Bunuel
A rectangle is 40 inches long. What is its area?
(1) Its perimeter is 140 inches.
(2) The length of the diagonal is 50 inches.
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.
In geometry, a rectangle has two variables which are a length \(l\) and a width \(w\).
From the original condition, since we have two variables a length \(l\) and a width \(w\) and we know the length \(l = 40\), D is most likely to be the answer.
Condition 1)
\(2(l+w) = 140\)
\(l+w = 70\)
\(w = 30\)
The area is \(l*w = 40*30 = 1200\).
The condition 2) is sufficient.
Condition 2):
\(l^2 + w^2 = 50^2\)
\(1600 + w^2 = 2500\)
\(w^2 = 900\)
\(w = 30\)
The area is \(l*w = 40*30 = 1200\).
The condition 2) is sufficient too.
Therefore the answer is D.
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.