People with serious financial problems are so worried about money that

OFFICIAL EXPLANATION

This problem is a classic example of how the GMAT attempts to disguise conditional reasoning. The stimulus can be diagrammed as follows: Sentence 1: SF—>~H. Sentence 3: H —>~SF. The sufficient condition in the first sentence is introduced by the phrase “people with.” The necessary condition in the third sentence is introduced by the phrase, “only if.” Note that the third sentence provides the contrapositive of the first sentence. The second sentence is not conditional and contains only general statements about the effects of their misery. The question stem uses the word “inferred” and can be classified as a Must Be True. When you encounter a stimulus that contains conditional reasoning and a Must Be True question stem, immediately look for a contrapositive or a repeat form in the answer choices. In problems with this same combination, avoid Mistaken Reversals and Mistaken Negations as they are attractive but wrong answer traps.

Answer choice (A): One reason answer choice (A) is incorrect is because it only refers to serious problems, not serious financial problems as in the stimulus. Even if the answer correctly referred to serious financial problems, it would still be incorrect because it would be a Mistaken Reversal of the first sentence and a Mistaken Negation of the third sentence.

Answer choice (B): The answer choice can be diagrammed ~SF—>H. This answer is incorrect because it is the Mistaken Negation of the first sentence. However, it is also the Mistaken Reversal of the third sentence, which you should recognize as the contrapositive of the first statement. This leads to the interesting point that the Mistaken Negation of a statement and the Mistaken Reversal of the same statement are contrapositives of each other. This fact reveals how important it is to diagram conditional statements correctly; otherwise, the makers of the test can lure you with answer choices which contain contrapositives of Mistaken Negations or Reversals.

Answer choice (C): This answer choice would be diagrammed the same way as answer choice (B), and it is incorrect for the same reasons.

Answer choice (D): The answer choice can be diagrammed as ~H—>SF. As such, it is the Mistaken Reversal of the first sentence and also the Mistaken Negation of the third sentence.

Answer choice (E): This is the correct answer. Answer choice (E) is the contrapositive of the first sentence and a repeat of the third sentence.

I said E.

Inferred --> Means we should hit the premises.....Premise..People with serious financial problems are so worried about money that they cannot be happy.

People with serious financial problems are so worried about money that they cannot be happy. Their misery makes everyone close to them—family, friends, colleagues—unhappy as well. Only if their financial problems are solved can they and those around them be happy.
Which one of the following statements can be properly inferred from the passage?
(A) Only serious problems make people unhappy.
(B) People who solve their serious financial problems will be happy. --> Best Answer
(C) People who do not have serious financial problems will be happy.
(D) If people are unhappy, they have serious financial problems.
(E) If people are happy, they do not have serious financial problems. We can infer that people are happy, they do not have serious financial problems....If they did have serious financial problems, they could not be happy.

I would go with E.

Premise 1:
People with serious financial problem -----> People Not Happy

Premise 2:
People and those around them happy ------> Financial problems solved

E is same as premise 1

People Happy ------> People don't have serious financial problems.

I am not sure if this kind of reasoning appears in GMAT.

People with serious financial problems -> worried ->cannot be happy->family, friends, colleagues—unhappy as well.
Only if financial problems are solved-> those around them happy.

Which one of the following statements can be properly inferred from the passage?
If people are happy, they do not have serious financial problems.

OA E

Similar to

If X then Y ==> If not Y, then not X.

X=serious financial problems
Y=not happy.

B cannot be the right answer , here is the explanation

conclusion :Only if their financial problems are solved can they and those around them be happy

B states : People who solve their serious financial problems will be happy.

there is clear difference between can and will, and a trap is present here , need to look closely.There can be several reasons for not being happy , besides financial problems.


E states : If people are happy, they do not have serious financial problems.

this is logical , as the premise is : People with serious financial problems are so worried about money that they cannot be happy .

so to be happy 1 necessary (but not sufficient) condition is to not have serious financial problems.

People with serious financial problems are so worried about money that they cannot be happy. Their misery makes everyone close to them—family, friends, colleagues—unhappy as well. Only if their financial problems are solved can they and those around them be happy.
Which one of the following statements can be properly inferred from the passage?

(B) People who solve their serious financial problems will be happy.
(E) If people are happy, they do not have serious financial problems.

e is the best here
let me try to explain situation with B,
if you go through the part in bold you can see never in the argument it has been mentioned " X is happy if he solves his problem"
its only mentioned that their problems are solved not that they solve their problem I prefer to say its shell game types answer.

I have a doubt in this question:

This question has two "if-then" relations.
Premise : Serious Financial Problems (SFP) ----> Not Happy ( H not)
Conclusion : SFP not -----> Happy

Now, as I read somewhere that the correct inference of if X---->then Y ,is, if not Y----->then not X (Please correct me if this concept is incorrect)
option D says : Happy not------> SFP ,which correctly infers the conclusion.
option E says : Happy-----> SFP not, which correctly infers the premise.

Can someone please identify and highlight the error in application of the concept or the concept itself I mentioned?

SFP is not the only cause of unhappiness.

(D) If people are unhappy, they have serious financial problems.
they could be unhappy because of other reasons as well (their team lost, and so on...), not ONLY because of sfp.

E is correct because the presence of happiness excludes the presence of SFP ( because if they were present they would NOT be happy).
(E) If people are happy, they do not have serious financial problems.

@Zarrolou

I may be the saying the same thing, but want to check whether my approach is fine.

"Only if their financial problems are solved can they and those around them be happy." ==> Necessary condition

implies that for a person to be happy, he must not have any serious financial difficulties.

So (E) => If a person is happy, then he must have crossed the necessary condition i.e. he does not face any serious financial problems.

"People with serious financial problems cannot be happy." ==> One of the factors to be unhappy

(D) => if people are unhappy, they have serious financial problems => one of the factors so they may have/not have financial problems => CAN'T INFER

Perfect.
Because we do not not if SFP is the ONLY cause of unhappiness, D is incorrect (there could be other factors).

You second explanation is correct.

About your first explanation:
The statement "Only if THEIR financial problems are solved can they and those around them be happy" is said about the people who had financial problems. However there could be other people who do not have financial problems but still are unhappy. Nothing has been said about these people. Hence the first explanation is not perfect.

B and E , both are correct as per the argument. How one can choose E over B . Experts please help

The passage states, "Only if their financial problems are solved, CAN they and those around them be happy." This implies that solving financial problems makes it possible for them to be happy. Whether they WILL actually be happy is not known, because there could be other reasons of being unhappy. Hence option B is incorrect.

For B, the argument says 'only if their financial problems are solved can they and those around them be happy'. Not surely that they will be happy. B says they will surely be happy, which is not correct.

E. If they are happy, we can be sure that they have no serious financial problem.

To solve this question I found helpful to review the logic of conditionality
If X then Y
This is the equivalent of: If non Y then non X.
Example: If it rains, then I will take an umbrella with me. I don't have a umbrella with me. That must mean it is not raining.
This is NOT equivalent to: If Y then X, or If Y then non X, or if non Y then X. In fact, if we know "If X then Y" and Y occurred, X may or may not happen.
Example. If it rains, then I will definitely take an umbrella with me. I have a umbrella with me today. Is it raining? It may or may not be raining. I said if it rains I will take an umbrella with me. But I could also take an umbralla with me just for the sake of it, even if it doesn't rain. By the same token, if it is not raining, do I have an umbralla with me? I may or may not have.
Using symbols:
X->Y nonY>nonX
nonX->Y nonY>X
X->nonY Y>non X

You can also think of it through the concept of necessary and sufficient conditions:
To get an A+ (sufficient) you must study (necessary).
Studying (necessary) is necessary to get an A+ (sufficient).
Only someone who studies can get an A+.

Sufficient indicator words: If, When, Whenever, Every, All, Any, People who, In order to
Necessary indicator words: Then, Only Only if, Must, Required, Unless, Except, Until, Without

Necessary conditions: If A is a necessary condition of B, that means A must happen for B to happen. In other words, if B happened, A must be true. If A is not true, then B can't happen. In summary: If B then A. If non A then non B.
Sufficient conditions: If A is a sufficient condition of B, that means if A happens B must happen. In other words, if B did not happen, A must be false. In summary: If A then B. If non B then non A.

Financial problems= not happy

Reverse and negate: Happy= No financial problems

Answer E