I was hanging out with a friend of mine the other day. She is a graduate student, and she asked me a question that she had come across during her research:
“A bat and a ball cost a dollar and ten cents in total. The bat costs a dollar more than the ball. How much does the ball cost?”
If you get it wrong, by the way, you’re in good company; this question was asked of a random sample of Princeton undergrads and University of Michigan undergrads, and roughly half of each group got the question wrong. I was totally fascinated by this result, because it really opened my eyes to how the GMAT can trick people so consistently with seemingly simple questions. The quant section isn’t hard because the math is confusing; it’s hard because the language is confusing. The corollary here is that you can’t study for GMAT quant just by studying formulas; you really need to study language as well.
So let’s study the language in the above problem. To do so, it’s important to realize how humans process information; we try to organize information as we take it in. Our brains are pretty amazing machines this way, but sometimes they get us into trouble. For instance, we hear “A bat and a ball cost a dollar and ten cents in total” and we (correctly) think, “This question is probably about the individual cost of either the bat or the ball.” We’ve created a knowledge gap that we want desperately to fill. Then we hear “The bat costs a dollar,” and we automatically translate that to “the ball must therefore cost the remaining ten cents, because the first sentence refers to a dollar and ten cents – two separate things.” We also probably know now that the question will ask about the price of the ball. In fact, that’s really the only information we care about at this point since we know everything else. And, in the end, the question asks exactly this, so our brains are satisfied.
Do you see the tricks yet?
The modifier “more than the ball” critically alters the meaning of “The bat costs a dollar” – it turns an absolute into a comparison. But because it comes mid-sentence, our brain registers it as unimportant, especially since we feel at this point that we have all the information we need to solve the problem. Furthermore, because the phrase “a dollar and ten cents” sounds like two separate things, we assign the dollar to one object and the ten cents to another object. If instead of $1.10, the question had said $3, it would be very easy to solve.
Ever since my friend told me this question, I’ve found several GMAT problems where the trap answer hinges on skipping a modifier, two sentences that look similar but are slightly different, or some other type of misreading. Make sure that when you read through a GMAT problem, you try and register all the information available before you start combining the various pieces to solve the problem!
By the way, the correct answer is 5 cents.
To read more about the original research, go to: