Ganganshu wrote:
mikemcgarry wrote:
Statement #1 does us the favor of making German irrelevant, so that we have a much simpler two-circle Venn diagram. We have 34 in Spanish, including those in French. We have 27 in French, including those in Spanish. Let's say
S = number of Spanish-only students
F = number of French-only students
B = number of students taking both, which is the number the prompt question wants.
We know S + B = 34 from the prompt.
We know F + B = 27 and S + F + B = 49 from Statement #1.
(S + B) + (F + B) = 34 + 27
S + 2B + F = 61
Subtract the second equation from the prompt:
B = 61 - 49 = 12
This statement gives us a clear numerical answer to the prompt question. Statement #1, alone and by itself, is sufficient.
Hi Mike ,
Shouldnot 34 includes student who learn Spanish only , spanish and french , and spanish and german .
So why you did not include Spanish and German .
Dear
Ganganshu,
I'm happy to respond.
My friend, in GMAT math, it's extremely important to distinguish what is required by mathematical rules and what is strategic. For example, if we have to solve the very simple equation 3x + 7 = 49, there would be nothing mathematically wrong to begin by multiplying both sides by 13, but that would be a spectacularly poor move in turns of strategy. That's a very simple obvious example, but you always have to be thinking in terms of both what is mathematically true and what can we do for strategic purposes.
In the prompt, the 34 students in French absolutely includes
(a) the French only students
(b) the French & Spanish students
(c) the French & German students
(d) any students in all three language classes.
That's big-picture true. In the overall picture of what is happening in this problem, this undeniably true.
Then, we get to Statement #1, which gives us a ton of information about Spanish and Spanish-French, but doesn't mention German even once. This suggests an extremely valuable strategy:
let's ignore German. Let's simply
pretend, for the sake of analyzing this particular statement, that the German class doesn't exist. Admittedly, this is not "true" in the largest view of the problem, but it's a simplifying assumption that allows us to focus on one aspect of problem-solving, and as it happens, the simplifying assumption leads to a definitive answer to the prompt question.
Compare this to another type of problem. Suppose I had to solve the inequality \(x^2 +4x - 45 > 0\). There are several methods of solution, but one would be to begin by solving the equation: \(x^2 +4x - 45 = 0\). It's perfectly true that in doing so, we are solving something different from what the question asked, and it's also true that the values that satisfy the equation absolutely will not satisfy this inequality. Nevertheless, this is highly productive from a strategic point of view, because the solutions to the equation form the boundary conditions that will allow us to "chunk" the number line and figure out the regions that work and don't work. The solutions to the equation are x = -9 and x = +5, and the solution to the inequality are x < -9 and x > +5.
Sometimes it is a highly strategic move to assume that something that is slightly different from what is true in the problem scenario in order to reach a solution. This happens in many areas of GMAT math, and the inability to see these routes of solution can be a huge deficit on the GMAT Quant.
Does all this make sense?
Mike
_________________
Mike McGarry
Magoosh Test PrepEducation is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)