How to Solve GMAT Quant Questions Using the Median in a Sequence:
Consider the following question from an Economist GMAT Tutor lesson:
If in a certain sequence of consecutive multiples of 50, the median is 625, and the greatest term is 950, how many terms that are smaller than 625 are there in the sequence?
How to use the median to solve this question
Remember that by definition, the median is equidistant from the first and last values in a sequence.
- Calculate the difference between the last value and median:
- Subtract 325 from the median to get the first value in the sequence:
The multiples of 50 that are smaller than 625 are therefore 300, 350, 400, 450, 500, 550 and 600—a total of 7. Hence, B is the answer.
How to spot the trap in these questions
If you were not paying attention to detail, you may have thought that 625 was a value in the sequence. You could quickly have calculated that there are 13 multiples of 50 between 300 and 950 (a difference of 650). You may have then thought that there would be six multiples of 50 below the median and 6 above the median. In that case you would have answered A.
Note that while 625 is the median of the sequence, it is not actually a value in the sequence. It is the average of the 6th and 7th values in the sequence—the average of 600 and 650. You would recognize this quickly because 625 is not a multiple of 50.
Be particularly careful on test day if you have a tendency to quickly land on answer choices like A. The test makers are often trying to get you to answer questions too quickly. When they are doing that, they will often put the incorrect answer choice right in front of your eyes—Answer A.
This post appeared first on the Economist GMAT Tutor blog.