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- Fri Jan 21, 2011 12:00 am
#26466
Complete Question Explanation
Must Be True—Principle, Sufficient and Necessary Conditions. 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.”
2. “A gift is selfish if it is given to benefit the giver or is less valuable than is customary.”
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:
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?
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?
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:
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.
Must Be True—Principle, Sufficient and Necessary Conditions. 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.
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.
