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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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

Let's let the set be {1, 2, 3, 4, 5}. We see that the mean = 3 and the median = 3 also. Now let's analyze the answer choices.

We can skip choices A, B, and C since multiplying, adding and subtracting a constant to each number in the set will definitely change the average and median in the set (unless the median is 0). Let's look at choice D.

Under the conditions in choice D, the set becomes {-7.2, -6.2, -5.2, 12.2, 13.2}. We see that the new median is -5.2, which is not the same as the original median of 3. So D is not correct either.

Under the conditions in choice E, the set becomes {6, 7, 3, 9, 10}. We see the new median is 7, which is not the same as the original median of 3. So E is not correct either.

Answer: None