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.
In the rectangular coordinate system, are the points (p,q) and (r,s) equidistant from the origin?
(1) |p| = |q|
(2) |q| = |r| = |s|
We obtain square root [(p-0)^2+(q-0)^2]=square root[(r-0)^2+(s-0)^2], p^2+q^2=r^2+s^2? if we modify the question and the original condition.
There are 4 variables (p,q,r,s) but only 2 equations are given by the 2 conditions, so there is high chance (E) will become the answer.
Looking at the conditions together, from p^2=q^2=r^2=s^2 p^2+q^2=r^2+s^2? --> 2p^2=2p^2, we can answer the question 'yes' and the conditions become sufficient. The answer therefore becomes (C).
For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.
_________________