Okay, let's break this baby down. First of all, this is a classic "
Inference" question, based on the flow of the question stem. It asks for a fact that "
must be true" on the basis of the facts the stimulus. "
Must be true" has a very high burden of proof. We can use this as leverage to eliminate answer choices. Any answer choice that could
possibly be false can be quickly eliminated. We know from the problem that 5 years ago the cases of schistosomiasis were \(40\%\) of the total. Thus,
\(S_\text{(5 yrs ago)}= (\frac{2}{5})T_\text{(5 yrs ago)}\). We also know that last year the number of schistosomiasis cases were \(30\%\) of the last year's total. Thus,
\(S_\text{(Last)}= (\frac{3}{10})T_\text{(Last)}\).
Let's take a look at each answer choice in turn:
(A) There were fewer cases of schistosomiasis last year than five years ago.Wrong. This is a classic trap that I like to call in my classes a "
Statistical Stretch." The text of the problem only gives us percentage information, not numerical values. While the percentage of the schistosomiasis cases dropped over the 5 year period, we don't know what happened to the
total number of cases. If the total number of cases drastically increased, it is possible for the number of cases to go up, even if the percentage drops. (For example, \(40\%\) of \(100\) is \(40\), while \(30\%\) of \(200\) is \(60\).) Get rid of "A".
(B) The percentage of disease cases from malaria has increased over the past 5 years.Wrong. Once again, we can destroy this answer choice because of the "
must be true" requirement. We only know that malaria accounted for more than half of all disease cases over the past 5 years, but we don't know how this percentage may have changed over time. It could have easily gone from \(60\%\) to \(50\%\), with the average still being above \(50\%\). The percentage didn't have to increase over time. Answer choice "B" can be swiftly eliminated.
(C) Some disease has experienced an increase in the number of its total cases, as long as the total number of disease cases went down by a number less than 30%.Wrong. This also fails the "
must be true" requirement. The easiest way to show this is to focus on the boundary established in this question. (In other words, we could check if it is possible to have NO increases in disease cases, even if the total number of disease cases went down by \(30\%\).) We just need one counter-example that shows "C" doesn't have to be true. Since the problem never gives us any numbers besides percentages, we can invent our own numbers. I call this strategy "
Easy Numbers" in my classes.
So, let's assume that the original number of cases was \(100\). \(50\) of those could be malaria cases, and \(40\) of them could be schistosomiasis. That leaves \(10\) for another possible disease (let's say "toe fungus.") If five years later the number of cases went down by \(30\%\), then we would only have \(70\) total cases. Schistosomiasis would have \(30\%\) of the \(70\) (or \(0.3*70 = 21\) cases. Malaria could still take \(49\) of those cases. But this would leave \(0\) cases of our mysterious toe fungus. Since since this situation disproves that the cases of some disease MUST increase, then answer choice "C" fails the "
must be true" test. Eliminate it.
(By the way, if you are thinking, "
But wait, you only had 50 malaria cases in that example! The problem says that malaria accounted for more than half of all disease cases!", you likely made a couple of assumptions that created poor logic. First of all, the phrase "half of all disease cases" is an aggregate across all five years. There might be some years where the number of cases exceeds \(50\%\) and some that might be lower than \(50\%\), as long as the total across all the years is sufficiently high. You might have also missed the fact that, in our hypothetical example, the total number of malaria cases dropped, but the percentage of malaria cases rose precipitously -- \(49\) of \(70\) total cases would actually be a whopping \(70\%\) of the total that year.)
(D) Each year over the past five, malaria has accounted for a larger percentage of disease cases than schistosomiasis.Wrong. Once again, this can be destroyed with a single-counterexample that proves it doesn't have to always be true. As mentioned in the above analysis, while the question stem states that "
Over the past five years, malaria has accounted for more than half of all disease cases," this doesn't mean that malaria must exceed \(50\%\) each year. There might be some years where the number of cases exceeds \(50\%\) and some that might be lower than \(50\%\), as long as the total across all the years is sufficient high. It is possible that in the third year there was a spike of schistosomiasis cases, coinciding with a temporary drop in malaria cases. The phrase "
each year" in this problem CANNOT be justified. Get rid of "D".
(E) If the total number of schistosomiasis cases increased over the past five years, then the total number of disease cases must have increased by more than 30%.Correct -- but some people fall for the trap here. This answer contains a "
Hypothetical" (the phrase "
If the total number of schistosomiasis cases increased over the past five years...") With inference questions, you can normally eliminate answers that clearly contain new information not mentioned in the conclusion. After all, you logically can't conclude something that you haven't already talked about! In my classes, I call this strategy the "
No-New-Information Filter." It can be a powerful analysis tool for Inference questions. However,
Hypotheticals trick test-takers into thinking that an answer choices contains information that goes beyond the facts in the problem. But hypotheticals aren't facts. They are just possibilities. In essence answer choice E states, "
Given what we know, if we also knew that the total number of schistosomiasis cases increased over the past five years, then we could conclude..." It requires a little bit of math to show this. The hypothetical in this answer choice tells us that, for purposes of analysis, we can assume that
\(S_\text{(Last)}>S_\text{(5 yrs ago)}\). Plugging in the first two equations into the hypothetical gives us:
\(S_\text{(Last)}>S_\text{(5 yrs ago)}\)\((\frac{3}{10})T_\text{(Last)}>(\frac{2}{5})T_\text{(5 yrs ago)}\)\(T_\text{(Last)}>(\frac{10}{3})(\frac{2}{5})T_\text{(5 yrs ago)}>(\frac{4}{3})T_\text{(5 yrs ago)}\)Thus, the total amount of disease cases increased by more than \(\frac{1}{3}\), or about \(33\%\). This is more than the minimum \(30\%\) required by answer choice E. Thus, it must always be true. E is the right answer.
Now, let’s look back at this problem from the perspective of strategy. For those of you studying for the GMAT, it is far more useful to identify
patterns in questions than to memorize the solutions of individual problems. This problem can teach us several solid patterns seen throughout the GMAT. First and foremost, use the wording of the problem as leverage to attack the problem. Extreme statements such as "
must be true" are easy pickings. We can eliminate any answer that could possibly be false. Second, when a problem gives you percentages or ratios without totals, inventing your own "
Easy Numbers" can turn abstract ideas into concrete possibilities. Lastly, the GMAT loves to conceal the right answers by hiding them behind constructions that we might not be expecting (such as the "
Hypotheticals" in this question.) Don't fall for the traps. Focus on exactly what the problem is asking. And
that is how you think like the GMAT.
_________________
Aaron PondVeritas Prep Teacher of the YearVisit me at https://www.veritasprep.com/gmat/aaron-pond/ if you would like to learn even more "GMAT Jujitsu"!