GMAT Challenge Question
A Data Sufficiency question consists of a question and two statements of data. You must decide whether the statements provide sufficient data to answer the question. Success requires a clear understanding of the directions and how to eliminate answers efficiently.
So if today were Test Day, how would you do?
Try this Data Sufficiency question and find out.
If b and c are integers, is bc odd?
(1) b = c
(2) 3b+ 3 is odd
(A) Statement (1) by itself is sufficient to answer the question, but statement (2) by itself is not.
(B) Statement (2) by itself is sufficient to answer the question, but statement (1) by itself is not.
(C) Statements (1) and (2) taken together are sufficient to answer the question, even though neither statement by itself is sufficient.
(D) Either statement by itself is sufficient to answer the question.
(E) Statements (1) and (2) taken together are not sufficient to answer the question, requiring more data pertaining to the problem.
And the answer is...
We can use the strategy of Picking Numbers to solve this question. With the method of Picking Numbers, all 4 incorrect answer choices must be eliminated because sometimes one or more incorrect answer choices will work for the particular values that we select. Let's let a = 6 and b = 3. Then a2 - b2 = 62 - 32 = 36 - 9 = 27. Looking at the answer choices, 27 is not a multiple of 6, 8, 10, or 12, which are the numbers in answer choices (A), (B), (D), and (E), respectively. So choices (A), (B), (D), and (E) can be eliminated. Now that all 4 incorrect answer choices have been eliminated, we know that choice (C) must be correct.
Step 1: Analyze the Question Stem
This is a Yes/No question testing knowledge of number properties. We are told that b and c are integers. We want to determine whether there is enough information to answer the question, "Is bc odd?" We can't simplify the statement (it's already quite simple), but we can notice that we are going to need information about both b and c to answer the question. More specifically, knowing both whether b is even or odd and whether c is even or odd will allow you to determine whether their product is odd, so this information will give you sufficiency.
Step 2: Evaluate the Statements
Statement (1): insufficient. If the numbers are equivalent, then b and c are either both even or both odd. Since the product of two even integers is even, and since the product of two odd integers is odd, it is impossible to tell whether bc is odd or even. The question cannot be answered definitively, so statement (1) is insufficient. Eliminate answer choices (A) and (D).
Statement (2): sufficient. If 3b + 3 is odd, then 3b must be even. Since the product of two odd integers is odd, and the product of an odd integer and an even integer is even, it follows that b must be even. Then bc must be even, regardless of whether c is even or odd. The question can be answered definitively, so the statement is sufficient. Answer choice (B) is correct.
If you were unfamiliar with odd/even number properties rules, you could have still solved this question using Picking Numbers, though not as quickly.