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Think about the last fight you had with your spouse (or significant other). For me, it was last week. We were driving to meet a friend named Tom at a local coffee shop called Mile Hi Coffee. I didn’t know quite where it was, but I knew the name. Tom had told me the name and approximate location when he set the appointment earlier in the week, and I confirmed it on Google Maps just before leaving the house. Everything was set.

As we were driving, my wife asked me if I’d ever been to Solid Grounds Coffee before. Solid Grounds, I ask? Yeah, where we’re meeting Tom, she said. No, we’re meeting him at Mile Hi Coffee, I argued. No, I’m sure it’s at Solid Grounds, she responded. And a fight ensued.

So, who was “right?” I was 100% sure I was right. She was 100% sure she was right.

Is it possible that were were BOTH right?

In this instance, we were both right! Yet how is that possible? How could two seemingly contradictory viewpoints (and two different coffee shop names) both be correct? What could possibly explain this apparent paradox?

### GMAT Critical Reasoning – “Paradox” Questions

This is the mindset and logical thinking that is necessary to answer “Paradox Questions” on the GMAT Critical Reasoning section. These questions may be worded in a number of different ways, including (but not limited to):

• Which of the following best explains the apparent paradox in the two opinions expressed above?
• Which of the following, if true, contributes most to an explanation of the difference between…?
• Which of the statements below provides the most likely explanation for the two seemingly contradictory statements above?

Just like in my recent argument with my wife, these types of questions present a logical argument that seems on the surface to contain opposing viewpoints that are incompatible. Yet, somehow they are. It’s like two sides of the same coin. If I hold up a coin and ask you to describe what a coin is, you may tell me that it’s shiny and round and made of metal and there’s a picture of someone’s head on it. I might tell you you’re crazy, that I also see a shiny metal object but that the picture is of a building, not someone’s head. You would be certain you’re right. I would be certain I’m right. And it turns out that we’d BOTH be right! The paradox is logically explainable. How? It’s because we’re simply looking at opposite sides of the same coin, of course!

It’s your job to figure out that type of logical explanation for the apparent paradox when you see these types of questions on the GMAT.

With that understanding in mind, try your hand at this sample GMAT critical reasoning question from GMAT Plan for GMAT Verbal:

Steve:            Rick and Harriet, two of my red-haired friends, are irritable. It seems true that red-haired people have bad tempers.

John:            That’s ridiculous. Red-haired people are actually quite docile. Jeff, Muriel, and Betsy — three of my red-haired friends — all have placid demeanors.

Which of the statements below provides the most likely explanation for the two seemingly contradictory statements above?

(A) The number of red-haired people whom Steve knows may be different from the number of red-haired people whom John knows.
(B) The number of red-haired people whom both Steve and John know may not be greater in total than the number of non-red-haired people whom both Steve and John know.
(C) It is likely that Steve or John has incorrectly assessed the temperament of one or more of his red-haired friends.
(D) It is likely that both Steve and John have friends who are not red-haired and yet who have bad tempers.
(E) The examples that Steve uses and the examples that John uses to support their conclusions are likely both valid.

It’s always a good idea to begin by becoming very clear about what the paradox is. Try to summarize it in your own words. You might put it something like this: Steve thinks red-haired people have bad tempers based on empirical evidence concerning two of his friends; John, on the other hand, thinks red-haired people have good tempers based on empirical evidence concerning three of his friends. Both people seem justified in their conclusions, based on their respective evidence. Can they both be right? How?

The key to this paradox lies in recognizing that both people are making representative assumptions — they are choosing selective examples that support their respective intended claims! In this case omitted evidence holds the key to understanding the validity of the argument; each person is simply unaware of evidence known by the other person.

And remember, we must take the underlying presmises as truth. The key to critical reasoning questions usually lies in the assumptions, not the premises. For that reason, then, answer choice A is wrong — the number of red-haired people that one person knows compared to the number the other person knows is irrelevant. In B, the relationship between the number of red-haired people to non-red-haired people that they both know is also irrelevant. Answer choice C attacks the validity of that underlying premise, which is a no-no; we take as given that they’ve assessed their friends’ temperaments correctly, and we’re simply trying to figure out what conclusions we can draw from those premises. So C is wrong. Finally, answer D is almost axiomatic — of course they probably know of friends who are not red-haired and have bad tempers, but this will do nothing to reconcile the contradictory statements. So, that leaves answer choice E, the correct answer. It in essence states what we already pre-determined — that it’s possible they’re simply looking at two sides of the same coin and that based on their respective experiences, they can both be right!

Great job if you got that correct answer on your own. If you didn’t, hopefully you now understand why the answer is what it is, and that you’re better equipped to answer these types of questions in the future.

### Finishing my Story: The “Coffee Shop Paradox”

Brett and Melanie, no longer fighting about coffee shops!

Now, back to my fight with my wife. What could possibly explain how we could both be right in terms of which coffee shop we were supposed to meet Tom at? Let me explain what happened when we finally got to the coffee shop. First, you should know that it was at the exact location provided by Google Maps for where Mile Hi Coffee should be. Yet, sure enough, the big sign above the entryway clearly said: “Solid Grounds Coffee.” So… my wife was right! And so was I. See, earlier in the day, Tom had texted Melanie (my wife) to make sure she knew that Mile Hi Coffee had recently changed its name to Solid Grounds Coffee. It was at the same place, just under a different name. Tom had clearly told me the name Mile Hi Coffee earlier in the week, and yet my wife had updated information that I didn’t have. As in the example above, omitted evidence was the key to reconciling our fight. (By the way, I think Melanie neglected to tell me about Tom’s text just to make sure she won the fight!)

In any event, it’s an important lesson to learn in relationships: If you’re sure you’re right, and your partner is sure she’s right…it’s possible that you’re both right and just looking at two different sides of the same coin.

Just as importantly on the GMAT, this same understanding will better help you to identify and accurately evaluate GMAT critical reasoning questions that ask you to explain an apparent paradox. Remember my fight with my wife, envision a coin with two sides, and apply this mindset to go out and dominate the GMAT!