I’ve written in the past about the GMAT’s tendency to use simple math concepts in the context of a Critical Reasoning question. One instance of this phenomenon is the test’s predilection for incorporating ratios in the Verbal section. It makes sense for the question-writers to do this. If we think about the types of core concepts you’re likely to encounter in your future MBA program: output/worker or price/earnings, etc., simple ratios are inescapable.
Here’s all we need to know:
- If the numerator increases and the denominator remains constant, the ratio will increase.
- If the denominator increases and the numerator remains constant, the ratio will decrease.
From this, we can also intuit that if the ratio doubled and the denominator remained constant, the numerator must have doubled. And if the ratio doubled and the numerator remained constant, the denominator must have been halved. Pretty simple, right? For whatever reason, these concepts tend not to produce any difficulty in the Quantitative section when test-takers are expecting them, but cause all sorts of problems when they crop up in Verbal questions. Let’s see an example.
That the application of new technology can increase the productivity of existing coal mines is demonstrated by the case of Tribnia’s coal industry. Coal output per miner in Tribnia is double what it was five years ago, even though no new mines have opened.
Which of the following can be properly concluded from the statement about coal output per miner in the passage?
A) If the number of miners working in Tribnian coal mines has remained constant in the past five years, Tribnia’s total coal production has doubled in that period of time.
B) Any individual Tribnian coal mine that achieved an increase in overall output in the past five years has also experienced an increase in output per miner.
C) If any new coal mines had opened in Tribnia in the past five years, then the increase in output per miner would have been even greater than it actually was.
D) If any individual Tribnian coal mine has not increased its output per miner in the past five years, then that mine’s overall output has declined or remained constant.
E) In Tribnia the cost of producing a given quantity of coal has declined over the past five years.
As soon as we see “per” we know we’re dealing with a ratio problem. In this case, we’re discussing coal output per miner. As a ratio, or fraction, this can be expressed as follows: Total Coal Output/Total Number of Miners. Further, we know that this ratio has doubled over the last five years. Employing the logic we used earlier, we now know that because the ratio doubled, if the number of miners (the denominator) remained constant, then the coal output (the numerator) doubled. And we also know that if the coal output (the numerator) remained constant, then the number of miners (the denominator) must have been halved. If we recognize this relationship, the correct answer is going to leap out at us.
- This is a restatement of the relationship we’ve already documented – namely that if the denominator remained constant, the numerator must have doubled. Clearly, we’ve got our answer. (But it’s still helpful to evaluate why all the wrong answer choices are incorrect, something you should be doing with every practice problem you attempt.)
- We can’t deduce what any individual coal mine has achieved based on the output per worker of all the mines in aggregate.
- Again, there’s no way to know what the productivity level of any mine might have been, let alone a hypothetical new one.
- If we understand how ratios work, we can see that this is not necessarily true. If the ratio has not increased, there are two possible explanations. First, the numerator has not increased. (This is what’s stated in the answer choice.) Second, the denominator has increased by more than the numerator has increased. Therefore we don’t know that output has declined or remained constant. It could be the case that the number of miners has gone up.
- This is out of scope. We don’t know what’s happened to the cost of producing coal.
The correct answer is A.
Takeaway: You see plenty of ratios in Critical Reasoning, so make sure you understand that when a ratio changes, it means that either the numerator or denominator (or both) has changed. If you treat these questions as simple Quant problems rather than as abstruse Verbal questions, you’re far less likely to be tripped up.