Many GMAT students have likened themselves to Sherlock Holmes at one point or another while studying for this test. It is a natural comparison: you are a detective looking for clues in order to reach a conclusion that must be true. Unfortunately there’s no Dr. Watson to help guide your efforts, but you can inspire yourself from the super sleuth in your quest to solve the nefarious puzzles of Professor G. MoriArTy.

During your preparation, you may sometimes come across questions that seem impossible. None of the five answer choices make sense and they all seem incorrect. This is when my favorite Sherlock Holmes quote fits perfectly: “when you have eliminated all which is impossible, then whatever remains, however improbable, must be the truth”. This is particularly useful in exercises in process of elimination. If none of the answer choices seem likely, start by eliminating the ones that are impossible. You should only be left with one, which will be the cleverly disguised correct answer. (For the record, my second favorite Holmes quote is: “Very sorry to knock you up, Watson”)

Let’s look at such a question that seems to have no clear answer among the choices given:

In Patton City, days are categorized as having heavy rainfall (more than two inches), moderate rainfall (more than one inch, but no more than two inches), light rainfall (at least a trace, but no more than one inch), or no rainfall. In 1990, there were fewer days with light rainfall than in 1910 and fewer with moderate rainfall, yet total rainfall for the year was 20 percent higher in 1990 than in 1910.

If the statements above are true, then it is also possible that in Patton City

(A) the number of days with heavy rainfall was lower in 1990 than in 1910
(B) the number of days with some rainfall, but no more than two inches, was the same in 1990 as in 1910
(C) the number of days with some rainfall, but no more than two inches, was higher in 1990 than in 1910
(D) the total number of inches of rain that fell on days with moderate rainfall in 1990 was more than twice what it had been in 1910
(E) the average amount of rainfall per month was lower in 1990 than in 1910

This question is another verbal question that relies on your knowledge of mathematics to answer correctly. Many GMAT verbal questions contain elements of math, as the GMAT is a truly integrated exam. Let’s start by eliminating the answer choices that cannot be mathematically correct, going from the most obvious to the least obvious (note: your ordering may differ, but the concepts remain the same)

Most glaringly, answer choice B (the number of days with some rainfall, but no more than two inches, was the same in 1990 as in 1910) cannot be correct. This is because it contradicts the question stem directly. If there were fewer days with light or moderate rainfall in 1990, there cannot simultaneously be as many days. B is out.

By the same token, answer choice C (the number of days with some rainfall, but no more than two inches, was higher in 1990 than in 1910) cannot be correct either. This is exactly as wrong as answer B, but it has the added difficulty of being a 180° answer choice, sounding correct but pointing in the wrong direction (must like a spin the bottle game gone horribly wrong)

Next, answer choice E (the average amount of rainfall per month was lower in 1990 than in 1910) cannot be true. The passage tells us that total rainfall was higher in 1990 than in 1910. If you took those two numbers and divided each of them by twelve, the bigger number will necessarily yield the bigger average. Multiplying or dividing by a constant won’t change the relation to the two numbers. If one was bigger before, it will remain bigger after, if one was smaller before, it will remain smaller after. It is thus mathematically impossible for answer choice E to be correct.

This leaves us with answer choices A and D. Neither of them appears to be correct at first glance, but one of them must be correct given that we’ve logically eliminated the other choices. If we take answer A (the number of days with heavy rainfall was lower in 1990 than in 1910), it is possible that there were 20 days in 1910 with over 2 inches of rainfall, but 15 days in 1990 with much more rainfall each per day. There is no upper limit, so picking numbers should unlock this concept nicely: if 1910 had 20 days at 2.5 inches/day, and 1990 had 15 days at 5 inches/day, then more rain would still fall in 1990 (75 inches vs 50 inches, just like my recent television purchase debate) even though there were fewer days . This may seem improbable, but it is not impossible.

What about answer choice D (the total number of inches of rain that fell on days with moderate rainfall in 1990 was more than twice what it had been in 1910)? This is actually a very common answer choice on this question, even though it is mathematically impossible! If moderate days are defined as having between 1 and 2 inches of rain, exclusively, then it’s impossible to have an average double and stay within these boundaries. Even if the average rainfall had been 1.001 inches, it would still go to 2.002 inches, above the upper limit to still be considered a moderate rainfall day. The fact that the argument could explain the increase in rain volume in 1990 versus 1910 is moot because the premise is unfeasible.

If we can recognize this, we eliminate 4 answer choices and end up with answer A.

As Sherlock Holmes taught us, the answer may not be obvious, but it must be plausible. Sherlock was a master of observation and reasoning, and would likely have aced the GMAT (he may have struggled with the timing limitations, though). If we use his approach of systematically and meticulously eliminating the answer choices that are impossible, then whatever remains, however improbable, must be the truth.

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Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam.  After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.