Data Sufficiency

Hi fambrini,

When dealing with a 'system' of equations (meaning that the number of equations matches the number of different variables), the given equations must be DISTINCT (meaning unique/different).

Here, the two equations offered in the two Facts are NOT distinct (it's the same equation both times), so you do NOT have a system of equations here. In this prompt, with the two variables and one equation that you're given, you cannot figure out the exact values of X and Y, so you cannot answer the question.

GMAT assassins aren't born, they're made,
Rich

fambrini wrote:What is the value of x + y?

1) 12x - 3y = 15

2) y = 4x - 5

OA: E

I can work though the statements. However, why can't I treat 1 and 2 together as a system of equations?

In DS, we need to find out the unique answer to the problem.

> If the questions is 'Yes/No' type, the answer should either always be YES or always be NO. An important thing to note is that if each statement seems sufficient to answer the question, both the statements should answer either 'Yes and Yes' or 'No and No.'

> Same is with 'What is the value?' type of questions. If each statement seems sufficient to answer the question, both the statements should return the same value. Say, for example, if statement 1 gives x = 1 (a unique value) and statement 2 gives x = 2 (a unique value), you must recheck your work. This situation is not possible. Each GMAT official DS question represents a holistic scenario and the statements are compatible to one other.

Unique vs. consistent solutions:

A single two-variable equation cannot render a unique solution; however, it can render infinite numbers of consistent solutions.

For example, an equation: x + y = 10 has no unique solution; however, there are infinite numbers of consistent solutions: x=5, y=5; x=4, y=6; x=0, y=10, etc.

In the given question, despite treating the given the equations separate, you will not get a unique solution, because both the equations are essentially the same. We are interested in getting a unique solution and not a consistent solution.

Hope this helps!

-Jay
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