alimad wrote:
In a certain year, the difference between Mary's and Jim's annual salaries was twice the difference between Mary's and Kate's annual salaries. If Mary's annual salary was the highest of the 3 people, what was the average (arithmetic mean) annual salary of the 3 people that year7
(1) Jim's annual salary was $30,000 that year.
(2) Kate's annual salary was $40,000 that year.
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.
Let \(M\), \(J\) and \(K\) be the salaries of Mary, Jim and Kate, respectively.
We have \(| M - J | = 2| M - K |\), \(M > J\) and \(M > K\) from the conditions of the original questions. And the question asks what is the value of \(\frac{M + J + K}{3}\).
Then we have 3 variables and 1 equation.
Thus C is the answer most likely.
This question is a key question by VA method, since it is related to Statistics. By CMT(Common Mistake Type) 4A, we should check the answer A or B too.
Since \(M > J\) and \(M > K\), we have \(M - J = 2(M-K)\) or \(M - J = 2M - 2K\), which is equivalent to \(M + J = 2K\).
Thus the question asks what is the value of \(\frac{M + J + K}{3} = \frac{3K}{3} = K\).
Condition 1)
From \(J = 30,000\), we can derive the values of \(M\) or \(K\).
Thus this is not sufficient.
Condition 2)
\(K = 40,000\).
This is just the average of \(M\), \(J\) and \(K\) described.
Thus this is sufficient.
Therefore, B is the Answer
Normally for cases where we need 2 more equations, such as original conditions with 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, we have 1 equation each in both 1) and 2). Therefore C has a high chance of being the answer, which is why we attempt to solve the question using 1) and 2) together. Here, there is 70% chance that C is the answer, while E has 25% chance. These two are the key questions. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer according to DS definition, we solve the question assuming C would be our answer hence using 1) and 2) together. (It saves us time). Obviously there may be cases where the answer is A, B, D or E.