SajjadAhmad wrote:

The costs of equities of type A and type B (in dollars) are two different positive integers. What is the total cost of 2 equities of type A and 3 equities of type B?

(1) 4 type A equities and 5 type B equities together cost 27 dollars.

(2) Cost of a type A equity plus the Cost of a type B equity is 6 dollars.

Source: Nova GMAT

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 \(a\) and \(b\) be the costs of equities of type A and B, respectively.

The question asks what the value of \(2a + 3b\) is.

There are 2 variables and 0 equation. By Variable Approach method, C is the answer most likely. However, since this question is about the area of integers, which is one of the key question areas, we need to check A or B by Common Mistake Type 4A . Key question areas are integers, statistics, inequalities, absolute values and probability.

Condition 1) : \(4a + 5b = 27\).

Since \(a\) and \(b\) are positive integers, we have a unique solution \(a = 3\) and \(b = 3\).

Thus this condition is sufficient.

Condition 2) : \(a + b = 6\).

This equation has many solutions, for example, \(a = 1\), \(b = 6\) or \(a = 2\), \(b = 5\).

Thus this condition is not sufficient.

Therefore, the answer is A.

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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