In your preparations for the GMAT math section, it is essential that you practice with retired real GMAT questions using the GMAT Official Guide (13th Edition) and the GMAT Quantitative Official Guide (2nd Edition). These two books provide you with a combined total of 430 Problem Solving and 322 Data Sufficiency practice questions.
Repetitive Problem Solving Questions
One interesting observation from our analysis of these questions is the frequency with which some questions closely mirror another question. Due to copyright issues, we cannot reprint these repetitive math questions from the Official Guides. But if you have your copies handy, compare the following sets of Problem Solving questions:
- 13E #128 (page 170) vs. 2E #132 (page 79): These two questions involving combinatorics are nearly identical, even using the same numbers in the problem and in the first three answer choices (one of which is the correct answer). Only the context changes: one question involves finding the minimum number of colors for a distribution center’s coding, and the other involves finding the minimum number of letters for an experiment’s coding.
- 13E #194 (page 179) vs. 2E #165 (page 84): Both questions provide three fractions of a total amount and the remaining balance that is unaccounted for, and ask us to calculate the total amount. One question relates to the amount of a trust fund whereas the other involves the number of students in a class, but the numbers within the problems are identical (except that one total is in thousands and the other is not).
- 13E #124 (page 169) vs. 13E #133 (page 171) vs. 2E #56 (page 69): These three questions all involve calculating the number of pairs that are possible out of a larger group. Two of these questions ask about the number of table entries needed to show the mileage between any two cities, and the third asks about number of games needed so that every team in a league plays each other once. For these types of questions, we teach our students a tabular approach, a combinatorics approach, and a summation approach.
- 13E #137 (page 171) vs. 13E #203 (page 181): At first glance, these two word problems seem unrelated. But the setup for both problems is identical: we have an unknown price and quantity, and when one goes up by a specified amount the other goes down by a specified amount in order to generate an equivalent revenue amount.
- 13E #111 (page 167) vs. 13E #170 (page 176): In both cases, we have a terminating decimal in the form of 1 / (2^x * 5^y) where x and y are specified exponents. Both questions entail counting digits.
- 13E #95 (page 165) vs. 13E diagnostic #13 (page 22): Both questions entail one positive integer divided by another, resulting in a quotient and a remainder equivalent to .12. Our objective is to use the .12 to deduce the value of the divisor in one question and to identify a possible remainder in the other question.
- 13E #45 (page 158) vs. 2E #57 (page 69): Both problems give us a quadratic equation using the variable x and a constant k. Given one root of the quadratic, we must find the other solution in one problem and the value of k in the other problem.
Repetitive Data Sufficiency Questions
Although the above are the most obvious examples of repetition in Problem Solving, there is much more repetition of concepts across questions. We also can find examples of repetition within Data Sufficiency, albeit to a lesser extent. As two obvious examples, compare the following sets of Data Sufficiency questions:
- 13E #2 (page 275) vs. 13E #21 (page 276): These two questions have identical setups, although with different numbers in different contexts. In both questions, statement 1 gives us what percent of women have a certain characteristic and statement 2 gives us what percent of men have the same characteristic. The questions both ask what percent of the total are women with that characteristic.
- 13E #57 (page 280) vs. 13E #59 (page 280): In both cases, we have two different denominations (of bills in one question and of gift certificates in the other). Statement 1 has an identical setup in both questions – the maximum number of the smaller denomination. In #57, the initial information tells us the minimum number of the larger denomination and statement 2 tells us the total value of both denominations combined. In #59, the initial information and that given in statement 2 are swapped.
Why does this repetition happen? Since the GMAT tests a finite number of concepts, these concepts will inevitably appear repeatedly in various forms. But since the GMAC must produce a vast number of questions each year to ensure a fair testing environment, one way to make the question development process more efficient is to borrow heavily from other questions. We also see concepts applied repetitively in Verbal questions, but the questions themselves are not as obviously duplicative as the Math questions that we’ve discussed.
What is the implication of this? One of our “6 Habits of Highly Effective GMAT Students” is to watch out for patterns. As you work through many practice GMAT problems in the Official Guides and elsewhere, you will inevitably encounter similar concepts. With sufficient practice, you will be able to identify the approaches that are most relevant to a given problem. Of course you should not blindly follow the same methodology used on another problem, since the concepts may be applied differently. But the more adept you are at quickly recognizing the relevant approaches to apply to questions on test day, the better your GMAT score will be.