Bunuel wrote:
In a certain set of five numbers the median is 200. Is the range greater than 80?
Say the set is {a, b, 200, c, d}. Question: is d-a>80?
(1) The average (arithmetic mean) of the numbers is 240 --> the sum of the numbers is 240*5=1,200. Now, let's see whether the range can be less than 80, so let's try to minimize the range. The range will be minimized if we maximize a and minimize d. Maximum value of a as well as b is 200 and minimum value of d is c, so our set will be: {200, 200, 200, d, d} --> 600+2d=1,200 --> d=300 --> the range=d-c=300-200=100>80. Sufficient.
(2) Three of the numbers in the set are equal. Clearly insufficient.
Answer: A.
Say the set is {a, b, 200, c, d}. Question: is d-a>80?
(1) The average (arithmetic mean) of the numbers is 240 --> the sum of the numbers is 240*5=1,200. Now, let's see whether the range can be less than 80, so let's try to minimize the range. The range will be minimized if we maximize a and minimize d. Maximum value of a as well as b is 200 and minimum value of d is c, so our set will be: {200, 200, 200, d, d} --> 600+2d=1,200 --> d=300 --> the range=d-c=300-200=100>80. Sufficient.
(2) Three of the numbers in the set are equal. Clearly insufficient.
Answer: A.
why b is clearly insufficient ?