This video explains GMAT Interquartile Range questions, review, and answers found on the GMAT Exam.
GMAT Interquartile Range Review [Video Transcript]
In this question, we want to find the range of set A. To find the range, we need to know the largest and smallest number in the set. So, our first step should be to arrange these values in ascending order. Now, the questions tells us that x < y, so we can easily arrange six of our eight terms as follows. Also, if x and y are positive, then 3x + y must be greater than y because we are taking y and adding 3x to it. As such, we can place 3x + y to the right of y. Finally, since x < y, we can conclude that x - y must be negative. Since the other seven values here are positive, x - y must be less than all of them. Now that we have arranged set A in ascending order, we can determine the range. The range is equal to the largest number in the set minus the smallest number. The largest number in the set is 3x + y so from this we will subtract the smallest number which is x - y.When we simplify this, we can see the range from set A is equal to 2x + 2y. So we can now take the target question and rewrite it as, "What is the value of 2x + 2y?" Okay, now let's examine the statements. Statement one tells us that the median of set A is 10. Now since set A has an even number of values, it will have two middle numbers. In these situations, the median will be the average of these two middle values. So the median will be x + y divided by 2, and this we are told is equal to 10. Now does this provide enough information to answer the target question? Yes, it does. Notice that if we take this equation and multiply both sides by 2, we get x + y = 20. And if we multiply both sides be 2 again, we get 2x + 2y = 40. If 2x + 2y = 40, then we can definitely answer the target question. Which means statement 1 is sufficient.Okay, now on to statement two. This tells us that the average of set A is 9. Well, to find the average of 8 values, we need to find their sum and then divide by 8. This we are told is equal to 9. Now, does this provide enough information to answer our target question? Well, to find out, let's first simplify the numerator and then multiply both sides by 8 to get 7x + 3y = 72. Since we cannot use this equation to find the value of 2x + 2y, statement two is not sufficient and our answer is A.