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I am kind of with you. D seems such a sweet choice - I picked D. It applies the principle.
E on the other hand does the opposite and you don't need a principle there since the offer is made in jest....

However, this is an LSAT question it seems based on the phrasing of the question stem and while helpful in practice is not quite what you would see on the GMAT. So maybe I am missing something too. I am with D.

GMATNinja - what do you think? Is E really the OA?
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OK. I have googled the question and the answer is indeed E. It is a nasty LSAT question.
But to solve the question you have to diagram it - something people do a lot on the LSAT.

The problem with D as I understood it is that it is the opposite of what the statement says:

Statement says: A contract is an offer that is accepted and it is not legitimate if someone can think it was made in jest.

Thus, the trick is the negation (big deal on the LSAT) that the offer is not made legitimate if nobody could think it was made in jest. I hope GMAT Ninja can better explain this. I am not at all comfortable with LSAT questions.
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I have tried to take a stab. Please let me know if there is any gaps in the reasoning.

A contract between two parties is valid only if one party accepts a legitimate offer from the other This is Necessary condition
Contract valid --> Legitimate offer

An offer is not legitimate if someone in the position of the party to whom it was made would reasonably believe the offer to be made in jest. This is sufficient condition
Made in jest --> Not Legitimate offer
Legitimate offer --> Not made in jest (contrapositive)

Combined
Contract valid --> Legitimate offer --> Not made in jest
OR
Made in jest --> Not Legitimate offer --> Not valid contract


(A) Joe made a legitimate offer to buy Sandy’s car and Sandy has not rejected the offer. Thus, there was a valid contract.
Reversed necessary and sufficient conditions

(B) Kenta accepted Gus’s offer to buy a shipment of goods, but Gus, unknown to Kenta, made the offer in jest. Thus, the contract was not valid.
The person (Kenta) in the position of the party to whom it was made would reasonably believe the offer to be made in jest. If they don't know, we can't say anything

(C) Frank’s offer to buy Mindy’s business from her was legitimate. Thus, if Mindy is a reasonable person, she will accept the offer.
There is no correlation. The prompt does say Accept offer if it is legitimate

(D) Hai’s offer to sell artworks to Lea was made in such a way that no one in Lea’s position would have reasonably believed it to be made in jest. Thus, if Lea accepts the offer, they have a valid contract.
Not made in jest doesn't lead me anywhere.

(E) The only offer that Sal made to Veronica was not a legitimate one. Thus, regardless of whether Sal made the offer in jest, there is no valid contract between them.
This makes sense
Made in jest --> Not Legitimate offer --> Not valid contract
GmatStuck
A contract between two parties is valid only if one party accepts a legitimate offer from the other; an offer is not legitimate if someone in the position of the party to whom it was made would reasonably believe the offer to be made in jest.

The principle stated above, if valid, most helps to justify the reasoning in which one of the following arguments?

(A) Joe made a legitimate offer to buy Sandy’s car and Sandy has not rejected the offer. Thus, there was a valid contract.

(B) Kenta accepted Gus’s offer to buy a shipment of goods, but Gus, unknown to Kenta, made the offer in jest. Thus, the contract was not valid.

(C) Frank’s offer to buy Mindy’s business from her was legitimate. Thus, if Mindy is a reasonable person, she will accept the offer.

(D) Hai’s offer to sell artworks to Lea was made in such a way that no one in Lea’s position would have reasonably believed it to be made in jest. Thus, if Lea accepts the offer, they have a valid contract.

(E) The only offer that Sal made to Veronica was not a legitimate one. Thus, regardless of whether Sal made the offer in jest, there is no valid contract between them.
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This is a conditional reasoning passage. So, 1st thing i do is break it down into what is sufficient and what is necessary most of the time the answer will depend on identifying that.

Contract between 2 parties = Sufficient
One Party accepts a legitimate offer from other = Necessary
Then there is a contrapositive statement given for the same conditional reasoning.

Trap Ans:
A: Both party needs to accept the offer to be a legitimate offer become a contract not just one.
B: Other party need to have reasonable believe of jest for the offer to be illegitimate.
C: Conditioning is on legitimate offer and accepting offer not reasonable and accepting offer.
D: this introduces mistaken reversal. if you accept the offer, then it becomes the contract is not aligned with what passage says about sufficient and necessary condition.
E : Correctly implemented contrapositive reasoning
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A few good takes here is what works for me notice how no one in leas position would accept it which is irrelevant only parties that are offered and believe in it's legitimacy can decide if it's in jest or not


this doesn't really help our base statement at all your job is to look for anecdotal evidence of sorts that support base statement

The last option clearly spells out the offer isn't legitimate there are two ways for it to not be legitimate as it's mentioned that the jestnpart doesn't matter it's clear that Veronica declined the offer making the jest part moot l.
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Inference 1: If offer is made in jest>>>Offer is not legitimate one
Inference 2: If offer is not legitimate one>>> Not a valid contract

This much is inferable from the argument
E is targeting second inference.
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