Data Sufficiency

There are 10 numbers, 70, 70, 80, 80, 80,...100. If each of the smallest 5 numbers plus x and each of the largest 5 numbers minus y, what is the difference between the average (arithmetic mean) of the original 10 numbers and the average (arithmetic mean) of the changed 10 numbers when x>y?

1) x+y=10
2) x-y=4


* A solution will be posted in two days.

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

There are 10 numbers, 70, 70, 80, 80, 80,...100. If each of the smallest 5 numbers plus x and each of the largest 5 numbers minus y, what is the difference between the average (arithmetic mean) of the original 10 numbers and the average (arithmetic mean) of the changed 10 numbers when x>y?

1) x+y=10
2) x-y=4

Modify the original condition and the question, suppose sum of the first five numbers S1 and the last five numbers S2. It becomes [(S1+5x)+(S2-5y)]/10-(S1+S2)/10=5(x-y)/10 and you only need to know x-y. Therefore, the answer is B.


� Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions.