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GMAT: Data sufficiency 1

1-5, pg. 278. Created by Sal Khan.

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Video transcript

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