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.
If each pencil is either 23 cents or 21 cents, how many 23 cent pencils did Martha buy?
(1) Martha bought a total of 6 pencil.
(2) Total value of pencils Martha bought was 130 cents
Most test-takers start the problem by taking x and y as the number of 23-cent and 21-cent pencils bought by Martha.
From the first statement they write the equation x + y = 6 . Since based on this alone, x cannot be calculated, they move on to the second statement.
Seeing that they can form another equation , 23x + 21y = 130, they choose option C since by solving both of these equations they can get the value of x.
The big mistake with this approach is not evaluating whether Statement (2) alone can be used to solve the question; on closer observation it is revealed that it can.
23x + 21y = 130 is possible only if x = 2 and y = 4; the best way to go about it is to substitute the values for x starting from 1 and it will be seen that this is the only combination possible. This is a classic DS trap!
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.