avgroh wrote:
Bunuel,
Could you please help with interpreting statement #2?
Thanks
Hi
avgroh,
Let's assume three numbers {a, b, c} arranged in ascending order. In this case b will be the median.
Statement-IISt-II tells that the sum of these three number is equal to 3 times one of the numbers. Let's take all the possible cases:
1. a + b + c = 3a i.e. 2a = b + c. However we know that a > b and a > c, therefore 2a > b + c. Thus we can reject this case.
2. a + b + c = 3c i.e. 2c = a + b. However we know that c < a and c < b, therefore 2c < a + b. Thus we can reject this case too.
3. a + b + c = 3b i.e. 2b = a + c. We know that b < a but b > c, thus this is the only possible case.
Solving this would give us b = (a + c)/2 i.e. b is the mean of a & c. Since the only other number in the set is b, we can say that b is the mean of the set {a, b, c}.
As b is also the median of this set we can definitely say that mean of the set = median of the set.
Hence st-II is sufficient to answer the question.
Statement-IAlso adding the explanation for St-I here: St-I tells us that the range of 3 numbers is twice the difference between the greatest number and the median.
For the set {a, b, c} arranged in ascending order, range would be the difference between the greatest and the smallest number i.e. st-I tells us that a - c = 2(a -b) i.e. b = (a + c)/2 which again tells us that b is the mean of the numbers a & c. Since the only other number in the set is b, we can say that b is the mean of the set {a, b, c}.
As b is also the median of this set we can definitely say that mean of the set = median of the set.
Hence st-I is sufficient to answer the question.
Hope this helps
Regards
Harsh