rohitgoel15 wrote:

What is x?

(1) |x| < 2

(2) |x| = 3x – 2

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.

Question

In the original condition, there is 1 variable \(x\) and 0 equation. So you need 1 equation.

Condition 1)

Since it is an inequality, there is no equation. Thus we can't identify the variable x and this is not sufficient.

Condition 2)

i) \(x \ge 0\)

\(|x| = 3x - 2\) is equivalent to \(x = 3x - 2\) or \(2x - 2 = 0\).

Thus we have \(x = 1\).

This is sufficient.

ii) \(x < 0\)

\(|x| = 3x - 2\) is equivalent to \(-x = 3x - 2\) or \(4x - 2 = 0\).

Thus we have \(x = 1/2\). However \(x = 1/2 > 0\).

There is no negative solution.

Therefore, we have a unique solution \(x = 1\).

This condition is sufficient.

The answer is B.

For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.

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