parkhydel wrote:
If the average (arithmetic mean) cost per sweater for 3 pullover sweaters and 1 cardigan sweater was $65, what was the cost of the cardigan sweater?
(1) The average cost per sweater for the 3 pullover sweaters was $55.
(2) The most expensive of the 3 pullover sweaters cost $30 more than the least expensive.
DS38720.02
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.
Visit
https://www.mathrevolution.com/gmat/lesson for details.
The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.
Assume \(p_1, p_2\) and \(p_3\) are costs with \(p_1 ≤ p_2 ≤ p_3\) for thee different pullover sweaters and c is that of the cardigan sweater.
Then we have \(\frac{{p_1 + p_2 + p_3 + c} }{ 4} = 65\) or \(p_1 + p_2 + p_3 + c = 260\).
The question asks the value of \(c\).
Since condition 1) tells \(\frac{{p_1 + p_2 + p_3} }{ 3} = 55\) or \(p_1 + p_2 + p_3 = 165\), we have \(165 + c = 260\) or \(c = 96\).
Thus condition 1) is sufficient.
Condition 2)
Condition 2) tells \(p_3 = p_1 + 30\).
Since we don’t know \(p_2\), condition 2) does not yield a unique solution and it is not sufficient.
Therefore, A is the answer.
If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
_________________