# Critical Reasoning – The Statistics Question 1

Critical Reasoning questions on the GMAT® , often have questions that have some stats. The most important thing to remember is that stats-based questions have stats-based answers or answers that require an interpretation of the stats. So answer options that give explanations that do not have a statistical implication can easily be ruled out.

Let us look at the question below.

EASY
Economist: On average, the emergency treatment for an elderly person for injuries resulting from a fall is \$11,000. A new therapeutic program can significantly reduce an elderly person’s chance of falling. Though obviously desirable for many reasons, this therapeutic program costs \$12,500 and thus cannot be justified.

Which of the following, if true, most seriously undermines the conclusion of the argument?

(A) Among the elderly people who had followed the programs for only a few months, the number of serious falls reported was higher than it was for people who followed the program for its recommended length of one year.
(B) Falls resulting in serious injures are less common among elderly people living in nursing home than they are among elderly people who live alone at home.
(C) A frequent result of injuries sustained in falls is long-term pain, medication for which is not counted among average per person costs of emergency treatment for elderly people’s injuries from such falls.
(D) The new therapeutic program focuses on therapies other than medication, since over-medication can cause disorientation and hence increase the likelihood that an elderly person will have a serious fall.
(E) A significant portion of the cost of the new therapeutic program is represented by regular visits by health care professionals, the costs of which tend to increase more rapidly than do those of other elements in the program.

The conclusion is clearly based on a stat — the cost of the new program is more than the cost of emergency treatment. This can be weakened only by an option that invalidates this stat or shows that it is erroneous.

The trap options are always seemingly correct. Option (D) for example argues that the new program is superior and tends to attract test-takers to it, but the last line of the passage actually admits that the new program might be superior — though obviously desirable for many reasons — but still cannot be justified on costs grounds.

So the correct option should show that the new therapeutic program will in fact be cheaper than the existing emergency treatments (over the shorter or longer-term). The only option that does this is C, which shows that the cost of the new therapeutic program that r- it ignores the cost of and will be higher over the longer-term.

Option E also compares the costs of the two programs but only to show that the new program’s cost is likely to increase over time, as a result strengthening and not weakening the argument.

When we speak of stats questions, it need not only mean questions with numbers in them; it can also mean questions which involve the increase or decrease in a particular metric — per capita income, ratio of women enrolling in a particular program or occupancy rates in hotels

MEDIUM
Demographers doing research for an international economics newsletter claim that the average per capita income in the country of Kuptala is substantially lower than that in the country of Bahlton. They also claim, however, that whereas poverty is relatively rare in Kuptala, over half the population of Bahlton lives in extreme poverty. At least one of the demographers’ claims must, therefore, be wrong.

The argument above is most vulnerable to which of the following criticisms?

(A) It rejects an empirical claim about the average per capita incomes in the two countries without making any attempt to discredit that claim by offering additional economic evidence.
(B) It treats the vague term “poverty” as though it had a precise and universally accepted meaning.
(C) It overlooks the possibility that the number of people in the two countries who live in poverty could be the same even though the percentages of the two populations that live in poverty differ markedly.
(D) It fails to show that wealth and poverty have the same social significance in Kuptala as in Bahlton.
(E) It does not consider the possibility that incomes in Kuptala, unlike those in Bahlton, might all be very close to the country’s average per capita income.

The above question is comparing the metric, average per capita income, of two countries Kuptala (K) and Bahlton (B), with the former having a very low per capita income compared to the latter. Despite this, unlike K, B has a high rate of poverty. The argument concludes that both the stats cannot be correct at the same time.

For anyone comfortable with statistics, this would be a very straightforward question that does not even require answer options.

The average of a set is not always representative of all the members in a set due to the presence of outliers. For example, in a particular b-school, a few students securing very high salaries can push the average salary of a batch upwards but there might be many students with a salary lower than the average. Whereas in an other school, the average salary might be lower but all students might have salaries in the same range with most students being close to the average.

Even in this question, the same can be true, average is higher in K but many people might not be close to the average, which is what option E states.

Most test-takers tend to view these questions as regular CR questions and end up choosing option B; B is incorrect since while the term “poverty” might have different definitions from the one used in the passage, the same definition is used in the case of both K & B.

Others are tempted to choose C since it sounds mathematical without necessarily understanding what it is saying. C says that the number of people living in poverty in both countries can be the same despite the percentages being different.

That the percentages are different is stated in passage — K has a very low percentage, lets say 1%, and B it is mentioned has almost 50%. That the numbers might be same is besides the point (50% of 10000 and 1% of 500000 are the same). The question is asking for an explanation for the per-capita income and poverty rate both being high at the same time.

In the next post we shall have a look at a few more stats questions that involve clearly understanding the terms defined in the passage.