In a previous post, we had discussed how the GMAT® does not really test formulae but logic. Along with logic, higher level GMAT problems test conceptual clarity. Such problems can be solved in almost no time, provided you know the concepts, and will leave you with time to solve the time-taking word problems. The GMAT® question below is a very good example of the same.

DIRECTIONS: Each data sufficiency problem below consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of counterclockwise), you are to option

A if statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;
B if statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;
C if BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient;
D if EACH statement ALONE is sufficient to answer the question asked;
E if statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Are at least 10% of people who are 65 and older employed?

(1) 11.3% of population is 65 or over.
(2) Of those 65 and older, 20% of men and 10% of women are employed.

From Statement (1), we can make no deduction. Test-takers usually read statement (1) and (2) and tend to assume that both statements are required to answer the question.

But a conceptual understanding of averages will tell you that if 20% of the men and 10% of the women are employed then for men and women together the number of people employed will definitely be greater than 10%.

For example if you are mixing two solutions, one with 10% water and one with 20% water, the combined solution will have a water concentration of between 10% and 20%, it can never be less than 10% and it will never be greater than 20%. To put it differently, the average for any set of values will always lie between the least and the maximum values in the set.

For test-takers with a high-level of conceptual clarity, this problem will take less than 45 seconds to solve. It is problems such as these that will ensure that you are able to comfortably solve the 37 questions on the GMAT® Quantitative section in 75 minutes.