## #11 - A gift is not generous unless it is intended to

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Complete Question Explanation

Must Be True—PR, SN. The correct answer choice is (D)

Statistically, this is a difficult question. The difficulty occurs because many students mis-diagram one or both of the conditional statements in the stimulus. Although the question stems asks you to identify the answer that follows from the principle, the principle contains two similar but distinct conditional statements, you must be aware that either could figure in the correct answer. We will now examine both of the statements (the conditional indicators are italicized):

1. “A gift is not generous unless it is intended to benefit the recipient and is worth more than what is expected or customary in the situation.”

Applying the Unless Equation, the phrase modified by “unless” becomes the necessary condition and the remainder is negated and becomes the sufficient condition:

G = a gift is generous
BR = the gift is intended to benefit the recipient
WM = the gift is worth more than what is expected or customary in the situation

BR
G +
WM

The application of a conditional principle similar to this one does not allow a conclusion to be drawn that someone is generous (however, a conclusion could be made via the contrapositive that someone is not generous).

2. “A gift is selfish if it is given to benefit the giver or is less valuable than is customary.”

Remember, “if” introduces a sufficient condition.

S = a gift is selfish
BG = the gift is given to benefit the giver
LV = the gift is less valuable than is customary

BG
or S
LV

Some students compare the two statements in the stimulus and conclude that the second is the contrapositive of the first. While the second relationship is very similar to the contrapositive of the first relationship, it is not an exact contrapositive because the logical opposite of “generous” is not “selfish” (it is “not generous”), the logical opposite of “benefit the recipient” is not “benefit the giver” (it is “not benefit the recipient”), and the logical opposite of “worth more than customary” is not “worth less than customary” (it is “not worth more than customary”).

As you examine the answer choices, keep in mind that the test makers will try to devise answer choices that are similar to the guidelines in the principle, but that do not match exactly. These answers will be incorrect. Remember also that the contrapositive of either conditional statement can be used to arrive at the correct answer.

Answer choice (A): This is a very attractive wrong answer choice.

To draw the conclusion that one’s gift is selfish, one must either give a gift that is given to benefit the giver or give a gift that is less valuable than is customary. Let us examine the answer choice and determine whether Charles’s gift meets either condition:

1. Was the gift given to benefit the giver?

No. Even though Charles hates opera, giving the tickets to his cousin did not benefit Charles (Charles was under no apparent obligation to attend the opera and could have left the tickets unused). In fact, they clearly benefitted his cousin, who loves opera.

2. Was the gift less valuable than is customary?

Unknown. Even though Charles paid nothing for the tickets, they still had value (they could have been resold, for example). Whether they were less valuable than customary for a birthday gift is unknown (although common sense suggests they were not less valuable).

Since neither sufficient condition has been met with certainty, it cannot be concluded that Charles’s gift was selfish.

Answer choice (B): Again, does the answer choice meet either sufficient condition?

1. Was the gift given to benefit the giver?

No, the gift was given in order to help keep Emily’s brother healthy.

2. Was the gift less valuable than is customary?

No, the gift was apparently given for no special occasion.

In any scenario under this principle, the consequences of the gift (in this case that Emily’s brother was hurt and offended) do not play a role in determining whether the gift was a selfish one.

Answer choice (C): This answer concludes that Amanda is generous on the basis of her actions. As discussed previously, there is no way to use the principle to conclude that an individual is generous.

Once you see the answer concluding that a sufficient condition (“generous”) occurred, you can eliminate the answer with speed and confidence. Simply put, structurally an answer of this type could never be correct in a problem such as this one.

Answer choice (D): This is the correct answer choice. In order to arrive at the judgment that a gift is not generous, one or both of the necessary conditions from the first conditional relationship must not be met. Does that occur in this answer?

1. Was the gift intended to benefit the recipient?

Yes. This gift was intended to benefit the recipient, and so this necessary condition was met.

2. Was the gift worth more than what is expected or customary in the situation?

No. The answer choice indicates that all the children in Olga’s family receive a computer for graduation. Since the gift of a computer is not worth more than is customary in the situation, this condition is not met and via the contrapositive we can conclude that Olga’s gift was not generous.

Since one of the necessary conditions in the principle was not met, we can conclude that the sufficient condition was not met, and Olga’s gift was not a generous one. As this matches the judgment in the answer choice, this is the correct answer.

Answer choice (E): Since the judgment in this answer (“not generous”) is the same as in answer choice (D), we can analyze this answer in the same way:

1. Was the gift intended to benefit the recipient?

Yes. Michael gave his nephew \$50 dollars, and in doing so the intention was to benefit the nephew. The fact that the nephew subsequently lost the money does not show that Michael’s intention was not to benefit his nephew. To some extent, this situation is like the one in answer choice (B) because in the principle the consequences of the gift do not play a role in determining the intentions of the giver.
2. Was the gift worth more than what is expected or customary in the situation?

Yes, the first line spells out that the gift of \$50 was more than Michael had ever given his nephew before.

Since both necessary conditions of the principle are met, the gift could be a generous one, a conclusion that does not conform to the judgment in the answer choice. Hence, the answer is incorrect.

A final note on this question: make sure you are comfortable with how the conditional relationship in this Must-PR problem is used to affect the answer choices (whether you can determine if someone is generous or not generous, selfish or not selfish). This form of Principle question has proven to be hard enough that the test makers will surely continue to place this type of question on the exam.
esolhtalab
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Can someone please provide an explanation for this question? I'm stuck between answers A and D. Online research has shown me that the correct answer is D. How can this be? Should we assume that because Olga got her children all the same type of gift that this is also means they were all in the same price range?

Can you please also explain why A is not the answer? I think my confusion might be the difference between cost and worth, as in the the tickets costing Charles nothing is not the same as the market value for the tickets.
Blueballoon5%
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Haha, I was just about to post this question. I did not understand the answer explanation for why C was a wrong choice.

But I can explain to you why A is the wrong choice.

Here is the stimulus in conditional form:
* Generous --> Benefit the receiver and worth more than expected (or customary in the situation)
* Benefit the giver or less valuable than customary --> selfish

(a) A is wrong because you cannot claim that Charles is selfish. The tickets do not meet the second conditional statement above. Charles did not benefit as the giver and the tickets were not considered to be "less valuable" (in fact, we know nothing about this).

(d) D is right. It is the contrapositive of the first conditional statement (above). The contrapositive is "Not benefit the receiver or Not worth more than expected ---> not generous." In the answer choice, "NOT worth more than expected ---> not generous."

For anyone who can help me, I do not understand the answer explanation (found online) for choice C: "This answer concludes that Amanda is generous on the basis of her actions. As discussed previously, there is no way to use the principle to conclude that an individual is generous. Once you see the answer concluding that a sufficient condition ("generous") occurred, you can eliminate the answer with speed and confidence. Simply put structurally an answer of this type could never be correct in a problem such as this one."

I do not understand this explanation. Why can't you conclude a sufficient condition? Why can't you use the principle to conclude something?
Clay Cooper
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Hi yall, thanks for your questions.

As to the first, esolhtalab's:

BlueBalloon's explanation and rule diagrams are spot-on. All that answer choice D is claiming to have proved is that Olga's gift is not generous. This is in fact proven by the piece of evidence that Olga gives all of her children the same gift at graduation; thus, the gift is customary on this occassion, and it fails to meet the second requirement of a generous gift as laid out in the rule BlueBalloon diagrammed.

As to the second, BlueBalloon's:

This answer choice (C) only involves the first of the two rules you diagrammed for us, the one that states: Generous --> intended to benefit the recipient AND more than what is expected or customary.

However, this rule will never enable us to prove that any gift is generous. In short, to answer your questions: you can in fact use the conditional rule we are examining to prove something, but only to prove necessary conditions - in other words, you can only ever prove conditions that appear on the right side of some conditional arrow. Our rule (Generous --> intended to benefit recipient AND more than expected) only enables us to prove that the certain gifts (those we know are generous) are inteded to benefit their recipients and are more than what was expected. Even its contrapositive does not put the term 'generous' on the right side of the arrow, into the land of conditions we can prove. The contrapositive (Not intended to benefit recipient OR Not more than what was expected --> Not generous) would only ever allow us to prove that certain gifts are not generous.

Again, in shorter and clearer terms: conditional rules only ever allow us to prove their necessary conditions, never their sufficient conditions, and no rule that we are given in the stimulus of this question has the term 'generous' as a necessary condition. Therefore, we can quickly and easily eliminate any answer choice that claims to have proved that a gift was generous.
temiolof
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I understand how D conforms to the conditions in the stimulus, but I'm having a hard time eliminating B. I accounted for the fact that Emily's brother felt hurt/offended by the gift in determining the gift's value. I concluded that his feelings about the gift reflected the value of the gift to him. I would assume it's not customary to give someone a gift that is so invaluable, it is considered hurtful/offensive by the beneficiary. On this basis, I thought the "less valuable than customary" criteria had been met.

But since this answer is incorrect, why is my reasoning wrong? I guess I overextended the brother's feelings as a proxy for valuation?
Jonathan Evans
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Hi, temiolof,

Good question. Answer choice (B) claims that the gift described is "selfish." For us to do anything with this answer, we'd need to find evidence from the stimulus about "selfish" gifts. Let's see what we know:

If a gift is given to benefit the giver or is less valuable than customary, then it's selfish.
We have two conditions that allow us to know with certainty that a gift is selfish:

1. Given to benefit the giver
2. Less valuable than customary

1. Seems like Emily is giving it to benefit her brother
2. Brother is hurt and offended
How do these facts square up with what we know from the stimulus? The gift is apparently given to benefit someone else, but that does not establish by itself that the gift is not selfish. The second fact is that the brother is hurt. Does the brother feeling hurt imply that the gift is less valuable than is customary? While as you point out the gift might not feel valuable to him, his feelings about the gift's value have no definite relationship to the customary value of a gift. To make (B) work, you have to introduce some additional assumptions into the reasoning that make this answer not as well supported as (D), which gives you a clear arrow that establishes that Olga's computer gift doesn't meet the criteria for generosity.

temiolof
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Jonathan, that is very helpful. Thank you!
FK00144
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what does the PR and SN stand for in the answer?
Stephanie Turaj
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FK00144 wrote:what does the PR and SN stand for in the answer?

Hi FK,

Thanks for the question!

"SN" is our abbreviation for Sufficient and Necessary, meaning Sufficient and Necessary conditions are present in the stimulus.

"PR" is our abbreviation for Principle, meaning that the question stem indicates that a principle must be used.

Thanks!