Data Sufficiency - Quant/Math - CAT 2008

The question for the day is a data sufficiency question. One important thing about Data Sufficiency questions is that more often than not these questions take you about 30 seconds to crack them. And it generally does not involve any difficult calculations which tend to take most of the time when you solve a problem. Here the question is about whether you can solve the problem with the information given and NOT about actually solving the problem.

In this question, there is a question statement which is followed by two statements. You have to decide whether the information provided in the two statements is sufficient for answering the question.

Mark 1

If the question can be answered by using one of the statements alone, but cannot be answered by using the other statement alone.

Mark 2

If the question can be answered by using either statement alone.

Mark 3

If the question can be answered by using both statements together, but cannot be answered by using either statement alone.

Mark 4

If the question cannot be answered even by using both the statements together.

Question:

Is x a positive number?

1. x² = 2x
2. is a real number.

Solution:

The question is to find out whether x is a positive number or not? If you can answer this question conclusively either with an Yes or with a No, then you have the answer.

Let us evaluate what statement A has got to offer.
Statement A: x² = 2x.
=> x² - 2x = 0 => x(x-2) = 0 => x = 0 or x = 2. From statement A, we get the value of x to be either ‘0' (which is neither positive nor negative) or ‘2' which is positive. Therefore, we cannot conclusively decide whether x is positive or not from the information provided in statement A.

Please do not make the mistake of cancelling x on both sides of the equation and get x = 2 alone as the solution. You will go wrong.

Statement B: is a real number. There ‘x’ which is the ()² will be a real number too which will be positive if . If = 0, which is also real, then x = 0. Therefore, from statement B, we again come to the same conclusion that either x is positive or x is ‘0'.

Using Statement A and Statement B: Combining the fact that x² = 2x and that is real does not lead us to any new conclusion other than what we have concluded using the both the statement independently.

Therefore, both Statement A and Statement B are not sufficient to answer the question conclusively and Choice (4) is the correct answer.

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