If y is negative, what is the value of x ?

Statement 1: \(x+y = -|y|+x\). As \(y\) is negative hence \(y = -|y|\). So adding same value \(x\) to both sides of the equation will not change the value of the Equality \(y = -|y|\). Hence \(x\) can be any real number. Insufficient

Statement 2: Cannot be solved as we have two variable and one equation. Hence Insufficient

Combining 1 & 2. we cannot find the value of \(x\) as we have only one equation and two variables. Hence Insufficient

Option E

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.

There 2 variables and 0 equation. Thus we need 2 equations to solve for the variables; the conditions provide 2 equations, so there is high chance that (C) will be the answer.


Condition 1) & 2)

\(x + y = -(|y| - x)\) is equivalent to \(x+y = -(-y-x)\) since y is negative.
Then we have \(x + y = x + y\).
We don't have any equation.

The only equation \(x - y = 2\) from the condition 2) is not sufficient.

Both conditions together, they are not sufficient.

Normally for cases where we need 2 more equations, such as original conditions with 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, we have 1 equation each in both 1) and 2). Therefore C has a high chance of being the answer, which is why we attempt to solve the question using 1) and 2) together. Here, there is 70% chance that C is the answer, while E has 25% chance. These two are the key questions. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer according to DS definition, we solve the question assuming C would be our answer hence using 1) and 2) together. (It saves us time). Obviously there may be cases where the answer is A, B, D or E.