The GMAT has a lot of hard questions. Last year, one of the highest-scoring people who ever took the test showed us five of the hardest problems. Now, you’re probably not going to see these exact questions on the test, but you could see the same type of question. It’s important when prepping for the GMAT to be well prepared for every type of problem. Here are five of the hardest problems ever seen, and how to tackle them:

Question 1:

A shelf contains hardcover and paperback books of either fiction or nonfiction. How many books are on the shelf?

1. Two-thirds of the books are fiction and one-quarter of the books are hardcover.
2. Fewer than 30 books are paperback and more than 10 are nonfiction.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.

C. Both statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient to answer the question asked.

E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Correct Answer: C.

This question focuses on how much information you need to solve a problem, a critically-important part of making decisions. As an executive, you need more than the ability to make a decision – you need to know if you actually have enough information to base your decision on, or if you need to learn more before you make your choice.

Part of finding the solution to this problem involves trial-and-error, determining whether or not the question can actually be answered based on the information provided. Remember, the right answer may not be the first thing you think of, so study the question instead of answering based on your gut feelings. Many test questions are written specifically to weed out applicants who don’t take the time to carefully consider them.

Question 2:

It is no surprise that Riyadh, the Saudi capital where people revere birds of prey and ride camels regularly, is home to the world’s largest hospital for falcons, a place where falcons from all over the world are treated in operating rooms, an ophthalmology department, and a pox area, and to the largest veterinary clinic for desert mammals, a place where camels and other desert species are expertly cared for .

A. an ophthalmology department, and a pox area, and to the largest veterinary clinic for desert mammals, a place where camels and other desert species are expertly cared for.

B. an ophthalmology department, a pox area, and the largest veterinary clinic for desert mammals, where camels and other desert species are expertly cared for.

C. an ophthalmology department, to a pox area, and to the largest veterinary clinic for desert mammals, a place where camels and other desert species are expertly cared for.

D. to an ophthalmology department, and to a pox area and the largest veterinary clinic for desert mammals, a place where camels and other desert species are expertly cared for.

E. an ophthalmology department and a pox area, and the largest veterinary clinic for desert mammals, a place where camels and other desert species are expertly cared for.

Correct Answer: A.

We’re used to thinking of sentences as addressing one subject, but a careful reading shows that the sentence in question is dealing with two main subjects instead. This detail throws off most of the people who read it, since they immediately try to categorize the question into a single easily-understood list of concepts. When reading the questions, be sure to carefully consider their meaning and avoid jumping to conclusions.

Question 3:

How many prime numbers n exist such that 90 < n < 106 and n is a factor of 99999919?

A. Zero

B. One

C. Two

D. Three

E. More than three

Correct Answer: C.

This problem assumes you have a thorough understanding of basic algebra, including concepts, terminology, and how to solve problems. The word ‘factor’ is a key part of the question, and leads to the conclusion that either multiplication or division are involved. Division can be easily ruled out (because none of the normal techniques for finding the answer work), which means you have to address it through multiplication. Once again, the real secret to answering this question is figuring out what it’s actually asking.

Question 4:

Among the 100 most profitable companies in the US, nearly half qualify as “socially responsible companies,” including seven of the top ten most profitable on that list. This designation means that these companies donate a significant portion of their revenues to charity; that they adhere to all relevant environmental and product safety standards; and that their hiring and employment policies encourage commitments to diversity, gender pay equality, and work-life balance.

Which of the following conclusions can be drawn based on the statements above?

A. Socially responsible companies are, on average, more profitable than other companies.

B. Consumers prefer to purchase products from socially responsible companies.

C. It is possible for any company to be both socially responsible and profitable.

D. Companies do not have to be socially responsible in order to be profitable.

E. Not all socially responsible companies are profitable.

Correct Answer: D.

This is a trick question, designed to manipulate you into giving a wrong answer by encouraging your emotions to take charge. Future MBAs are, for the most part, socially responsible individuals who are inherently biased towards both social responsibility and profitability, and this question tries to lead you to that choice. However, careful reading of the text provided (which is the only thing applicants should base their answers on) shows that the correct answer is actually D.

To avoid getting caught by these types of traps, try to set your biases aside the moment you read anything that sounds emotionally appealing. Chances are that’s a trap designed to trick you into making the wrong decision, and companies want managers who know how to avoid poor, emotion-based responses.

Question 5:

An auto-assembly plant performs six functions with each frame that arrives: add axles, add wheels to the axles, install the windshield to the frame, install the instrument panel, install the steering wheel, and install the interior seating. Once those six tasks are performed, each car goes to a separate building for finishing touches. If these tasks can be arranged along a linear assembly line in any order, except that the axles must be installed before the wheels can be added, how many ways can the assembly line be arranged?

A. 120

B. 240

C. 360

D. 480

E. 720

Correct Answer: C.

This isn’t a formula problem; it’s a logic problem disguised as a formula problem, and the answer is actually quite easy once you start to look at it from another direction. In this case, you can recognize that any given order either does or doesn’t have the wheels put on before the axles, which leads to the correct conclusion that half of the possible variations are workable.

What it all comes down to

As pointed out on the page with the sample questions, the main thing the GMAT is testing is your ability to identify and solve problems. It’s not really about the formulas you’ve memorized or your ability to recite facts. It’s about the way you think and approach problems. If you focus on building up these skills, chances are your final score on the test will be measurably higher.
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