In the previous post we saw how Data Sufficiency questions on the GMAT can be deceptively tricky in that they lure test-takers into choosing Option C. Let us have a look at another Data Sufficiency question that makes test-takers commit the same error.
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.
The difference between Mary and Jim’s salary was twice the difference between Mary and Kate’s. If Mary had the highest salary, what was the average of the three?
(1) Jim’s salary was $30,000
(2) Kate’s salary was $40,000
Most test-takers start the problem by taking M, J & K as the salaries of the three individuals and they form the equation : M – J = 2 (M – K).
They look at the two statements and decide that since from the two statements they are getting the values of M and K, they can use the equation above to calculate the value of J. Once they have all the three salaries, they can calculate the average salary, hence , C!
The first step to cracking Data Sufficiency questions is to precisely define what you need? In this case what you need to determine is (M+J+K)/3.
What do you have? M – J = 2 (M – K).
You need to evaluate the equation above (what you have) , to see what you really need to get the average or (M+J+K)/3.
If we expand M – J = 2 (M – K), we get M + J = 2K. If we substitute this in (M+J+K)/3, we realize that it becomes equal to K and thus all you need to know the average is Kate’s salary and hence Statement (2) alone is sufficient to solve the question!
Another way of visualizing this problem is using a number line. Since M is the highest, on a number line M , K & J will be three points which are equidistant from each other and in that order (since the difference between M & K is twice that of the difference between M & J)
M K J . So K will be exactly between M & J and hence the average!
So whenever option C seems the very obvious choice, beware! Ensure that it cannot be solved by either statement alone before you jump to the conclusion that both statements are required.