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GMAT: Data sufficiency 7

33-36, pg. 280. Created by Sal Khan.

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Problem 33 asks: What distance did Jane travel? What distance did she travel? So, one. Bill traveled 40 miles in 40 minutes, or essentially a mile a minute, which is 60 miles an hour, whatever, 1 mile a minute, right? That's what we can figure out. 1 mile per minute. That has no information about how far did Jane travel. It's useless. Two. Jane traveled at the same average rate as Bill. So that tells that Jane, if she went at the same average rate as Bill, that means that she also went 1 mile per minute. But we're not asking for how fast did Jane travel or what was her average rate. We're asking for how far did she travel? So with statements one and two combined, all we know is Jane's rate, but we don't know how long she traveled for. So we don't know the distance. So the answer is e, that both statements together are not sufficient. If statement two told us that Jane traveled at the same rate as Bill and she traveled at that rate for 10 minutes, then we would be able to solve this problem. But it didn't, so even with both pieces of information, we still don't know how far Jane traveled, only how fast she traveled. 34. What number is 15% of x? So what we want to know is 0.15x. That's what we're trying to solve for. Statement one tells us, 18 is 6% of x. So you normally wouldn't even have to solve for it. All you know is, by looking at this statement, you can solve for x. And if you can solve for x, then you can just multiply that times 0.15, and you'll have the answer to the original statement. So you immediately know that statement one is sufficient. If you don't believe me, you can just write this as a equation. 18 is equal to 6% of x. And then you just solve for x. So 18 divided by 0.06, and then multiply it times 0.15, and you've got your answer. Statement number two. 2/3 of x is 200. Once again, you look at this, and you say, this is a simple equation. I could solve for x. If I solve for x here, then I just substitute it back here, and I will know what 15% of x is, and I would be done. So each of these statements individually are sufficient to answer our question what is 15% of x. I don't think I've got to go through the exercise of actually solving for that, because I think you understand what I'm talking about. 35. Oh, I like these. So they say 3.2 rectangle triangle, or delta, 6. And they say, if rectangle and delta, or triangle, soon. each represent single digits in the decimal above. OK. So this is a decimal. I thought they might be operations. So this is a decimal. So it's four digits behind the decimal spot. What does rectangle represent? So we want to know what does this decimal-- what's the digit right here? Statement number one tells us, when the decimal is rounded to the nearest tenth, 3.2 is the result. The nearest tenth. So when you round, what you do is you look at-- if we're rounding to the nearest tenth, we look at this number, right? We look at the rectangle. And if the rectangle is 5 or greater, we would round up, so we would get to 3.3. If the rectangle is less than 5, then we would round down to 2. So statement number one tells us that rectangle is less than 5. And we know it's greater than or equal to 0, because it's a digit. It's 0, 1, 2, 3, or 4, right? So we can say it's 0, 1, 2, 3, or 4. That's rectangle. But that by itself does not allow to figure out what rectangle is. Now statement number two tells us, when the decimal is rounded to the nearest hundredth, 3.24 is the result. 3.24 is the result when you round to the nearest hundredth. OK. So this is interesting. So this number here is either going to be-- so when you're rounding to something, it's either going to be either rounding down or rounding up. So this tells us-- so this number right here can either be 3-- so we already know, it can be 0, 1, 2, 3, or 4. But which of these numbers when you round them could be rounded up or down to 4? Well, this could be 2, 3, 5, right? Let me give you one scenario. We could have 3.2356, where this is the rectangle and this is triangle. So this would round to 3.24. You could also have 3.2416. where this is the rectangle and this is the triangle. And either of these would round to 3.24. So this tells us essentially that the rectangle has to be either 3 or 4. And this tells us that it's either 0, 1, 2, 3, or 4. But even when you use them individually, they don't tell you exactly what the rectangle is. And when you use them together, you can just narrow down to 3 or 4, which just statement two alone tells you. So this actually turns out that when you use both statements together, you still can't get the answer. You'd either need a third term there, or we would have to have a little bit more information about what the triangle is. If they told us that the triangle rounds you up or is greater than 5 or less than 5 or something like that, then we could figure out what the rectangle is. So they answer here is E, if I haven't missed something. That together, both statements are not sufficient to answer the question. 36. A profit from the sale of a certain appliance increases, though not proportionally with the number of units sold. So it's not-- you know, the profits do not equal just some constant times units. It equals maybe some constant times units squared or something like that. Did the profit exceed 4 million on sales of 380,000 units? So is profit greater than 4 million-- this one is interesting-- when units is equal to 380,000? Let's see if we can figure this out. So they say that the profit exceeds 2 million on sales of 200,000. So statement one says profit is greater than 2 million when units is equal to 200,000. Now, if they told us that profit was proportional to units, then we could say, oh, well, if we increase the units from 200,000 to 380,000, then we're not doubling the units. So then we can't be-- well, it still would be ambiguous because they're not saying profit equals 2. They're saying that profit is greater than 2, so this actually still doesn't give me a lot of information. Statement number two. I'll do it in a different color. Statement number two says the profit exceeds 5 million on sales of 350,000 units. OK. So this is interesting. So this tells us that when units are 350,000, our profit is already greater than 5 million, so they're definitely greater than 4 million. And notice, they told us that the profit from the sale of an appliance increases, but not proportionally, with the number of units sold. So if we made more than 5 million when there are 350,000 units, we know that when you go from 350,000 to 380,000, we know from the statement of the problem that the profit has to increase. We don't know by how much, but it's going to increase. So the profit was already greater than 5 million. It's going to increase above 5 million. So statement two tells us that the profit is definitely going to be above 5 million, so it's definitely going to be above 4 million. So statement two alone is enough. And statement one actually tells us very little information because we don't know how does the profit change as you incrementally add units. Maybe every other unit-- maybe every unit above 200,000 that you add, you get, a millionth of a penny. And then it doesn't tell you anything. Or maybe you get a million pennies. So it's very hard to tell. Problem number-- actually, I'm already at 10 minutes. Let me do that in the next video. See