NarendraSure wrote:What is the perimeter of the triangle in the figure above?

1. The side across from interior angle z measures 2
2. 2x > y

Question : Perimeter = ?

Statement 1:The side across from interior angle z measures 2
From the figure we can see that
y = z and y = x
i.e. three angles of triangle are x - x - 2x
i.e. x+x+2x = 90
i.e. x = 45
in which one side is 2 i.e. other sides will be 2 and 2(root2)
i.e. Perimeter = 2+2+2(root2) = 4+2root2

SUFFICIENT

Statement 2: 2x > y
None of the sides of triangle is known hence
NOT SUFFICIENT



Answer: option A

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.

What is the perimeter of the triangle in the figure above?

1. The side across from interior angle z measures 2
2. 2x > y

We get from y=z=x, x+x+2x=180, x=45 and 2x=90, forming a right isosceles triangle.
Hence, aroot(2)a.
There is one variable (a) and 2 equations are given by the 2 conditions, so there is high chance (D) will be the answer.
For condition 1, perimeter=2+2+2root2. This is sufficient
For condition 2, from 2x>y, 2x>x, x>0 and we cannot determine a unique value of the perimeter, so the condition is insufficient and the answer becomes (A).

For cases where we need 1 more equation, such as original conditions with "1 variable", or "2 variables and 1 equation", or "3 variables and 2 equations", we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.