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Re: Set S contains the following numbers 10, 14, 19, 27, 36, 49, 67, 70 [#permalink]
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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.
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Re: Set S contains the following numbers 10, 14, 19, 27, 36, 49, 67, 70 [#permalink]
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debbiem wrote:
set s contains the following numbers 10, 14, 19, 27, 36, 49, 67, 70,94. It was found that Mark had inadvertently interchanged the digits of one of the numbers. Steve, in charge of statistics, rectified this error, and as a result mean and median were changed and the shift in mean was of 5.
Whats the number that was incorrectly noted?

A. 36
B. 49
C. 94
D. 27
E. 41



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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Re: Set S contains the following numbers 10, 14, 19, 27, 36, 49, 67, 70 [#permalink]
Dbalks wrote:
This is a little cumputational for GMAT math, but average the orignal set of numbers.

10+14+19+27+36+49+67+70+94 = 386
386/9 = 42.888

New mean had to be either 37.888 or 47.888
A 5 point swing means you need to either add 5*9 - 45 to the original total of 386 or subtract 45 from it.

What number when transposed has a difference of 45. 27 does.

72-27 = 45

If you are familiar enough with the concept of mean, you can skip all the nonsense above and just see there is 9 terms that go into the average, and if you mean changes by 5 you know that the total of all the numbers must have changed by 45 (9*5). Then guess and check to see which number when transposed yields a difference of 45.

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. :)
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Re: Set S contains the following numbers 10, 14, 19, 27, 36, 49, 67, 70 [#permalink]
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Re: Set S contains the following numbers 10, 14, 19, 27, 36, 49, 67, 70 [#permalink]
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