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A small School has three foreign language classes,one in French,one in [#permalink]

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30 Jun 2016, 13:49

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A small School has three foreign language classes,one in French,one in Spanish,and one in German.How many of the 34 students enrolled in the Spanish class are also enrolled in French class?

(1)There are 27 students enrolled in the French class,and 49 students enrolled in either the French class,the Spanish class,or both of these classes.

(2) One half of the students enrolled in the Spanish class are enrolled in more than one foreign language class.

A small School has three foreign language classes,one in French,one in Spanish,and one in German.How many of the 34 students enrolled in the Spanish class are also enrolled in French class?

(1)There are 27 students enrolled in the French class,and 49 students enrolled in either the French class,the Spanish class,or both of these classes.

(2) One half of the students enrolled in the Spanish class are enrolled in more than one foreign language class.

Dear AbdurRakib, I'm happy to reply. Great question!

In general, three-circle Venn diagrams are hard. It's hard to get specific information about specific regions.

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.

Now, forget statement #1.

Statement #2 tell us that half the Spanish students, 17, are taking at least one more class, but we don't know how many are in French and how many are in German. The three circle situation is problematic. We can't answer the question. Statement #2, alone and by itself, is insufficient.

First statement sufficient, second insufficient. Answer = (A)

Does all this make sense? Mike
_________________

Mike McGarry Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

Re: A small School has three foreign language classes,one in French,one in [#permalink]

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16 Dec 2016, 08:13

mikemcgarry wrote:

AbdurRakib wrote:

A small School has three foreign language classes,one in French,one in Spanish,and one in German.How many of the 34 students enrolled in the Spanish class are also enrolled in French class?

(1)There are 27 students enrolled in the French class,and 49 students enrolled in either the French class,the Spanish class,or both of these classes.

(2) One half of the students enrolled in the Spanish class are enrolled in more than one foreign language class.

Dear AbdurRakib, I'm happy to reply. Great question!

In general, three-circle Venn diagrams are hard. It's hard to get specific information about specific regions.

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.

Now, forget statement #1.

Statement #2 tell us that half the Spanish students, 17, are taking at least one more class, but we don't know how many are in French and how many are in German. The three circle situation is problematic. We can't answer the question. Statement #2, alone and by itself, is insufficient.

First statement sufficient, second insufficient. Answer = (A)

Does all this make sense? Mike

Hi Mike ,

Shouldnot 34 includes student who learn Spanish only , spanish and french , and spanish and german .

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 Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

A small School has three foreign language classes,one in French,one in [#permalink]

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17 Dec 2016, 04:34

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AbdurRakib wrote:

A small School has three foreign language classes,one in French,one in Spanish,and one in German.How many of the 34 students enrolled in the Spanish class are also enrolled in French class?

(1)There are 27 students enrolled in the French class,and 49 students enrolled in either the French class,the Spanish class,or both of these classes.

(2) One half of the students enrolled in the Spanish class are enrolled in more than one foreign language class.

Re: A small School has three foreign language classes,one in French,one in [#permalink]

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12 Nov 2017, 10:33

Hey mike,

What if B = 11, F = 16, S = 23 which satisfies both the conditions that S=34(23+11) and F = 27(16+11) and S+F+B = 49(23+16+11). However the answer to the Question asked becomes 11.

If you consider B=12, F=15, S = 23 which again satisfies all the above conditions, the answer to the question asked becomes 12.

So, i m not sure how A is sufficient to answer the Question ? I m not sure if my reasoning is right or if I'm missing something.

What if B = 11, F = 16, S = 23 which satisfies both the conditions that S=34(23+11) and F = 27(16+11) and S+F+B = 49(23+16+11). However the answer to the Question asked becomes 11.

If you consider B=12, F=15, S = 23 which again satisfies all the above conditions, the answer to the question asked becomes 12.

So, i m not sure how A is sufficient to answer the Question ? I m not sure if my reasoning is right or if I'm missing something.

thanks, Nitish

Hi nitishms! Carolyn from Magoosh here - I'll step in for Mike

It looks like you may have just made a few small calculation errors here! In the first case, you said S+F+B = 49(23+16+11). But when we add 23+16+11, we get 50 (not 49). So this case doesn't work.

And looking at your second case, if B = 12, F = 15, and S = 23, then the total number of people taking Spanish will be 23+12 = 35, not 34. So this case also doesn't work.

We can definitively solve this using the two equations that we can determine:

S + 2B + F = 61 S + F + B = 49

This system only has one solution for B, which is 12.

I hope that helps clear things up! -Carolyn
_________________