## Unconventional Graphs

### Transcript

Now we can talk about some unconventional graphs. So on the GRE Data Interpretation, it's certainly likely that you'll see some of the more common graphs, the ones that we've been talking about in these previous videos. You'll also see charts of numbers, and you'll see some charts and graphs of a less common sort.

In fact, there is no way this lesson or any number of lessons could exhaust the possibilities for charts or graphs you might see. You have to understand, ETS goes out looking at charts. It's, it's searching magazines, it's searching academic sources, it's finding all kinds of examples of absolutely bizarre, unique ways to present data and it loves to throw those onto the GRE.

First of all, if you see something like this, do not panic. If this graph is new to you, chances are very good that it's new to a vast majority of people taking the GRE. If it's new to everyone, you can be guaranteed a lot of people are gonna panic. A lot of people are just gonna skip the problem.

If you can just keep a level head. You are way ahead of the pack right there. The test will have to specify all the rules, if it's an out of the box graph, they're gonna have to explain in detail here's how the graph works. Just read carefully and use the same visual graph-reading skills that we have been discussing.

Here's a sample graph, pause the video and then we'll talk about this. Okay, so this graph if you happen to have studies physics then this graph might be familiar. If you've even taken say a thermodynamics course or something like this. For most people, this will be an unfamiliar graph.

And notice what we have here. We have a horizontal axis that's volume in liters. We have a vertical axis in pressure, ATM. That actually stands for atmospheres. You don't need to know that. And then we have three different curves.

Not one curve, but three different curves representing three different temperatures. And this is showing an interaction between volume and pressure and temperature. Very interesting. So now, let P be the percent increase in volume, at 3 ATM, from 100 to 300 degrees Celsius. So we're gonna stay on this horizontal line, 3 ATM, three atmosphere.

At 100 we're here, at 50. At 300, we're right around here, we're a little above 75. Now notice also how precise do we have to be? Let's look at the answers. 25, 50, 75, 100, 125 wildly spread out, so this is just an engraved invitation to estimation here.

So I'm not even gonna bother with a precise calculation, I'm just gonna say, we're going from 50 to 75. Of course that's an increase of 25 and 25 is half of 50, so an increase from 50 to 75 is a 50% increase. P is approximately a 50% increase. Now the second part, Q.

Let Q be the percent increase in pressure, at 75 liters. So now we're gonna stay on this vertical line, the 75 liter vertical line of fixed volume. And we're gonna increase from 100 to 200, so that's an increase from approximately 2 to 3. Two atmospheres to three atmospheres.

And so that's an increase of 1, 1 of course is half of 2. So this is also approximately a 50% increase. Notice that we're being very general with our approximations here. Well what's P plus Q, P plus Q is approximately 100%, answer choice D, done. So once you realize what's being asked, not very hard. Here's another unconventional graph.

Pause the video, and then we'll talk about this. So this graph shows over two-year period, the weekly sales of many models of cars. And, of course the models are broken up by type, sports cars, SUVs, minivans, and compact cars. And so for each one we're getting a range.

What's the most cars that they sold in a week, what's the fewest cars they sold in a week? So now the question is the minimum revenue from all compact cars combined is closest to how many times the minimum revenue from all sports cars combined. Interesting. Let's look at sports cars first.

So we're looking at the minimum values. The leftmost values, the leftmost dots. So the minimum values in a typical week. They would sell zero of those really expensive $75,000 sports cars. Those most be really impressive cars, but because they're so expensive sometimes their weeks they sell none of them.

They always seem to sell at least one of the RX3, which costs $45,000, so that's their revenue. I'm just gonna write it as 45. I'm gonna ignore the last three 0s cuz all these numbers have three 0s at the end. I'm just gonna ignore those. Okay.

Now the compact cars. So, we're gonna look at the leftmost points here. So, the SD Plus, which costs 40,000, they sell at least two of those. So, that would be 80,000. The SD, which costs 30,000, they sell 3 of those. So that would be a 120.

The TD+ costs $35,000, they sell three of those, so that would be 3 times 35 is a 105 and the TD, the regular TD, costs $25,000, their cheapest car. They always sell at least five of those. That would be a 125, 5 times 25. These two add up to 200.

105 and 125 add up to 230. Add those together, and we get 430. So that's the total minimum revenue from compact cars. And so, the question really is, 430 is approximately how many times 45? Well looks like it's pretty close to ten times. But, let's just think about this.

45 times 10 is 450. Subtract 45 from that, 405, that would be 45 times 9, so 430 is between 450 and 405, so 430 would be something like 9.5 times 45. Well, 9.5 is closer to 10 than it's closer to anything else. So, the answer here is D.

Those two problems were not necessarily hard once you realized the mathematics that you had to do, but they would be very unfamiliar to many folks taking the GRE. In fact, many folks taking the GRE might get to a question like that and might simply skip it. They might think, oh my god, I don't know how to do this kind of a graph. I've never seen this before, they just go into a panic and they skip it.

So it's very important to keep a level head. It's very important to keep a level head throughout the test, but certainly when you see a graph that's unconventional. The more demanding data interpretation questions involve two graphs, and we would have to relate these two graphs. So here's an example of this.

Pause the video and then we'll talk about this. So this is a relatively challenging problem. This involves currency exchanges as well as fluctuating prices. So the currency of the country of Malugia is Malugs, Malugia sells its own crude oil in this currency. The worth of $1 in Malugs is shown on the graph on the right.

So, the graph on the left, what we have is the fluctuating price of crude oil in this strange currency, Malugs, which is the, the currency of this imaginary country, Malugia. In the right, we have the equivalent of $1 US in Malugs and the question here is in which year was the price of a barrel of Malugian crude oil least expensive in US dollars?

So let's think about this. How much, how many Malugs does one US dollar buy? So say in years like this, the years that are high on the graph. Those are relatively good years to US's exchange. In other words, the US is buying lots of Malugs. And so it would make it easier to buy anything sold in Malugian currency.

When we got to here, this is a year that it's much harder to buy Malugs. In other words, a US dollar is worth, it's worth less than 100 Malugs at that point. Okay, that's the lowest, so that's when the Malugs are most expensive in terms of US dollars. So we want something that is good for the US dollar, making it good, that would be when the US dollar is high on the graph, but not necessarily the highest point.

Because now we go over to the price of the Malugian barrel of oil. Well here, the US dollar can buy lots of Malugs, but the price of oil is relatively high also, so that's not necessarily a win. Yeah, we can buy more Malugs with our US dollar, but then we have to spend more Malugs to buy the oil. We're not really having much of a gain.

But notice that when we're at this high point here, it's one of the lowest prices here. So this is the second highest point on this graph. And the second lowest point on that graph. That's a winner. Because in that year, which is 2004, we're buying a lot of Malugs with our US dollar.

And it doesn't cost that many Malugs to buy a barrel of crude oil. So that's our winner, answer choice B. That is a very hard question. If two graphs appear, you will have to combine the information from the two graphs in at least some of the questions. Once again, do not be intimidated by graphs with which you are unfamiliar or pairs of graphs that combine data.

Remember that this will be challenging for the majority of people who take the GRE. Simply, pay attention to the rules for the graphs and the logic of the situation.

Read full transcriptIn fact, there is no way this lesson or any number of lessons could exhaust the possibilities for charts or graphs you might see. You have to understand, ETS goes out looking at charts. It's, it's searching magazines, it's searching academic sources, it's finding all kinds of examples of absolutely bizarre, unique ways to present data and it loves to throw those onto the GRE.

First of all, if you see something like this, do not panic. If this graph is new to you, chances are very good that it's new to a vast majority of people taking the GRE. If it's new to everyone, you can be guaranteed a lot of people are gonna panic. A lot of people are just gonna skip the problem.

If you can just keep a level head. You are way ahead of the pack right there. The test will have to specify all the rules, if it's an out of the box graph, they're gonna have to explain in detail here's how the graph works. Just read carefully and use the same visual graph-reading skills that we have been discussing.

Here's a sample graph, pause the video and then we'll talk about this. Okay, so this graph if you happen to have studies physics then this graph might be familiar. If you've even taken say a thermodynamics course or something like this. For most people, this will be an unfamiliar graph.

And notice what we have here. We have a horizontal axis that's volume in liters. We have a vertical axis in pressure, ATM. That actually stands for atmospheres. You don't need to know that. And then we have three different curves.

Not one curve, but three different curves representing three different temperatures. And this is showing an interaction between volume and pressure and temperature. Very interesting. So now, let P be the percent increase in volume, at 3 ATM, from 100 to 300 degrees Celsius. So we're gonna stay on this horizontal line, 3 ATM, three atmosphere.

At 100 we're here, at 50. At 300, we're right around here, we're a little above 75. Now notice also how precise do we have to be? Let's look at the answers. 25, 50, 75, 100, 125 wildly spread out, so this is just an engraved invitation to estimation here.

So I'm not even gonna bother with a precise calculation, I'm just gonna say, we're going from 50 to 75. Of course that's an increase of 25 and 25 is half of 50, so an increase from 50 to 75 is a 50% increase. P is approximately a 50% increase. Now the second part, Q.

Let Q be the percent increase in pressure, at 75 liters. So now we're gonna stay on this vertical line, the 75 liter vertical line of fixed volume. And we're gonna increase from 100 to 200, so that's an increase from approximately 2 to 3. Two atmospheres to three atmospheres.

And so that's an increase of 1, 1 of course is half of 2. So this is also approximately a 50% increase. Notice that we're being very general with our approximations here. Well what's P plus Q, P plus Q is approximately 100%, answer choice D, done. So once you realize what's being asked, not very hard. Here's another unconventional graph.

Pause the video, and then we'll talk about this. So this graph shows over two-year period, the weekly sales of many models of cars. And, of course the models are broken up by type, sports cars, SUVs, minivans, and compact cars. And so for each one we're getting a range.

What's the most cars that they sold in a week, what's the fewest cars they sold in a week? So now the question is the minimum revenue from all compact cars combined is closest to how many times the minimum revenue from all sports cars combined. Interesting. Let's look at sports cars first.

So we're looking at the minimum values. The leftmost values, the leftmost dots. So the minimum values in a typical week. They would sell zero of those really expensive $75,000 sports cars. Those most be really impressive cars, but because they're so expensive sometimes their weeks they sell none of them.

They always seem to sell at least one of the RX3, which costs $45,000, so that's their revenue. I'm just gonna write it as 45. I'm gonna ignore the last three 0s cuz all these numbers have three 0s at the end. I'm just gonna ignore those. Okay.

Now the compact cars. So, we're gonna look at the leftmost points here. So, the SD Plus, which costs 40,000, they sell at least two of those. So, that would be 80,000. The SD, which costs 30,000, they sell 3 of those. So that would be a 120.

The TD+ costs $35,000, they sell three of those, so that would be 3 times 35 is a 105 and the TD, the regular TD, costs $25,000, their cheapest car. They always sell at least five of those. That would be a 125, 5 times 25. These two add up to 200.

105 and 125 add up to 230. Add those together, and we get 430. So that's the total minimum revenue from compact cars. And so, the question really is, 430 is approximately how many times 45? Well looks like it's pretty close to ten times. But, let's just think about this.

45 times 10 is 450. Subtract 45 from that, 405, that would be 45 times 9, so 430 is between 450 and 405, so 430 would be something like 9.5 times 45. Well, 9.5 is closer to 10 than it's closer to anything else. So, the answer here is D.

Those two problems were not necessarily hard once you realized the mathematics that you had to do, but they would be very unfamiliar to many folks taking the GRE. In fact, many folks taking the GRE might get to a question like that and might simply skip it. They might think, oh my god, I don't know how to do this kind of a graph. I've never seen this before, they just go into a panic and they skip it.

So it's very important to keep a level head. It's very important to keep a level head throughout the test, but certainly when you see a graph that's unconventional. The more demanding data interpretation questions involve two graphs, and we would have to relate these two graphs. So here's an example of this.

Pause the video and then we'll talk about this. So this is a relatively challenging problem. This involves currency exchanges as well as fluctuating prices. So the currency of the country of Malugia is Malugs, Malugia sells its own crude oil in this currency. The worth of $1 in Malugs is shown on the graph on the right.

So, the graph on the left, what we have is the fluctuating price of crude oil in this strange currency, Malugs, which is the, the currency of this imaginary country, Malugia. In the right, we have the equivalent of $1 US in Malugs and the question here is in which year was the price of a barrel of Malugian crude oil least expensive in US dollars?

So let's think about this. How much, how many Malugs does one US dollar buy? So say in years like this, the years that are high on the graph. Those are relatively good years to US's exchange. In other words, the US is buying lots of Malugs. And so it would make it easier to buy anything sold in Malugian currency.

When we got to here, this is a year that it's much harder to buy Malugs. In other words, a US dollar is worth, it's worth less than 100 Malugs at that point. Okay, that's the lowest, so that's when the Malugs are most expensive in terms of US dollars. So we want something that is good for the US dollar, making it good, that would be when the US dollar is high on the graph, but not necessarily the highest point.

Because now we go over to the price of the Malugian barrel of oil. Well here, the US dollar can buy lots of Malugs, but the price of oil is relatively high also, so that's not necessarily a win. Yeah, we can buy more Malugs with our US dollar, but then we have to spend more Malugs to buy the oil. We're not really having much of a gain.

But notice that when we're at this high point here, it's one of the lowest prices here. So this is the second highest point on this graph. And the second lowest point on that graph. That's a winner. Because in that year, which is 2004, we're buying a lot of Malugs with our US dollar.

And it doesn't cost that many Malugs to buy a barrel of crude oil. So that's our winner, answer choice B. That is a very hard question. If two graphs appear, you will have to combine the information from the two graphs in at least some of the questions. Once again, do not be intimidated by graphs with which you are unfamiliar or pairs of graphs that combine data.

Remember that this will be challenging for the majority of people who take the GRE. Simply, pay attention to the rules for the graphs and the logic of the situation.