Workbook Wednesdays: Medical Test Answer

The results from yesterday’s GMAT question are in!  See below for a detailed answer:

Question
A medical test for a certain liver enzyme can be given in the morning, in the afternoon, or in the evening; moreover, the result of the test can be low, average, or high. At least three-quarters of low and medium readings are not given in the evening. Sixty percent of exams are given in the morning or in the afternoon, and 20% of exams result in a high reading. What percent of exams given in the evening result in low or medium readings?

(A) 20%
(B) 30%
(C) 40%
(D) 50%
(E) 60%

Answer
The key to this problem is to realize that you can collapse certain categories together. The distinction between low and medium readings does not matter, because we are never given data about just low or just medium readings. Likewise, morning and afternoon tests can be combined, because the given information never distinguishes those times of day. Thus, we only have two categories for each dimension: time of day is either “morning+afternoon” or evening, and result is either “low+medium” or high.
We can now set up a 2×2 table, plus a total row and column (and labels):

We choose 100 for the total of all tests, since we are only dealing with percents. Filling in the table with the given information and completing the total row and column, we get the following:

Since the number of high morning+afternoon exams cannot be less than zero, it must actually be zero. This means that the table fills in this way:

Thus, the percentage of evening exams that do NOT result in a high reading is 20/40 x 100%, or 50%.

The correct answer is (D).