ajit257 wrote:

What is the area of rectangular region R ?

(1) Each diagonal of R has length 5.

(2) The perimeter of R is 14.

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.

A rectangular has 2 variables.

Since we have 2 variables and 0 equations, C is most likely to be the answer and so we should consider 1) & 2) first.

Conditions 1) & 2)

We have a^2 + b^2 = 5^2 = 25 from the condition 1).

We have 2(a+b) = 14 or a+b=7 from the condition 2).

2ab = (a+b)^2 - (a^2+b^2) = 7^2 - 25 = 49 - 25 = 24

Thus the area of the rectanglular ab is 12.

Therefore, C is the answer.

Regarding VA method for geometry, we can count the number of variables for geometry questions as follows.

A circle has 1 variable.

A triangle has 3 variables.

A square has 1 variable.

A rectangle has 2 variables.

A rhombus has 2 variables.

A parallelogram has 3 variables.

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.

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