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Current time:0:00Total duration:12:40

Now on problem 37. And they say what is the
value of xy minus yz. Statement one says,
y is equal to 2. Well, that by itself
doesn't help us. That just tells us
2x minus 2z. So if you don't know what x and
z are you can't figure out what this whole thing is if you
just know y is equal to 2. So that alone doesn't help. Statement two is x minus
z is equal to 5. Now this is interesting because
this expression, we can factor out the y. What happens if we factor
y out of both of these expressions? I'm going to just rewrite it. xy minus zy-- I just switched
the y and z-- that equals x minus z times y. Well, we can figure
out x minus z from statement number two. x minus z, this is equal 5. And we know what y is equal
to from statement one. So y is equal to 2. So we can definitely figure it
out as long as we have both statements and we can show
that the answer is y is equal to 2. So the answer is,
2 times 5 is 10. But we didn't have
to figure it out. We just have to know that we
could figure it out if we had both of these data points. One by themselves, you wouldn't
be able to solve it. So the answer is C. Both statements together
are sufficient but neither alone is. Problem 38. OK, they drew us a picture. Let me see if I can draw that
same picture, looks like some type of device. So it looks like that and then
they have the other end, and the other end looks like that. There are these handles,
or something that looks like handles. I haven't read the
problem yet. So they say will the first
10 volumes of a 20 volume encyclopedia fit upright in
the book rack shown above? So this is a book rack. So I guess the books get
stacked that way. And they labeled this right
here, this dimension is x. And they're saying, will the
first 10 volumes of a 20 volume encyclopedia
fit upright in the book rack shown above? So essentially I'm going to
put the first 10 in there. So the first statement they say,
is that x is equal to 50 centimeters. Well, that doesn't help me
because I don't know how big the first 10 volumes of
the encyclopedia are. If each of them are, at least
the first 10 are, less than 5 centimeters each or on average
less than 5 centimeters, then maybe I could fit them. But one by itself
doesn't help me. Two: 12 of the volumes have
an average thickness of 5 centimeters. Well, that doesn't help me
either because remember, they're saying will the first
10 volumes of a 20 volume encyclopedia? Maybe the 12 that have an
average thickness of 5 centimeters, maybe those are the
volumes 8 through 20 and maybe volumes 1 through 7 have
an average thickness of 50 centimeters each or 5 million
centimeters each. So even both of these conditions
combined don't help me know if I can definitely fit
the first 10 volumes of the 20 volume encyclopedia. So that is E. Both statements together are
still not sufficient. Problem 39. A circular tub-- OK, so
they've drawn this circular-looking tub. So the top looks like that. And then there's two sides. Let's me see how well I can
construct what they've drawn. And the bottom looks something
like that. And then they shade in a
little area, a strip of this, like that. And they say a circular tub has
a painted band around its circumference as show above. So this is the painted band
around its circumference. What is the surface area
of the painted band? And they tell us that
the height of the painted band is x. So in order to essentially know
the surface area, you'd have to know the height, which
is x, times the circumference of the circle, which would
be the length. So if you knew the height times
circumference of the circle, you'd be able to
know the surface area. So they tell us, the first
statement, x is equal to 0.5, whatever, meters. So this is in meters. 0.5 meters, so that alone
doesn't help us. We have to be able to figure out
the circumference of this tub in order to really be able
to figure out the surface area because the circumference times
this height will be the service area. Point two: they say the height
of the tub is one meter. So they're telling us that
this is one meter. Well that doesn't help us. That still doesn't tell us how
far around the tub goes. If they had given us the
diameter or the radius or the circumference then we could've
used our basic geometry to figure out the circumference. But they didn't. So either way-- it's a one meter
height-- both of these combined still do not allow us
to figure out the surface area of this green band. E again. Problem 40. What is the value
of integer n? And n as an integer. So statement number one: they
tell us that n times n plus 1 is equal to 6. Now we should already be able
to figure this out because n is an integer, n plus
1 is an integer. So what are the factorizations
of 6? You could have 1 times 6. But that doesn't fit n
and n plus 1, right? This is n and n plus 5. You have 2 times 3,
which work, right. If 2 is n, n plus 1 is
3 and they equal 6. So let me circle that. And then what other
factorizations? You don't have any other--
these are all of the factors 6. So just looking at the first
statement, you know that n has to be equal to 2. This is the only integer
where this is true. Actually, let me take
a step back. No, what if n is negative? Because I was assuming it's a
positive integer but they didn't say it's a positive
integer, so let me think about that. If I did minus 3 times minus
2, that also equals 6 and these are both integers. OK, so this isn't enough. Because in this case, n could
be-- this would be n and this is would be n plus 1-- so n is
either equal to 2 or n is equal to minus 3. That's a little tricky. The intuition is to just assume
that n is positive but it doesn't have to
be positive. So n could be 2 or
minus 3 here. That's a tricky one. So that one by itself does not
help us solve the problem. The second part of it, point
two it says, 2 to the 2n is equal to 16. And whenever you have these
in the SAT or the GMAT or anything, whenever you have a
variable in the exponent, your goal really is to just get
everything in the same base. So we could write the left-hand
side the same. So that's 2 to the 2n. And how do we write 16
with the base 2? Well, 16 is just 2 to
the fourth, right? And so we get 2n
is equal to 4. n is equal to 2. So this statement alone is
enough to figure it out. This statement alone is not. So the answer is B. Statement two alone
is sufficient. 40 is B. And this was tricky because one,
you think that 1n alone is sufficient but it is
ambiguous because and n could be minus 3. 41. OK. They've drawn a bunch of,
if I see this right, a bunch of-- two lines. Let's see if I can draw this. So a line and then there's
a bunch of circles. One circle, two circles
they have, and then they keep going. Three circles, and
then one more. It's going to be right there. Four circles. I think that's about right. And they say essentially that
the circles just keep going on and on. That's what I think the
drawing implies. They say the inside of a
rectangular carton is 48 centimeters long, 32 centimeters
wide and 15 centimeters high. OK. So that's the inside. Kind of from the other wall. This is the floor of the inside
of the container and then there would be
another up here. But I think you get the idea. The carton is filled to capacity
with k identical cylindrical cans of fruit that
stand upright in rows and columns as indicated in
the figure above. OK. So this is like a
top view of it. So we could say that this side
up here, this is 48 and then this is 32. So we don't care so much about
the height, I think. So, let's see, the carton is
filled to capacity with k identical cylindrical cans of
fruit that stand upright in rows and columns as indicated
in figure above. If the cans are 15 centimeters
high-- OK, so each of the cans are exactly 15 centimeters
high. So they literally are exactly
as high as the carton. If the cans are 15 centimeters
high, what is the value of k? So we have to figure out how
many of these cans will fit in this area essentially? And then they tell us point
number one: each of the cans have a radius of
4 centimeters. Radius is 4 centimeters. Well, if we know that each of
them have a radius of 4 centimeters then we know exactly
how much square area each of these circles will take
up, assuming that they're packed exactly like
this, right? Because if you think about it,
what is this area right here? Well, there's a bunch of
were different ways you could think about it. The easiest is that if the
radius is 4 centimeters, that the diameter right here
is 8 centimeters. So if this is 8 and you have a
48 length, you can only do 6 of these, right? 6 times 8 is 48. So you can only do 6 that way. And then if the diameter is 8
this way and this length is 32, you can only
do 4 this way. So statement number one, alone,
is enough to figure out how many you can put. It would actually
be 4 times 6. You could put 24, k would be 24
cans that you could fit in. So statement one, alone,
is enough. Now what does statement
two tell us? 6 of the cans sit exactly
along the length of the carton. So they're telling us that these
cans, there's 6 cans that fit right along the length,
which we figured out from statement number one. But that also gives you the same
information as statement number one. Because you know that these
are cylindrical cans. I think it's a safe assumption
to say that these are circles. Yeah. A cylinder, you're assuming
that the tops are circles. So if you say that 6 can fit
that way, then you know that the diameter of each of them is
8 centimeters and then you can make the same argument
that the diameter's 8 centimeters to say that 4 can
fit the other way down. So two, alone, is also
sufficient by itself. So the answer is,
what is that, C? Both statements-- no D, each
statement, alone, is sufficient. See you in the next video.