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Current time:0:00Total duration:10:35

Let's do some data sufficiency
problems. So the first problem, problem
number one on page 278. It says, how much is 20%
of a certain number? So we want to know
20% of a number. Let me just call that x. So what is that? So the first data point they
give us is that 10% of the number is 5. So we could say that 10%
times x is equal to 5. Or another way we can just
write that is 0.1 x is equal to 5. And then the second data point,
I guess you could call it, is 40% of twice the
number is equal to 40. So 40%, 0.4 times twice the
number, so times 2x, right? We chose x as our number--
is equal to 40. So what we have to figure out
is do either of these data points allow us to
figure out x? Or maybe we need both of them. Or maybe we can't figure it
out even with all of this information. Well, this is a simple
linear equation. A very easy way to think about
it is you could multiply both sides of this by 2, both
sides of the equation. And you end up with 0.2 times
x is equal to 10. Well, that's the same thing
is saying that 20% of x is equal to 10. So statement one alone is all
we need to figure out this. Let's see what statement
two gets us. So if we simplify this
expression just a little bit, we get 0.4 times 2. We have 0.8 times x
is equal to 40. And here, instead of multiplying
both sides of this equation by 2, we could divide
both sides by 4, right? Because we want to
get 20% of x. This is 80% of x. So if we divide both sides of
this by 4, we get what? We got 0.2 x is equal to 10. There you go. 20% of x is equal to 10. So either of these alone are
enough to solve that problem. And I always forget what the
letters are, but I think that is statement d. Each statement alone
is sufficient. All right. Problem number two. I don't want to waste too
much time on that. And I'm trying to do this in
real time without looking at the answers, because I really
want you to get a sense of how someone thinks about this
if they've never seen the problem before. And so I'll ask you to bear with
me a little bit because maybe I'll get a
problem wrong. And maybe that'll be instructive
if I do. OK, They say a thoroughly
blended biscuit mix includes only flour and baking powder. What is the ratio of the number
of grams of baking powder to the number
of grams of flour? So we want to know the ratio
of baking powder to flour. That's what we need
to figure out. Now statement number one, they
tell us exactly 9.9 grams of flour is contained in 10
grams of this mix. soon. So if there are 9.9 of flour,
and there's exactly 10, how much baking powder is there? Well, baking powder is going
to be equal to 10 minus the amount of flour. So it's going to be what? 0.1 grams. 9.9, we could say
that that is equal to flour. So we could easily, just using
this statement, figure out the ratio, right? The ratio of baking powder to
flour is 0.1, because we just took 10 minus the amount
of flour, to 9.9. Or you could say, it's 1:99,
whatever, however you need it. But that's what's fun about
these problems. You don't have to figure it out. We just have to say we
could figure it out. So one is enough by itself. Let's see what statement
two tells us. I'll do it in a slightly
different color. Let me scroll down
a little bit. Statement two says,
exactly 0.3 gram. I think that's an error
in the book. It should be grams. Exactly 0.3
gram of baking powder is contained in 30 grams
of the mix. So if we have 0.3 baking powder,
that's grams, and it tells us there's 30
grams of the mix. So how much flour do we have? What's 30 minus 0.3
is equal to what? It's equal to 29.7 flour. And so, once again, we can
easily figure out the ratio of baking powder to flour is
0.3:29.7, which is, once again, 1:99. But we didn't have to
figure that out. We just know that
this is enough. So once again, we know that
d, each statement alone is sufficient, unless I
missed something. All right. Problem number three. Let me scroll down
a little bit. What is the value of the
absolute value of x? So they want to know the
absolute value of x is equal to what? And the first statement, they
tell us is that x is equal to the minus absolute value of x. So what numbers is this true
for, that the number is equal to the minus absolute value? It's definitely not true for
positive numbers, right? Put a positive 1 there. 1 is not equal to-- the absolute
value of 1 is 1, so 1 is not equal to negative 1. This works for 0, right? 0 is equal to negative
0 is equal to 0. And this works for
negative numbers. Try it out. Negative 1 is equal to the
negative absolute value of negative 1. Well, the absolute value of
negative 1 is 1, so you get negative 1 is equal
to negative 1. So it works for 0 and
negative numbers. So all this tells us-- and maybe
this will help us in conjunction with the second
part, who knows? This tells us that x is less
than or equal to 0. It's just a convoluted
way of saying this. Let's see where that gets us. Now the second statement. Let's see, they say that x
squared is equal to 4. Well, this tells us that x is
equal to plus or minus 2. Now, if we were trying to figure
out what x is equal to, we would actually need both of
these statements because this statement says that x is
positive you 2 or negative 2. And then this statement
says that, oh, x is definitely negative. So if we were trying to figure
out what the value of x was, we would need both of
these statements. But notice, they're asking us
what's the value of the absolute value of x, right? So regardless of whether x is
positive or negative 2, the absolute value of either
positive or negative 2 is always going to be equal to 2. So really, this is
all you need. You only need statement two to
figure out this problem. And so that is b. You only need statement two. All right. I think I got that one right. Let's see. Problem number four. I'll do it in this
brownish color. Problem number four. Is r greater than 0.27? Very simple question. Is r greater than
0.27, they ask? OK, statement one tells us that
r is greater than 1/4. OK, well, that doesn't really--
r could still be-- this is 0.25, so r could still
be equal to 0.251, right? It could be 0.251, or
it could be 0.3. So this really doesn't give
us any information. We don't know whether r
is greater than 0.27. Let's see what the second
statement tells us. The second statement says
r is equal to 3/10. Well, that is equal to 0.3,
and that's definitely greater than 0.27. So this is all we need. We just need statement two. Statement one was a
little useless. So that is-- I always forget
what letters-- that's b. We only need statement two. All right. How am I doing on time? Oh, I have time. I think I can do a couple more
problems. These go fast, because you don't have to
actually do the math. Problem number five. What is the value of the sum of
a list of n odd integers? OK., and they didn't say
consecutive, and they didn't say where it starts. It's just n odd integers. Fair enough. OK, one, they tell us
n is equal to 8. So if I knew that I was going to
sum eight odd integers, can I know the sum? Well, no. I mean, it could be-- all of
these could be numbers in the millions, or they could be
negative, or they could be really small numbers. So that doesn't help me much. Point number two, they say the
square of the integers on the list is 64. So they're essentially saying
that n squared is equal to 64. And since we're talking about
numbers in a list, it can't be negative, so n is equal to 8. So these are really telling me
the same thing, just this is a little bit more convoluted. But really, they
don't help out. I could have eight numbers in
the billions, or I could have eight numbers in the hundreds,
and so obviously, you're going to get a different sum. I don't think I can figure
this out anyway. So that's what? That is statement e, that
together they're not sufficient. So both of these are useless. I still don't know the
answer, which is e. All right. Well, I think I'm out of time. I just passed the
10-minute mark. I will continue in
the next video. See