If we look at the first table, we can see that from 1990 to 2015 the world population did grow, which does support part of Malthus’s prediction. However, if we look at the second table, we see that from 1990-2015 the percentage of people living poverty actually decreases across each world region (and dramatically so in those regions that were >50% in 1990). Thus, as population increased, poverty decreased. This contradicts Mathus’s prediction overall so we can eliminate answer choices that claim to support his prediction: “ it supports Malthus’s prediction, because it shows that poverty is still a major problem in the world “ and “it supports Malthus’s prediction, because it demonstrates that poverty is a problem that can be solved in certain regions”.

Looking at the remaining options, “it contradicts Malthus’s prediction, because it demonstrates that poverty remains highest in the same regions of the world year after year” is a true statement based on the second table; however, this has nothing to do with Mathus’s prediction so we can eliminate it. This leaves us with, “it contradicts Malthus’s prediction, because it shows that poverty is decreasing even while the population is increasing” as the correct answer. This statement is supported by both of the tables and does contradict Malthus’s overall prediction because that tables show that as population increased, poverty decreased.

When looking to draw conclusions from the data presented in a table, we’re looking for the conclusion that must be true based on the given information. Here, the percent change did not increase in each of the years - or, according to the table, in each 5 year period. So, this is not something we can conclude. We also don’t know that the annual rate of growth was greater in 2000 than in 1995. The annualized rate of growth given was higher in 1995 (.31) as compared to 2000 (.21). If we look to do the math, or even just broadly compare the change, we can see that the growth amount was higher for the female population between 1947 and 2000 than it was for the male population. We do, however, know that “The total population of Japan exceeded 100,000 for each of the years displayed in the table.” This may not seem immediately obvious - but keep in mind, the data is displayed in thousands! So, even the smallest total population (that of 1947) was 78,010,000 - well over 100,000!

In this example, we’re looking to understand which option the table provides direct support for. Since the table does not include any information about either the conclusive vs. inconclusive nature of the percent data or any other factors that might come into play, and instead simply expresses the percent data, we can eliminate any option that addresses the idea that the “tulip mania” may not have represented an economic bubble. Additionally, while it is true that, based on the passage, “This phenomenon was so well-known that it has come to be the way many refer to an economic bubble,” we don’t have any direct support for this statement in the table. That said, the fact that the percent change both month-over-month and overall was highest for “tulip mania” as compared to all other economic bubbles supports the idea that “The extent of the change in price certainly merits its status as an economic bubble.”

In this question, we’re being asked to apply estimation and rounding to compare the percentage of its annual budget each city spent on sanitation. If we use a bit of estimation, we can round the percents, in fraction form, as follows:

Andersonville: 

Bronxtown:  (we can round a bit more generously to , or  and recognize that even if we’re not precise, Bronxtown is certainly less than all other cities. 

Chadwick:  

Dodgeville: 

Edgewater:  

So, by the process of elimination, we can see that Edgewater did in fact spend the largest percentage of its annual budget on sanitation. All incorrect answers are also quickly able to be disproven using the estimated fractions above.

This table provides us with an abundance of information - far more than we could feasibly be asked about in any one question. So, process of elimination is our friend here. If we look to our correct answer, “Every orange scented product experienced growth in unit sales from 2009 to 2010,” we can see that in each row for “orange,” the “% change” in unit sales is positive. Thus, we’ve found our correct answer! We cannot, however, conclude that “The product with the highest unit sales also had the highest percent change in dollar sales.” This is a tricky one. Superclean Spray Fresh comes in at a 23.2% increase over the last year. If we scan the rest of the column for percent change in dollar sales, we can see that this is the highest percent *increase* but not the highest percent *change,* as Deluxe Powder Lemon experienced a 23.8% decrease during this period. We also cannot conclude that “The product with the highest unit sales also had the highest dollar sales.” If we again look to Superclean Spray Fresh and scan to see if its dollar sales are also the highest, we quickly see that they are surpassed by the next cleaner up, Ultrashine Powder Lemon. Finally, it is untrue that every lemon scented bathroom cleaner sold more units in 2009 than in 2010. If we scan for lemon cleaners, we can quickly see that several have a negative “% change” in unit sales.

This table provides us with an abundance of information - far more than we could feasibly be asked about in any one question. So, process of elimination is our friend here. The table is already sorted such that we can easily identify the products with the highest and lowest dollar sales. Here, we cannot conclude that “The product with the lowest dollar sales in 2010 also had the lowest average price,” since Incredible Spray Lemon, our lowest dollar sales for 2010 costs $2.90, but if we scan the column for price, we can see that Deluxe Aerosol Orange comes in at a lower average price of $2.61, as does Dirt Blaster Spray Orange at $2.80. We also cannot conclude that “No product experienced growth in dollar sales but a decline in unit sales from 2009 to 2010.” If we scan the portion of the table where “% change” in dollar sales is positive, we will still find cases where “% change” in units is negative (for instance, Mrs. Grime Spray Unscented). We can also disprove that “The product with the highest dollar sales in 2010 also had the highest average price,” Since Ultra Shine Powder Lemon rings in at $3.99, and several other products have average prices above $4. 

We can, however, conclude that “Spray bathroom cleaners generated more dollar sales than any other single type of bathroom cleaner in 2010,” but we’ll need to do a bit of estimation, math, and comparison to get there.  Our only job is to try to identify whether any other type could have outsold “spray” cleaners. Of our varieties, Powder cleaners are irrelevant - there are only two such cleaners and the leading cleaner doesn't have enough separation from the field to make it a runaway category. The decision to be made is between Spray and Aerosol, so your mission is to determine which sold more. You can effectively do this by looking to the gap between the two, rather than the total. Spray starts with two higher-sellers than Aerosol, earning approximately $33M and $27M to Aerosol's two biggest totals, $22M and $21M. This gives Spray a $17M "gap" that Aerosol needs to make up, and with the next highest seller also a Spray Cleaner, the gap widens to nearly $18M. From there, you can simply compare one-to-one the remaining Spray and Aerosol cleaners on the Dollar Sales list to see whether the gap will come down to something competitive. It does not - notice that further down the list the dollar figures become so small that they'll make little if any dent in that gap between Spray totals and Aerosol totals. Rather than calculate, you can logically call this one a runaway just by judging the gaps at the top of the list and noting the limited opportunities for Aerosol to close it down.

When we’re asked to draw a conclusion that “must be true” based on the passage and/or table, we’ll want to use the process of elimination as a primary tactic. Here, we cannot determine that either month-by-month or in total, the level/percent change continue to decrease as we move chronologically through the listed events in the table. While this is true for the most part, in each case, we have a situation where this decreasing trend does not hold true. Additionally, we have no way of connecting the percent change to the impact on the economy, particularly because we don’t know how much the product at hand impacts the economy, or how long the bubble was in place for. 

We can, however, conclude that “Percent change may not be the only factor contributing toward the economic bubble status of an economic event,” since the passage points out that despite the impressive level of percent change, a usual indicator of an economic bubble, “tulip mania” may not have, itself, qualified as one.

In this example, we need to be careful to address the type of data we’ve been presented with in the table. Here, we were given the percent of individuals in each region who report believing in the supernatural. So, without population data, we cannot draw any conclusions about the *number* of individuals in each group with this belief. (Remember not to bring any outside information into your analysis!) Thus, we can eliminate “The same number of people believed in ghosts in the Americas in 2000 as believed in ghosts in Africa during that time” and “More people believed in ghosts in Africa in 2010 than believed in them in Europe during that time.”

We also cannot conclude that “For each region, belief in ghosts grew between 2000 and 2010,” as there is a clear decrease in the percent of people who believe in ghosts in the region for both the Americas and Asia. We can, however, conclude that “Belief in ghosts was more prevalent in Asia than in any other region in 2010,” as a higher percentage of the population in Asia reported believing in the supernatural than did any other region in 2010. Keep in mind, even if you weren’t sure the meaning of the word “prevalent,” we can use context and process of elimination to arrive at the correct answer, as we have here.

In this example, we’re looking for an answer option that aligns with, and thus helps to explain, the data trends represented in the table. If “A widespread cultural trend toward television programs that hunt for and expose supernatural forces became popular in America during the period between 2000 and 2010,” we would expect this trend to increase belief in the supernatural - but such belief decreased in the Americas during this period, allowing us to eliminate this option. The fact that “Europe has long been known to have a population with a particular affinity for belief in ghosts as compared to the other major regions of the world,” since Europe had the lowest percentage who reported believing in the supernatural in both 2000 and in 2010. If “In America, belief in the supernatural and astrological belief, an increasing trend between 2000 and 2010, tend to be strongly positively correlated with one another,” we would again expect belief in the supernatural to have increased among Americans during this time. The data, however, shows us that this was not the case, so this option can also be eliminated. 

This leaves us with our correct answer: “In Africa, an improvement in educational access in rural regions included a learning module explaining the science behind a phenomenon previously believed by many to be the work of the supernatural.” If access to education allowed for more widespread knowledge of the science behind a phenomenon previously believed to be the work of the supernatural, this could provide us with a rationale for why the percent of the population in Africa who reported believing in the supernatural decreased during this time.

Since the angles are supplementary, their sum is 180 degrees.  Because they are in a ratio of 1:4, the following expression could be written: