Set S contains the following numbers 10, 14, 19, 27, 36, 49, 67, 70

Nice way to solve the problem. I confess I was stuck at this problem for very long (over 3 mins) without luck anyway.
I want to know if this is the best way to solve such problems. Calculating the sum and average of 9 numbers might be a little time consuming, although 700-level questions might have such calculations. But I wonder if we will be able to accomplish such a feat within 2 minutes. Even if we were to use the shortcut method of using the concept of the mean, finding 9 differences between the transposed number and the original number would take time. In the worst case scenario, we would have to compute at least 8 differences before we get to the right answer. Of course, with the presence of options, this number would come down to 4. I still wonder if there is another shortcut and more effective way to solve the problem.

Appreciate your solution and approach nonetheless. Congrats for your Kudos.

Even 49 and 94 when reversed can increase/decrease the mean by 5 but they would not affect the Median . Only 27 on reversing will change the Median.

When you find yourself drowning in computation know that there is usually an easier way. For this problem, we know that the average changes by 5. Because there are 9 numbers in the set, the total increases by 9x5 = 45. The only two numbers that change by 45 when you reverse their respective digits is 27 and 94. However when 94 is switched to 49 the median is still 36. When 27 becomes 72, the median shifts to 49. Therefore the answer is 27.

Firstly the NEW median will be 27 or 49...

secondly the change in SUM will be 9*5 = 45, so the difference in number and in reversed order will be 45...
and the reversed NUMBER and actual number should be on either side of the MEDIAN 36..

lets see the choices on these points..

A. 36... reverse = 63 but \(63-36\neq{45}\).... eliminate
B. 49... reverse = 94, and 94-49 = 45, BUT both 49 and 94 lie on the SAME side of 36, so no effect on MEDIAN... ELIMINATE
C. 94... SAME as B.. eliminate
D. 27.... reverse = 72.. 72-27 = 45.. yes and 27 is lesser than 36 and 72 is >36 so median will shift to 49... XORRECT
E. 41.... reverse 14, but \(41-14\neq{45}\).. eliminate

D

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