fozzzy wrote:
Is the standard deviation of the numbers X, Y and Z equal to the standard deviation of 10,15 and 20?
(1) Z - X = 10
(2) Z - Y = 5
Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Since we have 3 variables and 0 equations, E is most likely to be the answer and so we should consider 1) & 2) first.
The distance 10 and 20 is 10 and the distance 15 and 20 is 5.
The distance X and Z is 10 and the distance Y and Z is 5.
Since the distributions of two data sets are same, their standard deviations are same.
Both conditions 1) & 2) are sufficient.
Since this is an integer question (one of the key question areas), we should also consider choices A and B by CMT 4(A).
Condition 1)
Since we don't know anything about Y, this is not sufficient.
Condition 2)
Since we don't know anything about X, this is not sufficient.
Therefore, C is the answer.
Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.