PSAT Math Multiple-Choice Question 72: Answer and Explanation

Question: 72

The sum, S, of a set of n consecutive integers is given by the equation S = . What does a + k represent?

• A. The sum of the two least integers
• B. The sum of the least and greatest integers
• C. The sum of the two middle integers
• D. The sum of the two greatest integers

Correct Answer: B

Explanation:

B

The question asks for the meaning of an expression in context. Start by reading the full question, which asks for the meaning of the expression a + k. Then label the parts of the equation with the information given. The question states that S is the sum of a set of consecutive integers, and n is the number of integers in the set. None of the answer choices are clearly inconsistent with the labels, so plug in. Plug in 2, 3, and 4 as the consecutive integers. In this case, S = 2 + 3 + 4 = 9 and n = 3. The equation becomes 9 = (3). Divide both sides of the equation by 3 to get 3 = . Multiply both sides by 2 to get a + k = 6. This is the target, circle it. Plug the correct values into each answer choice to see which one matches the target. Choice (A) becomes 2 + 3 = 5. This does not match the target, so eliminate (A). Choice (B) becomes 2 + 4 = 6. This matches the target, so keep (B), but check the other answers just in case. Choice (C) doesn't work because there is only one middle integer; eliminate (C). Choice (D) becomes 3 + 4 = 7. Eliminate (D). The correct answer is (B).