ziyuen wrote:

There are 5 integers such that the difference of the biggest number and the median is 3. Is the average (arithmetic mean) of the integers smaller than the median?

1) The median of the 5 integers is 16.

2) The difference of the median and the smallest number is 8.

With 5 integers, median will be the middle number.

5 integers: ______, _______, M, ______, M+3

Question: Is the average smaller than M?

In other words, from M, is the deviation of integers smaller than M more than the deviation of integers greater than M?

Since the greatest integer is M+3, we know that the maximum deviation of numbers greater than M, from M is 3 + 3 = 6 (in case both numbers are M+3).

1) The median of the 5 integers is 16.

Tells us nothing about the deviation of integers.

Not sufficient.

2) The difference of the median and the smallest number is 8.

The smallest number has a deviation of 8 from M. This means that the deviation of numbers smaller than M IS CERTAINLY MORE THAN the deviation of numbers greater than M (which is 6).

Sufficient.

Answer (B)

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Karishma

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