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

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