Data Sufficiency

[GMAT math practice question]

The figure below shows the dimensions of triangle ABC. What is ∠OBI?
1) AB = AC,
2) Point O is the circumcenter and point I is the incenter of triangle ABC.

=>

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.

Since a triangle has 3 variables, E is most likely the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)
Since triangle ABC is an isosceles, we have interior angles ∠ABC = ∠ACB = (1/2)(180 - ∠A) = (1/2)(180 - 36) = 72.
Since O is the circumcenter of triangle ABC, we have ∠OBA = ∠OCA = (1/2) ∠A = (1/2)36 = 18.
Since I is the incenter of triangle ABC, we have ∠IBA = (1/2) ∠ABC = (1/2)72 = 36.
Thus, we have ∠OBI = ∠IBA - ∠OBA = 36 – 18 = 18.

Since both conditions together yield a unique solution, they are sufficient.

Therefore, C is the answer.
Answer: C

In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B, or D. Since E (i.e. conditions 1) & 2) are NOT sufficient when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2) when taken together. Obviously, there may be occasions in which the answer is A, B, C, or D.