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First, given the figure, how could we know that a c d is on a lign? I thought if that information is not given, we cannot suppose it. Tha's why I answered (E). The information give is just that a c b is a triangle...

Second point, I've learn in different GMAT DS tips, that for variables to be solved, there needs to be at least as much as equations as unknown. It doesn't seem to work if we consider following

So with (1) we have:
a+b+c=180
c+d =180
a + c + d = 225

4 variables and 3 equations are not enough to solve it => right

with (2)
a+b+c=180
c+d =180
a-d=55

It 's the same, we have 4 variables and 3 equations => false

why can't we say it isn't enough to solve it. Where's the flaw?

First, given the figure, how could we know that a c d is on a lign? I thought if that information is not given, we cannot suppose it. Tha's why I answered (E). The information give is just that a c b is a triangle...

Second point, I've learn in different GMAT DS tips, that for variables to be solved, there needs to be at least as much as equations as unknown. It doesn't seem to work if we consider following

So with (1) we have: a+b+c=180 c+d =180 a + c + d = 225

4 variables and 3 equations are not enough to solve it => right

with (2) a+b+c=180 c+d =180 a-d=55

It 's the same, we have 4 variables and 3 equations => false

why can't we say it isn't enough to solve it. Where's the flaw?

First, given the figure, how could we know that a c d is on a lign? I thought if that information is not given, we cannot suppose it. Tha's why I answered (E). The information give is just that a c b is a triangle...

- I think you can assume a line is straight if it's drawn straight. I can't recall the exact things you cannot assume in geometry as it's been a long time since I touched geometry. But I think the OG has a list of those items you can safely assume

Second point, I've learn in different GMAT DS tips, that for variables to be solved, there needs to be at least as much as equations as unknown. It doesn't seem to work if we consider following

- You're wrong on this one. In fact, for DS, having x number of variables does not mean you need x number of equations.

Anyway, for St1: we know c+d = 180, and so a = 45. However, we can't solve for b as we do not know c and we can't manipulate the variables to fit into the sum of angles for a triangle.

The most we can get via manipulation is

a+b+c = 180 45+b+180-d = 180 b-d = -45 --> We still have two variables left.

However, with St 2:

You can easily write d = a+55 So c = 180-a-55 = 125-a

Thanks Ywilfred for your explanation.
Concerning the solving of the equations (1) and (2), I totally understand and agree. But I was looking for a "shortcut" to answer such questions more quickly. If I knew after few seconds that in any DS involving equations that there have less or as much equations as variables, I could straight give an answer that we have( or not) enough information too answer.

So what should one think about such a statement taken out of Kaplan, in light of this DS triangle problem.

"Remember this matematical principle.Whatever number of different variables you need to solve for, you will need that same number of different equations relating at least one of those variables.

There are usually a few tough DS problems that can be made easy by applying this principle and the Kaplan Method for DS word problem. If you get such a problem, ask yoursel,' how many variables do I need to solve for? How many equations do I have?'"