SAT Math Multiple Choice Practice Question 85: Answer and Explanation
19. Four consecutive even integers are written down. Which of the following statements must be true?
A. The average (arithmetic mean) of the numbers is even.
B. The median of the numbers is even.
C. The sum of the numbers is 21/2 times the largest number.
D. The median is not one of the numbers on the list.
E. The largest number on the list is more than twice as large as the smallest.
Correct Answer: D
D. To begin this problem, I'll try using 2, 4, 6, and 8 as my numbers to see what happens. Their average is (2 + 4 + 6 + 8) ÷ 4 = 20 ÷ 4 = 5, which isn't even, so Choice (A) is false. The median is the middle number, but because there are four numbers in the list, you have to average the two numbers closest to the middle. Here, those numbers are 4 and 6, so the median is also 5, which makes Choice (B) false, too. Now, I'm going to skip to Choice (D) for a moment because it also deals with the median. Notice that whatever four numbers I use for my list, I'll always have to do the same thing as I just did before: average the two middle numbers, which will give me a number that isn't on the list. Therefore, Choice (D) is the answer because it's always true. You may be wondering about Choices (C) and (E). They're true for the list 2, 4, 6, 8, but they aren't always true. For example, if you choose 10, 12, 14, and 16 as your numbers, Choices (C) and (E) are false.
When you try to solve a problem with an example, as you did in Question 13, there's always a danger that what works for your example won't work for someone else's. Be on the lookout! If you have time, try out two examples to make sure your answer works for all examples — and isn't specific to yours.