In a DS question where a value is required as an answer, sometimes, one may have to go till the very end to find an actual answer, and that’s where it can go either ways. You may end up learning a lot from the question, but you may also take some extra time in solving the question.
This is one such question. To find the value of the expression, we will have to use Algebra to solve the resulting equations and find values for the variables, which will give us our answer.
Clearly, the individual statements, I and II, when taken alone are insufficient. This is because they end up expressing the variable y in terms of x, but this doesn’t give us an equation to solve.
Answer options A, B and D can be eliminated. Possible answer options at this stage are C or E.
When we combine the statements I and II, we can say,
x (x-3) (x+3) = -5x. Simplifying this, we have, \(x^3\) -4x = 0, which gives us x (x-2) (x+2) = 0.
Substituting the value of y from statement I in the question stem and simplifying, we get,
2 x (x-2) (x+2). Since x (x-2) (x+2) = 0, the value of the expression = 0.
Substituting the value of y from statement II in the question stem and simplifying, we get,
\(x^3\) – 4x = 0. Clearly, we have already seen that this expression gives us 0.
This means, regardless of which statement we use, we get a unique value for the expression i.e. 0.
The correct answer option is C.
Hope this helps!
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Crackverbal Prep Team
www.crackverbal.com