BTGmoderatorDC wrote:In a set of five consecutive integers, which of the following must change the average of the set without changing its original median ?
A. Multiplying each of the numbers in the set by 6.
B. Adding 10 to each of the numbers in the set.
C. Subtracting 3.5 from each of the numbers in the set.
D. Adding 8.2 to the 2 largest numbers and subtracting 8.2 from the 3 smallest numbers in the set.
E. Adding 5 to the 2 largest and to the 2 smallest numbers in the set.
OA E
Source: Princeton Review
Say the five consecutive integers are 1, 2, 3, 4 and 5. Thus, we have Median = 3 and Mean = 3. We have to choose an option that will change the mean but not the median.
Let's take each option one by one.
A. Multiplying each of the numbers in the set by 6.
Number would be 6, 12, 18, 24, and 30. New mean = 18; median = 18 ≠3. Incorrect option.
B. Adding 10 to each of the numbers in the set.
Number would be 11, 12, 13, 14, and 15. New mean = 13; median 13 ≠3. Incorrect option.
C. Subtracting 3.5 from each of the numbers in the set.
Same as option B, mean as well as, the median will change, Incorrect option.
D. Adding 8.2 to the 2 largest numbers and subtracting 8.2 from the 3 smallest numbers in the set.
It should be 'larger numbers' and 'smaller numbers.'
Number would be -7.2, -6.2, -5.2, 12.2 and 13.2. New mean = 1.36; median -5.2 ≠3. Incorrect option.
E. Adding 5 to the 2 largest and to the 2 smallest numbers in the set.
Number would be 6, 7, 3, 9 and 10. Arranging the numbers in ascending order, we have 3, 6, 7, 9 and 10. New mean = 7; median 7 ≠3. Incorrect option.
No option seems to be correct. Is there any typo?
The correct answer:
None
Hope this helps!
-Jay
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