Politician: The current crisis in mathematics education must be overco

This question is based on logical structures.

It is saying:

If Crisis in mathematics education overcome, we will remain competitive. --(1)

For this, we need new teaching methods.

No method successful, unless students spend more time. --(2)

From 2, we can infer Students donot spend more time means method not successful. -- (3)

From (1) and (3), we can infer method not successful means not competitive.

Also, remember the rules: If P, then Q NEVER means ~P--> ~Q. It means ~Q --> ~P.

Now look at the options:

(A) If students spend a significant amount of time outside of class studying mathematics, the current crisis in mathematics education will be overcome. This is too broad. We know that what would happen if they donot spend time, but not the other way. Or ~P--> ~Q is incorrect. Hence, this option is incorrect.
(B) The current crisis in mathematics education will not be overcome unless students spend a significant amount of time outside of class studying mathematics. Correct, as per our analysis above.
(C) Few subjects are as important as mathematics to the effort to remain competitive in the global economy. : Other subjects are OFS.
(D) Only if we succeed in remaining competitive in the global economy will students spend a significant amount of time outside of class studying mathematics. Again, ~P--> ~Q.
(E) Students’ spending a significant amount of time outside of class studying mathematics would help us to remain competitive in the global economy. Same as D
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Thanks for the explaination

Can you please elaborate the explanation for E ?

I thought : Students’ spending a significant amount of time outside of class studying mathematics ->help to overcome The current crisis in mathematics education ->help to to remain competitive in the global economy

It is based on the another rule --> P, unless Q.

Which means P will not be true unless Q is true but vice versa is not true. I mean you cannot say If Q is true, P must be true.

Let me elaborate it more.

P = No method successful
Q = Unless students spend more time.

So, E is on the same lines.

E is saying, Students spend more time, fine. But that doesn't mean method is going to be successful, which further doesnt guarantee competitiveness.

I hope it is clear now.
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I understood using SC and NC.
Comp. -> Crisis overcome
Crisis Overcome - > Success in Teach

Now need help in disecting the following
"No method of teaching a subject can succeed that does not get students to spend a significant amount of time outside of class studying that subject. ".
Please help me out. how to interpret this sentence into SC -> NC format. Thank you.

Sorry, I couldn't understand what SC and NC you are talking about.

Can you please elaborate so that I can help you disect it further?
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SC = Sufficient Condition
NC = Necessary Condition.
SC -> NC .
The conditional reasoning .
- CR powerscore Bible.

Oh. Sorry, it is 12 midnight for me and my brain has now exhausted after doing so many questions and work related stuffs. I hope you will understand.

Ok, To answer your question:

Please look at the solution I provided here: https://gmatclub.com/forum/politician-t ... l#p1845999

SC: Sufficient amount of time
NC: Method Succeeded.

Apply the rule now, you will get your answer. This is very similar to P, unless Q.
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A. If X happens, Y will happen => Y may happen without X => X is not necessary to happen Y.
B. Y will not happen unless X not happen => Y will not happen without X => X is required to happen Y.
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the word "logic" in the question is ambiguous. Test takers should look at the options in order to identify the question type. Here, it is an inference question.

C and D are out.
E does not show a causal relationship => E is wrong.
A and B sound similar, but they are not same. B is right, but A is wrong because the causal relationship can only happen in one way, not vice versa.

abhimahna,
I just want to make it clear to myself
answer E states that the frist outcome "would" lead to the very main goal, and as of the stimulus, it indeed would
is it not correct, because it may not lead, even if there is a possibility?
Because as I understand, the causal relationship in E isn't hurt.

Please explain why B is correct. Unable to clearly articulate in If A then B format...

Politician: The current crisis in mathematics education must be overcome if we are to remain competitive in the global economy. Alleviating this crisis requires the employment of successful teaching methods. No method of teaching a subject can succeed that does not get students to spend a significant amount of time outside of class studying that subject.

Type- inference
The current crisis in mathematics education must be overcome if we are to remain competitive in the global economy--> 'current crisis in mathematics education must be overcome' is a necessary condition for 'we are to remain competitive in the global economy'

Alleviating this crisis requires the employment of successful teaching methods.--> 'the employment of successful teaching method is necessary for Alleviating this crisis

No method of teaching a subject can succeed that does not get students to spend a significant amount of time outside of class studying that subject. --> 'Getting students to spend a significant amount of time outside of class studying that subject' is a necessary condition for a method of teaching to succeed

(A) If students spend a significant amount of time outside of class studying mathematics, the current crisis in mathematics education will be overcome. - incorrect, 'students spend a significant amount of time outside of class studying mathematics' is a sufficient condition here
(B) The current crisis in mathematics education will not be overcome unless students spend a significant amount of time outside of class studying mathematics. - Correct
'Crisis can NOT be overcome' unless 'significant time out of class studying maths'. Students spending a significant amount of time outside of class studying maths is a necessary condition here
(C) Few subjects are as important as mathematics to the effort to remain competitive in the global economy. - incorrect, "as important" is a baseless comparison
(D) Only if we succeed in remaining competitive in the global economy will students spend a significant amount of time outside of class studying mathematics. - incorrect
"only if" indicates a necessary condition. This reverses the logic.
(E) Students’ spending a significant amount of time outside of class studying mathematics would help us to remain competitive in the global economy.- incorrect
' Students’ spending a significant amount of time outside of class studying mathematics ' is neither necessary nor sufficient as per E. It is something that would help us. But E is making a bit of stretch.

Answer B
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Hi Folks,
This is a good example of necessity vs sufficient condition.
Premise 1: Current condition-crisis in mathematics education
Premise 2: Aim-remain competitive in global economy.
Premise 3: Solution-employ successful teaching method.
Premise 4: Condition-No method of teaching could succeed without students spending significant amount of time outside class studying that subject.

There is no conclusion in the argument. Probably, we will be asked to draw one.
Trigger points: No method.... As soon as we see such a statement, it should raise a red flag as a condition is about to follow. Identify what type of condition it is. In this case it is a necessary condition because it also depends upon teaching method. X AND Y lead to Z.

Question statement: Which one of the following statements follows logically from the statements above?
So we are asked to draw a conclusion.


A TRAP statement. This statement makes a given necessary condition to a sufficient one. Loser.

Absolutely true. Spending significant time outside class is a necessary condition and unless it is true, one will not overcome the current crisis. Contender.

Well, they could or could not be. we do not care.Loser

Now this option presents another condition but we cannot derive this from the information presented to us.Loser

No it will not. It is one of the two necessary conditions to alleviate crisis in mathematics education NOT to remain competitive in global economy. Loser

So, B is the best option to choose.

Note: Necessity vs sufficient conditions could be easily understood if you have the basic knowledge of AND and OR logical gates. This could be really simple for someone from engineering background.
Just treat Necessary condition as AND operation and sufficient as OR operation. This makes things way easier than they are.
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The current crisis in mathematics education must be overcome if we are to remain competitive in the global economy. Alleviating this crisis requires the employment of successful teaching methods. No method of teaching a subject can succeed that does not get students to spend a significant amount of time outside of class studying that subject. => spend a significant amount of time outside of class studying that subject [A] is necessary for any method of teaching to succeed [B]

[A] is necessary for [B] to happen

Which one of the following statements follows logically from the statements above?

(A) If students spend a significant amount of time outside of class studying mathematics, the current crisis in mathematics education will be overcome. [A is necessary for B to happen but we can't say that it's sufficient]
(B) The current crisis in mathematics education will not be overcome unless students spend a significant amount of time outside of class studying mathematics. [ Yes because it's necessary as we inferred earlier]
(C) Few subjects are as important as mathematics to the effort to remain competitive in the global economy. [I don't care about other subjects]
(D) Only if we succeed in remaining competitive in the global economy will students spend a significant amount of time outside of class studying mathematics. [This is saying the reverse]
(E) Students’ spending a significant amount of time outside of class studying mathematics would help us to remain competitive in the global economy. [It is necessary but we can't say that it's sufficient]