Sample GMAT Problem Solving Questions

We’ve already covered why studying with official practice questions is the best way to prepare for the GMAT.  But even if you come up with the correct answer to an official problem, you still might not understand the underlying principles used to create that particular question, leaving yourself open to traps and pitfalls set by the test writers.  In the explanations below, I will use some of the core tenets of the Menlo Coaching GMAT curriculum to breakdown two official GMAT problem solving questions and provide important principles for correctly attacking this question type in the future. 

The multiple choice “problem solving” questions, one of the two types of GMAT math questions, are the most familiar, yet students generally do not approach them properly. To succeed on these questions, you obviously need the requisite knowledge related to the content area being tested—math skills related to arithmetic, algebra, etc. However, it is just as important to read carefully, leverage every hint, and choose the right strategy (backsolving, number picking, conceptual thinking, etc.) People think of multiple-choice problem solving questions as just plain math questions, but this GMAT sample question shows that they are much more than that. Take a look at the following:

GMAT Problem Solving, Sample Question #1

Rates for having a manuscript typed at a certain typing service are $5 per page for the first time a page is typed and $3 per page each time a page is revised. If a certain manuscript has 100 pages, of which 40 were revised only once, 10 were revised twice, and the rest required no revisions, what was the total cost of having the manuscript typed?

  1. $430
  2. $620
  3. $650
  4. $680
  5. $770
Answer & Explanation
Correct Answer is (D). 

This problem has been circulating in the official practice tests for over a decade. It is amazing how many smart, high-scoring students miss it! There is no hard math present and you just need to follow specific instructions, but people are far too casual on these types of “reading comprehension” math questions. When you are performing well on this exam, there is something hard about every question, so always try to identify where that difficulty is coming from. In this example, the key is to carefully note that the question says, “40 were revised only once.” The “sucker” incorrect answer on this question is calculated as follows:

100 x $5 = $500
40 x $3 = $120
10 x $3 = $30 (incorrectly assuming that you have accounted for the first charge of $3 in the first revision category)

The last calculation is wrong because the ones revised “only once” and “twice” are two completely separate categories—there is no overlap. So, the pages revised twice will cost $6 for each page and the correct charge for those is $6 x 10 = $60. Correct answer is thus $680, not $650. 
When I review an official practice test with a student who misses this question, I literally yell: “You cannot miss this question!” Never be casual with any question regardless of how simple it seems and always find the trap; otherwise, you are surely falling for it. I always emphasize that the “soft skills” on the quant side—reading carefully, critical thinking, strategy—are just as important as hard quant skills, if not more.

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GMAT Problem Solving, Sample Question #2

A certain airline’s fleet consisted of 60 type A planes at the beginning of 1980. At the end of each year, starting with 1980, the airline retired 3 of the type A planes and acquired 4 new type B plans. How many years did it take before the number of type A planes left in the airline’s fleet was less than 50 percent of the fleet?

  1. 6
  2. 7
  3. 8
  4. 9
  5. 10
Answer & Explanation
Correct answer is (D)

This problem is extremely easy to solve if you leverage the answers by backsolving, but it can be confusing and time-consuming if you try to create an equation or inequality. Since it will be clear on this question if you need a smaller or larger number after your first try at backsolving, start in the middle with (C). In 8 years, there will be 60-8(3) or 36 type A planes and (8)(4) or 32 type B planes. No: B is not greater than A, so you need a larger number. In 9 years, there will be 60 – (9)(3) or 33 type A planes and (9)(4) or 36 type B planes. Jackpot: 9 is the first answer that makes B > A so (D) is correct. You can literally sit back in your chair and do this with very little mental effort in under one minute with backsolving. If you solved this problem in any other way, you simply did not choose the best approach (and there is a good chance you got it wrong or spent 3+ minutes). In other algebraic interpretation questions, it might be better to use algebra—backsolving will be either impractical or impossible—but not so on this question!
 
In working with students, I use this question to see if they are truly leveraging the full toolbox to solve GMAT quant questions. If you don’t see the easy backsolving approach here, it means you are not looking for it. There are numerous ways to solve GMAT problem solving questions: you can use algebra or other “traditional” math approaches; you can pick numbers to remove abstraction in percent or variable word problems; you can use conceptual thinking or logic; you can actively leverage the answer choices (backsolving). 
 
When GMAT math questions are created, they are designed to punish people who always approach questions the same way. A typical 700+ level question on the exam will make you use fairly hard algebra to go most of the way to the answer, but then the only way to get it correct at the end is to leverage the answers. The problem can’t be solved without answer choices to leverage, yet the “algebra machine” student will knock his or her head against the computer trying to solve the problem in a vacuum without actively using the answers. More commonly, questions are created in which one approach is extremely difficult or time consuming, while another approach is quite simple (as in this question). 
 
Before you jump headfirst into a problem, always take the time to consider what approach will work best. You will not always make the right choice initially, but your instincts will become better and better as you complete more GMAT official practice problems. Remember: You can’t be a one-trick pony on this test if you want to score highly!