shahparth1984 wrote:
The rate of smoking, globally, is higher now than ever before. In fact, 20% more people smoke today than did 20 years ago. In the nation of Patrio, 20% of people smoke; in Paisi, 25%. And in the last twenty years, the number of people who smoke increased by 13% in Kokua and 27% in Kappa.
Which of the following conclusions can most properly be drawn from the information above?
(A) There are more smokers in Paisi than in Patrio.
(B) There were fewer smokers in Kappa twenty years ago then there are in Paisi today.
(C) The world's population is less than 120% of its value 20 years ago.
(D) The average rate of smoking in any of the world's countries must be at least 13%.
(E) At no point over the last 20 years was the world's smoking rate less than 13% below the rate 20 years ago.
OFFICIAL EXPLANATION:
Reading the question: this prompt is not quite like any we've seen so far, in that it presents statistics and no argument. This setup is perfect for proof by stronger terms: the conclusion that is "most properly drawn" will be one that must be drawn--in other words, the answer choice that must be true. We can head straight to the answer choices to establish that proof.
Logical proof: first, must (A) be true? No; we are given only percentages, not numbers, and we have no way of inferring numbers. We could have a case in which Paisi's population is very, very small. So (A) is out. Must choice (B) be true? No; these two countries are mentioned in different facts that remain unconnected. It could be that Paisi is very, very small and Kappa is very, very big. Skipping (C) for a moment, we can quickly knock out (D) and (E) also by analysis by cases: we can imagine different cases for countries that haven't been mentioned, or years that haven't been mentioned, and that data could diverge wildly or not at all and still leave the above true.
We're left with (C). Must (C) be true? In the prompt, we have that 20% more people smoke than 20 years ago. Also, the first sentence says that the rate is higher than ever before. Combining them, say the population 20 years ago was 100, and x% of them smoked, which is 100x people. Today, the number of people that smoke is 1.2(100x). But the rate of smoking now is x or greater ("higher than ever before"), meaning that 1.2(100x) divided by the current population is greater than or equal to x:
\(\frac{1.2(100x)}{P} \geq x\)
Multiplying both sides by P and dividing both sides by x, we have:
\(1.2(100) \geq P\)
Indeed, today's population P can be no greater than the population of 20 years ago, which we had picked to be 100 but could have left as a variable. Here we used a technique that is common in GMAT Problem Solving: when working with percentages, try assuming a total value of 100 to make your line of reasoning more concrete.
The correct answer is (C). _________________