:06.270
figure out that distance.

00:06:06.270 --> 00:06:08.640
And how do we figure
out that distance?

00:06:08.640 --> 00:06:12.600
Well this is a right triangle,
so we could use the

00:06:12.600 --> 00:06:14.470
Pythagorean theorem.

00:06:14.470 --> 00:06:17.340
2 squared-- this is the
hypotenuse, right?

00:06:17.340 --> 00:06:19.640
The green side I drew, that's
the longest side and it's

00:06:19.640 --> 00:06:22.320
opposite the 90-degree angle,
so it's the hypotenuse.

00:06:22.320 --> 00:06:30.260
So 2 squared plus 4 squared is
equal to-- let's call this x--

00:06:30.260 --> 00:06:32.162
is equal to x squared.

00:06:32.162 --> 00:06:36.860
So this is 4 plus 16 is
equal to x squared.

00:06:36.860 --> 00:06:41.750
20 is equal to x squared.

00:06:41.750 --> 00:06:47.380
So x is equal to the
square root of 20.

00:06:47.380 --> 00:06:49.870
So x is equal to-- let's try to
simplify this, that's the

00:06:49.870 --> 00:06:53.440
square root of 4
times 5, right?

00:06:53.440 --> 00:06:54.990
And we know what the square
root of 4 is, so we

00:06:54.990 --> 00:06:55.720
can take that out.

00:06:55.720 --> 00:06:59.630
So that's x is equal
to 2 root 5.

00:06:59.630 --> 00:07:01.750
I find that this is actually
where most people have a lot

00:07:01.750 --> 00:07:05.000
of trouble, simplifying
root 20 to 2 root 5.

00:07:05.000 --> 00:07:08.440
All we did is we factor 20 as a
product of a perfect square

00:07:08.440 --> 00:07:10.690
and another number that's
not a perfect square.

00:07:10.690 --> 00:07:11.930
And then we took the
perfect square out.

00:07:11.930 --> 00:07:14.630
We said the square root of 4 is
2, so we can take it out.

00:07:14.630 --> 00:07:17.850
So x is 2 root 5.

00:07:17.850 --> 00:07:18.660
So what's the perimeter?

00:07:18.660 --> 00:07:21.640
It's 4 plus 2 plus 2 root 5.

00:07:21.640 --> 00:07:26.050
So 4 plus 2 is 6
plus 2 root 5.

00:07:26.050 --> 00:07:28.750
Now let me see what
the choices are.

00:07:28.750 --> 00:07:30.620
Oh, I didn't even have
to do 2 root 5.

00:07:30.620 --> 00:07:34.150
They actually have choice
c says 6 plus the

00:07:34.150 --> 00:07:36.640
square root of 20.

00:07:36.640 --> 00:07:39.480
So I didn't even have to do this
but that's good to know.

00:07:39.480 --> 00:07:41.110
This, what I did here,
is good to learn.

00:07:41.110 --> 00:07:43.840
But they made it so we didn't
have to do that.

00:07:43.840 --> 00:07:47.540
So it never hurts to glance at
your choices before you move

00:07:47.540 --> 00:07:50.900
forward like I just did.

00:07:50.900 --> 00:07:52.150
Invert colors.

00:07:52.150 --> 00:07:54.840
I'm getting tired of this
color, so I will switch.

00:07:54.840 --> 00:07:58.240
Problem number 5.

00:07:58.240 --> 00:08:12.570
They give us a sequence: 8,
17, 26, 35, 44, and so on.

00:08:12.570 --> 00:08:16.260
The first five terms in a
sequence are shown above.

00:08:16.260 --> 00:08:20.970
Each term after the first is
found by adding 9 to the term

00:08:20.970 --> 00:08:22.620
immediately preceding it.

00:08:22.620 --> 00:08:30.180
Which term in the sequence
is equal to 8 plus 26

00:08:30.180 --> 00:08:34.309
minus 1 times 9?

00:08:34.309 --> 00:08:35.590
Fascinating.

00:08:35.590 --> 00:08:42.080
So each term is equal to 9 plus
the previous term, right?

00:08:42.080 --> 00:08:47.410
So the first term, let's
say term one, let's

00:08:47.410 --> 00:08:49.820
call this the term.

00:08:49.820 --> 00:08:53.130
Term one is 8.

00:08:53.130 --> 00:08:57.310
Term two, let's call
this t for term.

00:08:57.310 --> 00:08:59.680
Term two is 17.

00:08:59.680 --> 00:09:02.340
And an equation we could have
gotten that is we could've

00:09:02.340 --> 00:09:12.130
gotten 8 plus 2 times-- oh
sorry, 8 plus 9 times what?

00:09:12.130 --> 00:09:16.740
The term minus 1, right?

00:09:16.740 --> 00:09:19.730
Because that's just 8 plus
9 so if the term is 2,

00:09:19.730 --> 00:09:21.360
2 minus 1 is 1.

00:09:21.360 --> 00:09:24.470
So we multiply it times
9 and we add it to 8.

00:09:24.470 --> 00:09:28.930
Similarly, the third
term, which is 26.

00:09:28.930 --> 00:09:31.020
That's essentially
8 plus 16, right?

00:09:31.020 --> 00:09:35.310
So that's 8 plus-- I'm
sorry, 8 plus 18.

00:09:35.310 --> 00:09:38.950
So it's 8 plus 9 times--
once again, t minus

00:09:38.950 --> 00:09:40.800
1, or 3 minus 1.

00:09:40.800 --> 00:09:43.920
Right here it's 2 minus 1,
here it's 3 minus 1.

00:09:43.920 --> 00:09:48.450
So in general, this
is the t-th term.

00:09:48.450 --> 00:09:54.030
This is the equation of the t-th
term, which looks oddly

00:09:54.030 --> 00:09:57.100
familiar to what they give
us in the beginning.

00:09:57.100 --> 00:09:59.790
And if we do a little pattern
matching, we see that t is

00:09:59.790 --> 00:10:01.850
equal to 26.


SAT Prep: Test 5 Section 3 Part 6

WEBVTT
Kind: captions
Language: en

00:00:00.630 --> 00:00:06.110
We are on problem 18.

00:00:06.110 --> 00:00:07.200
They give us an equation.

00:00:07.200 --> 00:00:20.520
h of t is equal to c minus d
minus 4t, all of that squared.

00:00:20.520 --> 00:00:24.480
At time equals 0, a ball was
thrown up from an initial

00:00:24.480 --> 00:00:25.880
height of 6 feet.

00:00:25.880 --> 00:00:28.280
Until the ball hit the ground,
its height in feet after t

00:00:28.280 --> 00:00:31.130
seconds was given by the
function h above.

00:00:31.130 --> 00:00:32.820
And c and d are positive
constants.

00:00:32.820 --> 00:00:34.990
So they're telling us at
time 0 we're already

00:00:34.990 --> 00:00:37.020
at height 6, right?

00:00:37.020 --> 00:00:44.060
So h of 0, time 0, the
height is already 6.

00:00:44.060 --> 00:00:47.290
If the ball reaches its maximum
height of 106 feet at

00:00:47.290 --> 00:00:57.330
time 2.5, so h of 2.5 is equal
to 106, what is the height in

00:00:57.330 --> 00:00:59.280
feet of the ball at
time t equals 1?

00:00:59.280 --> 00:01:01.970
So we want to figure
out h of 1.

00:01:01.970 --> 00:01:04.629
That's what they want to know.

00:01:04.629 --> 00:01:06.850
So in order to figure out h of
1, we essentially have to

00:01:06.850 --> 00:01:11.220
figure out what c and d are
going to be, right?

00:01:11.220 --> 00:01:12.100
So how can we do that?

00:01:12.100 --> 00:01:15.570
Well, we know what h of 0
is, so let's substitute.

00:01:15.570 --> 00:01:18.350
So h of 0 gives us this.

00:01:18.350 --> 00:01:19.680
Let's put t equals 0 here.

00:01:19.680 --> 00:01:30.240
You get c minus d minus
4 times 0 squared.

00:01:30.240 --> 00:01:33.100
And that is equal to 6.

00:01:33.100 --> 00:01:37.880
And then if we simplify this,
this is, of course, 0, right?

00:01:37.880 --> 00:01:45.360
So you get c minus d squared
is equal to 6.

00:01:45.360 --> 00:01:49.470
Now the second equation, h
of 2.5 is equal to 106.

00:01:49.470 --> 00:01:57.180
So that means that c minus d
minus-- what's 4 times 2.5?

00:01:57.180 --> 00:01:59.300
4 times 2.5 is 10, right?

00:01:59.300 --> 00:02:00.750
I put 2.5 in for t.

00:02:03.340 --> 00:02:07.040
I just did that to save some
space. d minus 10 squared is

00:02:07.040 --> 00:02:09.130
equal to 106.

00:02:09.130 --> 00:02:12.310
And now if we want to multiply
this out just to see where

00:02:12.310 --> 00:02:13.910
this takes us, because actually
I don't know where it

00:02:13.910 --> 00:02:19.680
will, you get c minus-- I'll
put it in brackets because

00:02:19.680 --> 00:02:22.040
it's going to be a long
expression-- multiplying this

00:02:22.040 --> 00:02:28.840
out, you get d squared
minus 20d plus 100.

00:02:28.840 --> 00:02:31.710
All that equals 106.

00:02:31.710 --> 00:02:35.370
And then video. distribute the
negative signs, you get c

00:02:35.370 --> 00:02:38.050
squared-- sorry, this isn't a
square, I don't know where I

00:02:38.050 --> 00:02:39.300
got the squared from.

00:02:39.300 --> 00:02:41.170
See what happens when
you take the SAT?

00:02:41.170 --> 00:02:47.670
c minus d squared plus 20d minus
100-- I just distributed

00:02:47.670 --> 00:02:51.500
the negative sign--
is equal to 106.

00:02:51.500 --> 00:02:54.680
And then, let's see, we could
add 100 to both sides.

00:02:54.680 --> 00:03:01.790
You get c minus d squared plus
20d is equal to 206.

00:03:01.790 --> 00:03:03.540
I just added 100
to both sides.

00:03:03.540 --> 00:03:05.500
So we're left with
two equations.

00:03:05.500 --> 00:03:08.780
We're left with this: c minus
d squared is equal to 6.

00:03:08.780 --> 00:03:12.710
And then we're left with this:
c minus d squared plus 20d d

00:03:12.710 --> 00:03:14.225
is equal to 206.

00:03:14.225 --> 00:03:16.410
And something should be
jumping out at you.

00:03:16.410 --> 00:03:19.280
There's a c minus d squared
in both terms. c minus

00:03:19.280 --> 00:03:20.650
d squared is 4.

00:03:20.650 --> 00:03:23.420
Oh no, sorry, c minus d squared
is 6, the previous

00:03:23.420 --> 00:03:24.460
equation tells us.

00:03:24.460 --> 00:03:26.960
So we can substitute
6 right here.

00:03:26.960 --> 00:03:33.110
So if you put 6 there, you got
6 plus 20d is equal to 206.

00:03:33.110 --> 00:03:35.240
Subtract 6 from both sides.

00:03:35.240 --> 00:03:38.100
20d is equal to 200.

00:03:38.100 --> 00:03:40.780
d is equal to 10.

00:03:40.780 --> 00:03:43.910
Now if we substitute d equals
10 back in to c minus d

00:03:43.910 --> 00:03:46.370
squared, what do we have?

00:03:46.370 --> 00:03:47.950
d is equal to 10, right?

00:03:47.950 --> 00:03:55.730
So c minus 100 is equal to
6, or c is equal to 106.

00:03:55.730 --> 00:03:58.290
And if you have an intuition
for how parabolas look, you

00:03:58.290 --> 00:04:00.660
probably could've not guessed,
you probably

00:04:00.660 --> 00:04:01.320
would have known that.

00:04:01.320 --> 00:04:04.620
You would have known that c is
actually going to be the peak

00:04:04.620 --> 00:04:05.930
point of this parabola.

00:04:05.930 --> 00:04:09.850
And they tell us that the peak
point is at point 106.

00:04:09.850 --> 00:04:11.240
And then you could've solved
for d from there.

00:04:11.240 --> 00:04:13.340
But if you didn't have that
intuition, you could've just

00:04:13.340 --> 00:04:15.350
chugged through the algebra
like we just did.

00:04:15.350 --> 00:04:19.360
So we know c, we know d, so we
know the function is now h of

00:04:19.360 --> 00:04:32.300
t is equal to 106, minus 10,
minus 4t, all of that squared.

00:04:32.300 --> 00:04:36.250
And so we want to know what
happens when t equals 1, so h

00:04:36.250 --> 00:04:46.190
of 1 is equal to 106, minus
10 minus 4 squared.

00:04:46.190 --> 00:04:54.280
So that equals 106 minus 6
squared equals 106 minus 36,

00:04:54.280 --> 00:04:56.620
which is equal to 70.

00:04:56.620 --> 00:04:57.690
And we are done.

00:04:57.690 --> 00:05:02.970
h of 1 is equal to 70, which
took us a little time, but it

00:05:02.970 --> 00:05:04.200
was worth it.

00:05:04.200 --> 00:05:05.990
I'll see you in the next


SAT Prep: Test 5 Section 3 Part 2

WEBVTT
Kind: captions
Language: en

00:00:00.890 --> 00:00:04.450
I always rush those videos at
the end because right when I

00:00:04.450 --> 00:00:07.180
was talking I saw that I was
getting kind of down on the

00:00:07.180 --> 00:00:09.920
YouTube 10 minute limit, but I
just want to make sure that

00:00:09.920 --> 00:00:11.760
you understand what I did.

00:00:11.760 --> 00:00:14.720
I used the first few examples--
and essentially

00:00:14.720 --> 00:00:18.100
what they told us-- to figure
out an equation that tells me

00:00:18.100 --> 00:00:21.510
well, if I know the term
t, how do I get

00:00:21.510 --> 00:00:23.810
the t'th term, right?

00:00:23.810 --> 00:00:26.230
Actually, it works here too.

00:00:26.230 --> 00:00:30.520
We could write 8 plus
9 t minus 1.

00:00:30.520 --> 00:00:32.940
Because here, this is the first
term, so this t minus 1

00:00:32.940 --> 00:00:36.760
term goes to 0, and that's
why we only have 8.

00:00:36.760 --> 00:00:40.300
And it works on all of these,
and it makes sense.

00:00:40.300 --> 00:00:43.290
Every term is going to be 9 more
than the previous one.

00:00:43.290 --> 00:00:46.970
We start at 8, and the reason
why it's t minus 1 instead of

00:00:46.970 --> 00:00:54.640
t is because we only start
adding 9 after the first term.

00:00:54.640 --> 00:01:00.960
For example, if this was
actually 9, 18, 27, if we just

00:01:00.960 --> 00:01:02.660
went like that, we could've
just said

00:01:02.660 --> 00:01:06.080
it's 9 times t, right?

00:01:06.080 --> 00:01:07.550
That could have been
the formula.

00:01:07.550 --> 00:01:11.760
Or we could've said 9 plus
9 times t minus 1.

00:01:11.760 --> 00:01:13.840
These would have been
the same thing.

00:01:13.840 --> 00:01:16.400
But it started at 8, so that's
why we had to make it a little

00:01:16.400 --> 00:01:17.900
bit more cloogy.

00:01:17.900 --> 00:01:20.540
Hopefully that explains it
a little bit better.

00:01:20.540 --> 00:01:21.790
Let's do the next problem.

00:01:26.690 --> 00:01:33.140
Problem six I will
do in yellow.

00:01:33.140 --> 00:01:35.540
They draw a bunch of lines,
so they draw three lines.

00:01:35.540 --> 00:01:42.425
One line, two lines, then
we have a third line.

00:01:50.360 --> 00:02:05.300
OK, so this is s degrees, r
degrees, t degrees, z degrees,

00:02:05.300 --> 00:02:08.395
y and x degrees.

00:02:11.039 --> 00:02:13.410
Three lines intersect
in a point as shown

00:02:13.410 --> 00:02:14.560
in the figure above.

00:02:14.560 --> 00:02:18.620
Which of the following pairs
of angle measures is not

00:02:18.620 --> 00:02:23.620
sufficient for determining
all six angle measures?

00:02:23.620 --> 00:02:25.060
Is not, so they're going
to make us go

00:02:25.060 --> 00:02:25.770
through all of them.

00:02:25.770 --> 00:02:27.010
Hopefully one of the
early choices.

00:02:27.010 --> 00:02:31.070
So choice a, t and z.

00:02:31.070 --> 00:02:34.470
So I'm going to do choice
a in this brown color.

00:02:34.470 --> 00:02:36.150
So choice a, t and z.

00:02:41.660 --> 00:02:43.720
Well first of all, if I know
t, I immediately know z

00:02:43.720 --> 00:02:45.860
because they're opposite
angles, right?

00:02:45.860 --> 00:02:47.590
So I could figure out that.

00:02:47.590 --> 00:02:49.490
I could figure out that.

00:02:49.490 --> 00:02:52.530
Well if I know either of those,
I could then figure

00:02:52.530 --> 00:02:58.620
out-- let's see, in order to do
anything from here, I need

00:02:58.620 --> 00:02:59.870
to know one of the
other angles.

00:03:04.860 --> 00:03:07.110
And this is actually the way you
should think about it. t

00:03:07.110 --> 00:03:12.540
and z only gives us the
relationship between these two

00:03:12.540 --> 00:03:14.790
purple lines, right?

00:03:14.790 --> 00:03:17.640
It essentially tells us at what
angle these two purple

00:03:17.640 --> 00:03:20.270
lines intersect.

00:03:20.270 --> 00:03:25.450
But it gives us no information
about the angle that this

00:03:25.450 --> 00:03:27.190
yellow line intersects, right?

00:03:27.190 --> 00:03:30.390
Think about it, if I welded
these purple lines together, I

00:03:30.390 --> 00:03:35.340
could still move this yellow
line around without

00:03:35.340 --> 00:03:36.960
changing t or z.

00:03:36.960 --> 00:03:40.800
So there's no way just knowing
t or z I can figure out what

00:03:40.800 --> 00:03:43.000
angle this yellow line is at.

00:03:43.000 --> 00:03:46.920
And if you did the other
choices, you could try it out.

00:03:46.920 --> 00:03:53.340
For example, if I didn't know t
and instead they told me r,

00:03:53.340 --> 00:03:55.480
then I would be in business.

00:03:55.480 --> 00:03:59.270
If I knew r, for example, then
I could use the fact that s,

00:03:59.270 --> 00:04:01.520
r, and z all form one line.

00:04:01.520 --> 00:04:03.070
And I could figure out s.

00:04:03.070 --> 00:04:05.150
If I knew z, then I
could figure out t

00:04:05.150 --> 00:04:06.050
because they're opposite.

00:04:06.050 --> 00:04:07.555
If I know r, I could
figure out s

00:04:07.555 --> 00:04:08.610
because they're opposite.

00:04:08.610 --> 00:04:11.050
And then if I knew s, I could
figure out y, right?

00:04:11.050 --> 00:04:15.150
So z and t alone will not help
you, so our choice is a.

00:04:15.150 --> 00:04:17.440
And normally on the SAT when
they give you something where

00:04:17.440 --> 00:04:20.750
you have to kind of try out
every choice they give you,

00:04:20.750 --> 00:04:23.150
it's normally going to be one
of the first choices because

00:04:23.150 --> 00:04:28.580
they try to make the questions
as fast as possible.

00:04:28.580 --> 00:04:31.090
They don't want you to
waste too much time.

00:04:31.090 --> 00:04:32.930
If you ever see yourself wasting
too much time on a

00:04:32.930 --> 00:04:35.320
question, you're not necessarily
doing it wrong,

00:04:35.320 --> 00:04:40.760
but you may not be doing it
the quickest possible way.

00:04:40.760 --> 00:04:42.840
Problem number seven.

00:04:42.840 --> 00:04:47.670
The sum of two numbers that
differ by one is t.

00:04:47.670 --> 00:04:49.430
So let's call those two
numbers x and y.

00:04:57.910 --> 00:05:04.600
We know that the sum of x
plus y is equal to t.

00:05:04.600 --> 00:05:09.030
But we also know that the
numbers differ by 1.

00:05:09.030 --> 00:05:12.850
And then they say in terms of
t, what is the value of the

00:05:12.850 --> 00:05:14.330
greater of the two numbers.

00:05:14.330 --> 00:05:18.160
So let's just assume that
x is greater than y.

00:05:18.160 --> 00:05:21.330
Let's just write x is
greater than y.

00:05:21.330 --> 00:05:25.560
So that means that x minus y is
going to be equal to what?

00:05:25.560 --> 00:05:27.610
Well they told us that the
sum of two numbers

00:05:27.610 --> 00:05:28.680
that differ by 1.

00:05:28.680 --> 00:05:31.640
So x is actually exactly
1 more than y.

00:05:31.640 --> 00:05:34.960
So that when I subtract
y from x I get 1.

00:05:34.960 --> 00:05:38.060
So if I want to know the value
of the greater of the two

00:05:38.060 --> 00:05:40.600
numbers-- I defined x, actually,
as the greater of

00:05:40.600 --> 00:05:43.100
the two numbers-- I just have
to solve the system of

00:05:43.100 --> 00:05:45.561
equations for x.

00:05:45.561 --> 00:05:47.540
So let's add the
two equations.

00:05:47.540 --> 00:05:50.400
x plus x is 2x.

00:05:50.400 --> 00:05:52.150
What's y plus negative y?

00:05:52.150 --> 00:05:53.990
Well, they cancel out, right?

00:05:53.990 --> 00:05:55.250
0.

00:05:55.250 --> 00:05:57.460
Then what's t plus 1?

00:05:57.460 --> 00:05:59.310
Well it's t plus 1.

00:05:59.310 --> 00:06:01.930
And now to solve for x, you
get x is equal to-- divide

00:06:01.930 --> 00:06:07.450
both sides by 2 or multiply
by 1/2-- t plus 1 over 2.

00:06:07.450 --> 00:06:09.200
And we are done.

00:06:09.200 --> 00:06:12.780
And that is choice c.

00:06:12.780 --> 00:06:14.030
Next problem.

00:06:15.930 --> 00:06:17.800
Problem number eight.

00:06:17.800 --> 00:06:19.075
This color is getting
obnoxious.

00:06:23.150 --> 00:06:27.660
OK, number of siblings per
student in a preschool class.

00:06:27.660 --> 00:06:30.960
So let me draw this chart.

00:06:30.960 --> 00:06:39.830
So this is number of siblings,
number of students.

00:06:42.760 --> 00:06:46.030
The table above shows how many
students in a class of 12

00:06:46.030 --> 00:06:51.630
preschoolers had 0, 1,
2, or 3 siblings.

00:06:51.630 --> 00:06:54.880
OK, right, I haven't actually
included the information.

00:06:54.880 --> 00:06:57.410
0, 1, 2, 3.

00:07:00.370 --> 00:07:06.630
So 3 kids had 0 siblings, 6 kids
had 1 sibling, 2 kids had

00:07:06.630 --> 00:07:10.990
2 siblings, and then 1
kid had 3 siblings.

00:07:10.990 --> 00:07:15.280
Later, a new student joined
the class, and the average

00:07:15.280 --> 00:07:20.150
number of siblings per student
became equal to the median

00:07:20.150 --> 00:07:23.110
number of siblings
per student.

00:07:23.110 --> 00:07:27.220
How many siblings did the
new student have?

00:07:27.220 --> 00:07:28.510
Fascinating.

00:07:28.510 --> 00:07:33.320
OK, so let's say the new
student has x siblings.

00:07:33.320 --> 00:07:37.310
x siblings is how many
the new student has.

00:07:37.310 --> 00:07:42.180
So we don't know where the new
student falls in, but let's

00:07:42.180 --> 00:07:49.140
figure out where the average and
the median are before the

00:07:49.140 --> 00:07:51.100
student even joins.

00:07:51.100 --> 00:07:52.600
So the median number
of siblings.

00:08:02.140 --> 00:08:07.680
The average number of siblings
per student became equal to

00:08:07.680 --> 00:08:09.940
the median number of siblings
per student.

00:08:09.940 --> 00:08:12.070
So what is the average number
of siblings per student?

00:08:12.070 --> 00:08:13.950
We just add the number of
siblings for all of the

00:08:13.950 --> 00:08:17.620
students, so we should get 12
terms. So we can multiply 3

00:08:17.620 --> 00:08:23.070
times 0-- that's essentially 0
plus 0 plus 0-- plus 6 times

00:08:23.070 --> 00:08:29.870
1, plus 2 times 2, plus 3
times 1, divided by 12.

00:08:29.870 --> 00:08:33.210
This is the current average
of siblings per student.

00:08:33.210 --> 00:08:38.990
This is 0, so this equals
6 plus 4 plus 3 over

00:08:38.990 --> 00:08:44.310
12, which is what?

00:08:44.310 --> 00:08:46.430
13.

00:08:46.430 --> 00:08:50.270
This equals 13/12,
which is 1 1/12.

00:08:50.270 --> 00:08:54.900
So before this new student
joins, there's 1 1/12.

00:08:54.900 --> 00:08:56.150
This is the average.

00:08:59.380 --> 00:09:00.810
That's before the new
student joins.

00:09:03.520 --> 00:09:04.350
What's the median?

00:09:04.350 --> 00:09:06.887
Let's list out all of the-- let
me do it in another color

00:09:06.887 --> 00:09:11.170
because I'm running out of
space-- so I have a 0, 0, 0,

00:09:11.170 --> 00:09:14.320
there are three students
with 0.

00:09:14.320 --> 00:09:15.870
Then you have 6 students
with 1.

00:09:15.870 --> 00:09:20.000
1, 2, 3, 4, 5, 6.

00:09:20.000 --> 00:09:24.390
Then you have how many
students with 2?

00:09:24.390 --> 00:09:25.230
2, 2.

00:09:25.230 --> 00:09:26.850
And then one student with 3.

00:09:26.850 --> 00:09:30.060
So there are 12 terms in all,
and what's the middle one?

00:09:30.060 --> 00:09:34.160
1, 2, 3, 4, 5, 6.

00:09:34.160 --> 00:09:36.090
So the middle term is 6.

00:09:36.090 --> 00:09:42.190
So the median before that
student joined is 1, right?

00:09:42.190 --> 00:09:44.820
And the average before that
student joined is a little bit

00:09:44.820 --> 00:09:48.140
over one, it's 1 1/12.

00:09:48.140 --> 00:09:52.040
So the only way that you can
bring the average down--

00:09:52.040 --> 00:09:53.780
right, because that's
essentially what we have to

00:09:53.780 --> 00:09:57.130
do, this new student-- to bring
this average down, he

00:09:57.130 --> 00:10:00.020
either has to have 1 sibling
or 0 siblings.

00:10:00.020 --> 00:10:01.950
Or 0 siblings.


SAT Prep: Test 5 Section 3 Part 5

WEBVTT
Kind: captions
Language: en

00:00:00.700 --> 00:00:01.850
Welcome back.

00:00:01.850 --> 00:00:04.059
Or maybe you didn't even watch
the last video, but anyway, we

00:00:04.059 --> 00:00:07.540
are on problem number 15.

00:00:07.540 --> 00:00:10.450
The Acme Plumbing Company will
send a team of three plumbers

00:00:10.450 --> 00:00:12.390
to work on a certain job.

00:00:12.390 --> 00:00:14.040
The company has four
experienced

00:00:14.040 --> 00:00:15.720
plumbers and four trainees.

00:00:25.950 --> 00:00:29.500
If a team consists of one
experienced plumber and two

00:00:29.500 --> 00:00:32.810
trainees, how many such
teams are possible?

00:00:32.810 --> 00:00:35.670
So we're going to send three
plumbers, right?

00:00:35.670 --> 00:00:36.420
Three plumbers.

00:00:36.420 --> 00:00:39.240
So it's one, two, three.

00:00:39.240 --> 00:00:42.220
And one of them has to be
experienced, right?

00:00:42.220 --> 00:00:42.900
And then these are

00:00:42.900 --> 00:00:45.290
inexperienced, these are trainees.

00:00:45.290 --> 00:00:48.490
So this is the team, one
experienced and two trainees.

00:00:48.490 --> 00:00:51.630
And now we're going to have
to pick from a set.

00:00:55.450 --> 00:00:57.790
Let's say my four experienced
plumbers are

00:00:57.790 --> 00:01:01.150
plumbers A, B, C, D.

00:01:01.150 --> 00:01:02.400
These are experienced.

00:01:05.660 --> 00:01:13.020
And let's say my trainees
are E, F, G, H.

00:01:13.020 --> 00:01:14.270
So these four are trainees.

00:01:18.070 --> 00:01:21.130
So how many different
experienced plumbers can I

00:01:21.130 --> 00:01:22.920
have heading up the team?

00:01:22.920 --> 00:01:25.170
Well, there's four
possibilities, right?

00:01:25.170 --> 00:01:28.520
So there's four different people
I can stick in here.

00:01:28.520 --> 00:01:31.660
Four choices, or four
possibilities.

00:01:31.660 --> 00:01:36.380
Now, independent of who I put
into the experienced slot, how

00:01:36.380 --> 00:01:38.740
many trainees-- let's say this
is trainee slot one and

00:01:38.740 --> 00:01:42.100
trainee slot two, not that
there's a difference-- so now

00:01:42.100 --> 00:01:46.000
if I'm picking who can go into
trainee slot one, how many

00:01:46.000 --> 00:01:47.480
choices do I have?

00:01:47.480 --> 00:01:50.040
Well, I have four choices
because none of them have been

00:01:50.040 --> 00:01:50.660
staffed yet.

00:01:50.660 --> 00:01:54.700
So I can put four people here.

00:01:54.700 --> 00:01:57.960
Not four people, I'm putting one
person, but I can pick one

00:01:57.960 --> 00:02:00.840
of four, so there's four
possibilities here.

00:02:00.840 --> 00:02:04.760
Once I've already filled trainee
slot one, one of these

00:02:04.760 --> 00:02:05.790
people are going to disappear.

00:02:05.790 --> 00:02:09.949
Then the set is going to
be one less, right?

00:02:09.949 --> 00:02:11.630
There's only going to be three
trainees left once

00:02:11.630 --> 00:02:13.810
I've filled slot one.

00:02:13.810 --> 00:02:16.960
So how many trainees can
I put in slot two?

00:02:16.960 --> 00:02:18.570
Well, there's only three
possibilities I could put

00:02:18.570 --> 00:02:21.940
because I already stuck
one in slot one.

00:02:21.940 --> 00:02:24.480
So there's four possible
experienced people, four

00:02:24.480 --> 00:02:27.540
possible choices for trainee
in slot one.

00:02:27.540 --> 00:02:30.560
And then since one trainee will
already have been staffed

00:02:30.560 --> 00:02:34.060
in slot one, there's only three
choices for slot two.

00:02:34.060 --> 00:02:36.920
So it's 4 times 4 times 3.

00:02:36.920 --> 00:02:37.700
So what is that?

00:02:37.700 --> 00:02:42.340
4 times 12, which is
48 possibilities.

00:02:42.340 --> 00:02:43.590
Next problem.

00:02:43.590 --> 00:02:46.880
And the trick here is just
realizing that once you staff

00:02:46.880 --> 00:02:49.890
one of the trainees, you only
have 3 left that you can put

00:02:49.890 --> 00:02:53.730
in the other one, in the
second trainee slot.

00:02:53.730 --> 00:02:54.980
Next problem.

00:02:57.650 --> 00:02:58.500
Problem 16.

00:02:58.500 --> 00:03:02.720
All right, we've got some
circles going on here.

00:03:02.720 --> 00:03:04.890
Let me draw a circle.

00:03:04.890 --> 00:03:08.100
So they have one circle
like that.

00:03:08.100 --> 00:03:11.930
And they have a bigger circle
that looks something like--

00:03:11.930 --> 00:03:16.040
oh, I don't know if I--
no, let me undo that.

00:03:16.040 --> 00:03:17.600
Edit, undo.

00:03:17.600 --> 00:03:22.350
OK, let me see if I can
make it more even.

00:03:22.350 --> 00:03:24.670
That's pretty good.

00:03:24.670 --> 00:03:28.700
OK, let me fill it in with
a pleasant color.

00:03:28.700 --> 00:03:29.800
All right.

00:03:29.800 --> 00:03:31.780
The figure above consists
of two circles that

00:03:31.780 --> 00:03:33.380
have the same center.

00:03:33.380 --> 00:03:45.890
If the shaded area is 64 pi
square inches and the smaller

00:03:45.890 --> 00:03:50.730
circle has a radius of 6 inches,
so that distance right

00:03:50.730 --> 00:03:54.960
there is 6, what is the
radius in inches

00:03:54.960 --> 00:03:57.650
of the larger circle?

00:03:57.650 --> 00:04:02.740
So, we want to figure out radius
of the larger circle.

00:04:02.740 --> 00:04:07.570
Radius of the larger circle I'll
do in this green color.

00:04:07.570 --> 00:04:10.120
Let's call that x.

00:04:10.120 --> 00:04:13.430
So what's going to be the area
of the shaded circle?

00:04:13.430 --> 00:04:15.880
How would we figure it out if
we knew the radius of the

00:04:15.880 --> 00:04:16.880
larger circle?

00:04:16.880 --> 00:04:19.390
What would be the area
of the large circle?

00:04:19.390 --> 00:04:23.600
Area of the large circle minus
the area of the small circle

00:04:23.600 --> 00:04:27.550
is going to equal
64 pi, right?

00:04:27.550 --> 00:04:31.310
Because if the whole thing was
filled in in mauve or whatever

00:04:31.310 --> 00:04:33.810
color this is, then it would
just be the area of the large

00:04:33.810 --> 00:04:36.420
circle, but we're subtracting
out the area of the small

00:04:36.420 --> 00:04:39.810
circle to get the
mauve region.

00:04:39.810 --> 00:04:42.760
So what's the formula for the
area of the large circle?

00:04:42.760 --> 00:04:45.440
It's pi times its
radius squared.

00:04:45.440 --> 00:04:50.560
So we already set that radius to
be equal to x, so it's pi x

00:04:50.560 --> 00:04:52.370
squared-- and that's what we're
trying to figure out in

00:04:52.370 --> 00:04:55.690
this problem-- minus the area
of the small circle.

00:04:55.690 --> 00:04:57.310
What's the area of
the small circle?

00:04:57.310 --> 00:05:00.120
Well, its radius is 6 so
it's pi r squared, so

00:05:00.120 --> 00:05:04.060
it's pi times 6 squared.

00:05:04.060 --> 00:05:07.010
And that is going to
be equal to 64 pi.

00:05:07.010 --> 00:05:09.930
And just to simplify things, we
can just divide both sides

00:05:09.930 --> 00:05:11.380
by pi just to get them
out of the way.

00:05:15.130 --> 00:05:17.270
But you don't have to do that,
that just simplifies things

00:05:17.270 --> 00:05:18.990
for my simple mind.

00:05:18.990 --> 00:05:25.080
So you get x squared minus
36 is equal to 64.

00:05:25.080 --> 00:05:30.860
Add 36 to both sides, you get
x squared is equal to 100.

00:05:30.860 --> 00:05:33.260
So x could be equal-- if you
just solved it, it would be

00:05:33.260 --> 00:05:35.790
plus or minus 10, and of course,
a radius can't be

00:05:35.790 --> 00:05:38.190
negative, so it's plus 10.

00:05:38.190 --> 00:05:42.550
So x is 10, or the radius of
the larger circle is 10.

00:05:42.550 --> 00:05:43.440
Next problem.

00:05:43.440 --> 00:05:51.210
Problem 17.

00:05:51.210 --> 00:05:53.910
If p, r, and s are three
different prime numbers

00:05:53.910 --> 00:05:57.990
greater than two-- let me just
write them down, p r, and s--

00:05:57.990 --> 00:06:01.950
three different prime numbers
greater than two and n is

00:06:01.950 --> 00:06:09.810
equal to p times r times s, how
many factors including one

00:06:09.810 --> 00:06:13.510
and n does n have?

00:06:13.510 --> 00:06:15.430
How many factors?

00:06:15.430 --> 00:06:18.190
This is a good problem.

00:06:18.190 --> 00:06:25.300
This is essentially the prime
factorization of n, right?

00:06:25.300 --> 00:06:29.400
And we want to know how many
positive factors including 1

00:06:29.400 --> 00:06:31.290
and n, right?

00:06:31.290 --> 00:06:34.010
So what are all of
the factors here?

00:06:34.010 --> 00:06:39.530
So if we just made a factor
tree-- let's make a

00:06:39.530 --> 00:06:42.660
combination of all the numbers
that when I multiply the pair

00:06:42.660 --> 00:06:44.050
can equal n.

00:06:44.050 --> 00:06:47.950
So one times n is equal to n.

00:06:47.950 --> 00:06:55.660
Another number that would equal
n is pr times s would

00:06:55.660 --> 00:06:57.420
also equal n, right?

00:06:57.420 --> 00:07:00.880
Because obviously p times r
times s is n, so p times r

00:07:00.880 --> 00:07:05.270
times s is n, but I'm saying p
times r is a number, right?

00:07:05.270 --> 00:07:06.740
Hopefully that makes
some sense.

00:07:06.740 --> 00:07:14.420
Similarly, we could say that
p times rs is equal to n.

00:07:14.420 --> 00:07:15.090
Same logic.

00:07:15.090 --> 00:07:17.130
I'm saying r times s
is a number, right?

00:07:17.130 --> 00:07:18.810
Some number.

00:07:18.810 --> 00:07:27.950
And then finally we could say
that sp times r, with sp as a

00:07:27.950 --> 00:07:32.990
number, is also equal
to n, right?

00:07:32.990 --> 00:07:42.100
So all of these numbers that I
said-- 1, 2, 3, 4, 5, 6, 7,

00:07:42.100 --> 00:07:45.800
8-- all of these numbers
are factors of n.

00:07:45.800 --> 00:07:47.940
So that's how many factors there
are, there are eight

00:07:47.940 --> 00:07:51.310
factors including 1 and n.

00:07:51.310 --> 00:07:54.270
If this seemed a little bit
abstract to you, try it out

00:07:54.270 --> 00:07:56.590
with some numbers.

00:07:56.590 --> 00:07:58.640
Actually, that's the best way
you could do it if this was

00:07:58.640 --> 00:07:59.690
too abstract.

00:07:59.690 --> 00:08:09.920
You could say, what if p is
3, r is 5, and s is 7.

00:08:09.920 --> 00:08:11.410
Then what is n?

00:08:11.410 --> 00:08:15.530
Well, n is going to
be 15 times 7.

00:08:15.530 --> 00:08:18.200
So n is 15 times 7,
what is that?

00:08:18.200 --> 00:08:22.480
70 plus 35, n is 105.

00:08:22.480 --> 00:08:24.930
So if n is 105, this
is 1 times 105.

00:08:24.930 --> 00:08:27.810
pr, this is 15 times 7.

00:08:27.810 --> 00:08:32.450
This would be 3 times 35.

00:08:32.450 --> 00:08:34.980
Is that right?

00:08:34.980 --> 00:08:37.280
Oh no, sorry, 85.

00:08:37.280 --> 00:08:38.650
No, sorry.

00:08:38.650 --> 00:08:49.330
If 5 times 7 is 35 times 3,
oh right, it's 105, right?

00:08:49.330 --> 00:08:57.210
So we would write 3 times 35,
and sp is 21 times 5.

00:08:57.210 --> 00:08:58.580
So those would be the
actual numbers.

00:08:58.580 --> 00:09:01.380
So hopefully that makes a little
bit more sense to you.

00:09:01.380 --> 00:09:04.100
But this is the way you could
do it in a general way.

00:09:04.100 --> 00:09:06.820
It looks like I'm running out
of time, so I will do number

00:09:06.820 --> 00:09:10.470
18 in the next video.

00:09:10.470 --> 00:09:13.920
But this is a little bit of
a non-intuitive problem.

00:09:13.920 --> 00:09:16.300
Just remember, this is the prime
factorization, and then

00:09:16.300 --> 00:09:18.500
you can construct its--
what I call the normal

00:09:18.500 --> 00:09:20.560
factorization-- you can
construct that by just taking

00:09:20.560 --> 00:09:22.570
combinations of the
prime numbers.

00:09:22.570 --> 00:09:25.560
And hopefully the actual numbers
make a little bit more

00:09:25.560 --> 00:09:26.950
sense to you.

00:09:26.950 --> 00:09:28.200
See you in the next video.


SAT Prep: Test 5 Section 3 Part 3

WEBVTT
Kind: captions
Language: en

00:00:01.040 --> 00:00:01.700
Welcome back.

00:00:01.700 --> 00:00:04.150
I keep rushing to try to get
under the wire for these

00:00:04.150 --> 00:00:07.080
problems, but let me explain
it properly.

00:00:07.080 --> 00:00:09.680
So what we did is, we said
that a new student joins.

00:00:09.680 --> 00:00:13.510
And the average after he joins
is equal to the median.

00:00:13.510 --> 00:00:15.610
And what we did is we figured
out, what's the average and

00:00:15.610 --> 00:00:17.750
the median before the
student joins.

00:00:17.750 --> 00:00:21.490
Well, the average before the
student joined was 13/12, and

00:00:21.490 --> 00:00:25.580
the median before the student
joined was 1.

00:00:25.580 --> 00:00:31.160
If the new student has 1 or 0--
and we established that

00:00:31.160 --> 00:00:34.200
the only way to bring this
average down is for the new

00:00:34.200 --> 00:00:40.260
student to have less than
the average number

00:00:40.260 --> 00:00:41.880
of siblings, right?

00:00:41.880 --> 00:00:46.040
That's the only way we can
go from 1 1/12 to 1.

00:00:46.040 --> 00:00:50.240
And I'll tell you right now that
he's actually going to

00:00:50.240 --> 00:00:54.380
have a 1/13 impact, right,
if he's 1 away.

00:00:54.380 --> 00:00:58.050
So actually I can tell you right
now he has one sibling,

00:00:58.050 --> 00:00:59.790
but I'll show it to you
mathematically if you don't

00:00:59.790 --> 00:01:01.430
have that intuition
on averages.

00:01:01.430 --> 00:01:03.380
But the important thing to
realize is that he's either

00:01:03.380 --> 00:01:06.590
going to have 0 or 1 sibling.

00:01:06.590 --> 00:01:09.165
He's going to have to have less
than 1 1/12 siblings, so

00:01:09.165 --> 00:01:12.690
it's either 0 or 1 in order
to bring the average down.

00:01:12.690 --> 00:01:16.560
And regardless of whether he has
0 or 1 sibling, the median

00:01:16.560 --> 00:01:18.220
won't change.

00:01:18.220 --> 00:01:19.910
If he has one sibling, then
we're just going to have

00:01:19.910 --> 00:01:22.910
another one here and then
this'll become the median.

00:01:22.910 --> 00:01:25.900
If he has 0 siblings, then
that's going to be a 0 there,

00:01:25.900 --> 00:01:27.610
but that's still going
to be a median of 1.

00:01:27.610 --> 00:01:29.840
The median is not
going to change.

00:01:29.840 --> 00:01:32.110
So what we have to do is figure
out how many siblings

00:01:32.110 --> 00:01:38.040
does he have to have for the new
average to be exactly 1?

00:01:38.040 --> 00:01:40.050
So we can go back to
this calculation.

00:01:40.050 --> 00:01:43.720
Let's take the average, but now
let's take it with him.

00:01:43.720 --> 00:01:45.940
So this was our previous average
where we said well,

00:01:45.940 --> 00:01:48.590
there's three students with 0
siblings, six students with 1,

00:01:48.590 --> 00:01:49.640
et cetera, et cetera.

00:01:49.640 --> 00:01:52.240
But now we're going to add
this new student in.

00:01:52.240 --> 00:01:55.690
There's one student with
x siblings, right?

00:01:55.690 --> 00:01:59.060
And instead of 12 in the
denominator, we have 13.

00:01:59.060 --> 00:02:02.350
Because we now have 13
students, right?

00:02:02.350 --> 00:02:03.670
So what happens?

00:02:03.670 --> 00:02:07.800
You essentially have 13,
so this becomes x plus

00:02:07.800 --> 00:02:09.530
6 plus 4 plus 3.

00:02:09.530 --> 00:02:12.730
This becomes 13 plus
x, and then the

00:02:12.730 --> 00:02:15.770
denominator is equal to 13.

00:02:15.770 --> 00:02:17.700
And actually I was wrong before,
he's actually going to

00:02:17.700 --> 00:02:21.140
have to have 0, my intuition
was a little bit off.

00:02:21.140 --> 00:02:25.390
Because look, this is the new
average, 13 plus x over 13.

00:02:25.390 --> 00:02:32.540
The new average is going to be
13 plus x over 13, right?

00:02:32.540 --> 00:02:34.550
13 plus x over 13.

00:02:34.550 --> 00:02:36.710
And what does that new average
have to equal?

00:02:36.710 --> 00:02:39.230
It has to equal 1.

00:02:39.230 --> 00:02:40.790
Because that's the new median.

00:02:40.790 --> 00:02:43.320
Or the old median, because we
said the mean doesn't change.

00:02:43.320 --> 00:02:46.100
So how can 13 plus x
over 13 equal 1?

00:02:46.100 --> 00:02:50.680
Well, if you can't eyeball that,
you can just say 13 plus

00:02:50.680 --> 00:02:55.310
x, multiply both sides by
13, is equal to 13.

00:02:55.310 --> 00:02:59.690
And then subtract 13 from
both sides and you get

00:02:59.690 --> 00:03:01.690
x is equal to 0.

00:03:01.690 --> 00:03:05.630
So that new student
has 0 siblings.

00:03:05.630 --> 00:03:08.200
I know that was a little bit
convoluted, so let me just

00:03:08.200 --> 00:03:09.690
tell you what I did again.

00:03:09.690 --> 00:03:12.970
I said what is the
current median?

00:03:12.970 --> 00:03:15.280
And I just listed out all of the
number of siblings, and I

00:03:15.280 --> 00:03:18.440
took the middle number,
and that was 1.

00:03:18.440 --> 00:03:20.790
Then I said well, what is
the current average?

00:03:20.790 --> 00:03:23.470
And the current average
was 1 1/12.

00:03:23.470 --> 00:03:25.050
And this might confuse
you a little bit.

00:03:25.050 --> 00:03:29.370
You could just say, well this is
the same thing as 0 plus 0

00:03:29.370 --> 00:03:34.850
plus 0 plus 1 plus 1 plus
1 plus 1 plus 1

00:03:34.850 --> 00:03:36.270
plus 1 and so forth.

00:03:36.270 --> 00:03:39.410
Instead I said that's three
students with 0, six students

00:03:39.410 --> 00:03:42.490
with 1 sibling, two students
with 2 siblings, and so forth.

00:03:42.490 --> 00:03:44.260
And I figured out that the
current average-- and I

00:03:44.260 --> 00:03:47.470
divided by 12-- was 1 1/12.

00:03:47.470 --> 00:03:50.600
So I said well, no matter how
many siblings the next student

00:03:50.600 --> 00:03:53.070
has-- and actually, it didn't
even matter, even if you had

00:03:53.070 --> 00:03:55.750
more or less, one of the middle
numbers still would

00:03:55.750 --> 00:03:56.620
have been the 1.

00:03:56.620 --> 00:03:59.090
So the median will not change
regardless of where the new

00:03:59.090 --> 00:04:00.870
student falls into the mix.

00:04:00.870 --> 00:04:04.230
So we said, how many siblings
does that student need to have

00:04:04.230 --> 00:04:08.440
for the average to come
down back to 1?

00:04:08.440 --> 00:04:11.590
And then I just added x to my
previous average and I divided

00:04:11.590 --> 00:04:14.490
by 13 instead because we now
have an extra student.

00:04:14.490 --> 00:04:15.674
This was a 13 too.

00:04:15.674 --> 00:04:19.580
And we got this equation: 13
plus x over 13 has to equal my

00:04:19.580 --> 00:04:22.100
new average, which is 1.

00:04:22.100 --> 00:04:23.810
And then I solved for
x, which is 0.

00:04:23.810 --> 00:04:27.910
So the new student
had 0 siblings.

00:04:27.910 --> 00:04:30.960
Next problem.

00:04:30.960 --> 00:04:33.730
And the really fast way of doing
this-- not to harp on

00:04:33.730 --> 00:04:36.410
this problem too much, and I
should have done this from the

00:04:36.410 --> 00:04:39.460
beginning-- is to figure out
that the median is 1, then

00:04:39.460 --> 00:04:42.920
figure out that it doesn't
matter how many siblings the

00:04:42.920 --> 00:04:44.660
student has, the median's
still going to be 1.

00:04:44.660 --> 00:04:47.280
You can insert a number anywhere
in this list and the

00:04:47.280 --> 00:04:49.290
median would have still been
1 because there's so many

00:04:49.290 --> 00:04:51.510
students with one sibling.

00:04:51.510 --> 00:04:55.550
And then you just have to figure
out well, how many

00:04:55.550 --> 00:04:58.060
siblings does the student
have to have for the

00:04:58.060 --> 00:05:00.660
average to become 1?

00:05:00.660 --> 00:05:02.350
That's probably the most
convoluted explanation I've

00:05:02.350 --> 00:05:06.760
given, but let me just
hope it helps you.

00:05:06.760 --> 00:05:08.860
OK, problem number 9.

00:05:11.540 --> 00:05:21.050
If 2 times x minus 3 is equal to
8, what does x minus 3 over

00:05:21.050 --> 00:05:24.700
x plus 3 equal?

00:05:24.700 --> 00:05:26.140
What does that equal?

00:05:26.140 --> 00:05:29.350
Well, let's just solve for x.

00:05:29.350 --> 00:05:34.390
So we get x minus 3 is equal
to-- I'm just going to divide

00:05:34.390 --> 00:05:39.070
both sides by 2, so 8 divided
by 2 is 4, right?

00:05:39.070 --> 00:05:41.900
2 divided by 2 is 1, so
x minus 3 equals 4,

00:05:41.900 --> 00:05:43.330
x is equal to 7.

00:05:43.330 --> 00:05:44.390
So you go here.

00:05:44.390 --> 00:05:45.860
What's x minus 3?

00:05:45.860 --> 00:05:48.690
Well it's 7 minus
3, which is 4.

00:05:48.690 --> 00:05:51.710
We also figured out that x
minus 3 was 4 up here.

00:05:51.710 --> 00:05:53.080
And then what's x plus 3?

00:05:53.080 --> 00:05:56.350
That's 7 plus 3, so that's 10.

00:05:56.350 --> 00:06:00.180
4/10, we can reduce that to 2/5,
dividing the numerator

00:06:00.180 --> 00:06:01.900
and the denominator by 2.

00:06:01.900 --> 00:06:05.150
So that's our answer,
2/5 or 0.4.

00:06:05.150 --> 00:06:08.210
Problem 10.

00:06:08.210 --> 00:06:11.060
When twice a number-- so
whenever I start writing it,

00:06:11.060 --> 00:06:12.050
let's say x is the number.

00:06:12.050 --> 00:06:15.570
So they say when twice an
number-- so when 2 times x,

00:06:15.570 --> 00:06:18.930
that's twice a number--
is decreased by 3.

00:06:18.930 --> 00:06:23.810
So, twice a number is
decreased by 3,

00:06:23.810 --> 00:06:29.080
the result is 253.

00:06:29.080 --> 00:06:29.830
What is the number?

00:06:29.830 --> 00:06:32.090
Well, while reading
it, I set it up.

00:06:32.090 --> 00:06:34.180
So now we just have to solve.

00:06:34.180 --> 00:06:35.770
So we add 3 to both sides.

00:06:35.770 --> 00:06:39.220
2x is equal to 256, right?

00:06:39.220 --> 00:06:40.900
I added 3 to both sides.

00:06:40.900 --> 00:06:46.100
x, divide both sides by
2. x is equal to 128.

00:06:46.100 --> 00:06:47.520
And we are done.

00:06:47.520 --> 00:06:48.770
Next problem.

00:06:53.300 --> 00:06:55.110
Problem 10.

00:06:55.110 --> 00:06:59.240
OK, this says Outdoor Sneaker
Company's July production.

00:06:59.240 --> 00:07:04.430
So we have white, black,
and then total.

00:07:04.430 --> 00:07:10.215
And then they have high-tops,
low-tops, and then total.

00:07:13.990 --> 00:07:16.510
I don't know if people even
wear high-tops anymore.

00:07:16.510 --> 00:07:18.080
I used to.

00:07:18.080 --> 00:07:20.290
I guess for basketball.

00:07:20.290 --> 00:07:22.625
OK, high-tops, low-tops,
and total.

00:07:22.625 --> 00:07:24.040
I'm very not plugged-in.

00:07:30.670 --> 00:07:33.520
High-tops, low-tops,
and then total.

00:07:33.520 --> 00:07:37.480
And what numbers do they
have in the box?

00:07:37.480 --> 00:07:50.130
So there are 3,600 here, 1,500
here, 5,500, and then 10,000.

00:07:50.130 --> 00:07:52.280
So even before reading this
question, I could tell you

00:07:52.280 --> 00:07:55.540
they're just going to want us
to fill in this diagram.

00:07:55.540 --> 00:07:57.450
10,000 here.

00:07:57.450 --> 00:07:59.870
Outdoor Sneaker Company
manufactures only white

00:07:59.870 --> 00:08:02.990
sneakers and black sneakers,
both of which are available as

00:08:02.990 --> 00:08:05.030
either high-tops or low-tops.

00:08:05.030 --> 00:08:06.990
On the basis of the information
in the table

00:08:06.990 --> 00:08:11.820
above, how many black sneakers
did Outdoor Sneaker Company

00:08:11.820 --> 00:08:13.440
manufacture in July?

00:08:13.440 --> 00:08:15.690
So how many black sneakers-- so
they didn't differentiate

00:08:15.690 --> 00:08:17.310
between the high-tops or
low-tops-- so they want to

00:08:17.310 --> 00:08:19.930
know, how many total
black sneakers.

00:08:19.930 --> 00:08:22.010
So that is black total.

00:08:22.010 --> 00:08:25.120
So we need to figure
out this square.

00:08:25.120 --> 00:08:26.320
Total black.

00:08:26.320 --> 00:08:27.660
So let's see what we
can figure out.

00:08:27.660 --> 00:08:30.570
I'll do my figuring out
in this magenta.

00:08:30.570 --> 00:08:34.789
So if low-tops-- I need a total
of 5,500 low-tops--

00:08:34.789 --> 00:08:39.320
1,500 are black, how
many are white?

00:08:39.320 --> 00:08:42.870
Well, it's going to
be 4,000, right?

00:08:42.870 --> 00:08:44.830
I just took 5,500 minus 1,500.

00:08:44.830 --> 00:08:46.210
4,000.

00:08:46.210 --> 00:08:49.990
Similarly, if I made a total of
10,000 sneakers and 5,500

00:08:49.990 --> 00:08:53.570
are low-tops, how many of
them are high-tops?

00:08:53.570 --> 00:09:00.070
Well, it's going to be 10,000
minus 5,500, so this is 4,500.

00:09:00.070 --> 00:09:04.820
And out of the high-tops, if
3,600 are white and I made a

00:09:04.820 --> 00:09:07.760
total of 4,500, how many
black are there?

00:09:07.760 --> 00:09:11.740
Well, 4,500 total minus the
white ones, that's what?

00:09:11.740 --> 00:09:14.820
That's 900.

00:09:14.820 --> 00:09:17.070
And so if we want to figure out
the total black, we now

00:09:17.070 --> 00:09:19.880
know how many high-top blacks
there are and how many low-top

00:09:19.880 --> 00:09:21.920
black sneakers there are,
so we just add.

00:09:21.920 --> 00:09:25.480
So 900 plus 1,500 is 2,400.

00:09:25.480 --> 00:09:28.540
So I actually wasted both of our
times figuring this out,

00:09:28.540 --> 00:09:30.310
so I could have saved a few
seconds I didn't do that.

00:09:30.310 --> 00:09:32.780
But I was just mindlessly
chugging along.

00:09:32.780 --> 00:09:35.030
Anyway, I'll see you
in the next video.