fitzpratik wrote:

A, B, C, and D are points on a line in that order. If AD = 13, what is the length of BC?

1. AC = 5

2. BD = 10

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.

Let \(x\) = AB, \(y\) = BC and \(z\) = CD. Then we have \(x + y + z = 13\). The question asks what the value of \(y\) is.

We can assume 3 varaibles and 1 equation. Thus C could be the answer most likely.

Condition 1) AC = 5

\(x + y = 5\)

This is not sufficient.

Condition 2) BD = 10

\(y + z = 10\)

This is not sufficient.

Condition 1) & 2)

\(x + y = 5\)

\(y + z = 10\)

\(x + 2y + z = 15\) by adding the above equations

\(x + y + z = 13\) from the original condition.

\(y = 2\).

Both conditions are sufficient.

Therefore, C is the answer as expected.

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.

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