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I'm working through a logical reasoning problem and am stumped on why the provided answer is correct. I've laid out the premises and my own logical deduction, which points to a different answer. I'd appreciate it if someone could point out the flaw in my reasoning.

Here is the question stem:

Hypothesizing that lullabies, characterized by their slow tempos, are universally calming to infants, Constance M. Bainbridge and colleagues played a lullaby sung in the Scottish Gaelic language and a non-lullaby sung in the Seri language to a group of infants.

The team found that the infants' heart rates decreased more during the lullaby than during the non-lullaby. Since a decrease in heart rate is associated with relaxation, the team concluded that the lullaby relaxed the infants.

Noting that reduced heart rate can also be associated with increased attention, one critic argues that instead, the lullaby simply attracted the infants' attention. Bainbridge and colleagues also measured pupil size, as pupils typically become larger when a stimulus captures a person's attention.

Question:

Which finding, if true, would most directly weaken the critic’s claim?

A. Blinking, which indicates attention, was equally frequent whether infants were listening to the song in Scottish Gaelic or song in Seri.

B. Neither the Scottish Gaelic language nor the melody of the traditional Scots lullaby was familiar to infants in the study.

C. The infants' pupils were smaller when the infants were listening to lullabies than when they were listening to non-lullabies.

D. Parents of infants in the study chose the lullaby over the non-lullaby when asked which song they would use to calm their child.

The correct answer is supposedly A, but I can't understand why. My analysis points squarely to C as the most direct rebuttal.

Below is my attempt at this problem:

Let L represent "The infants were listening to the lullaby."

Let A represent "The infants' attention was attracted."

Let P represent "The infants' pupils were larger."

Premise 1: L → A (If Lullaby, then Attention)

Premise 2: A → P (If Attention, then Larger Pupils)

Logical Conclusion: L → P (Therefore, if Lullaby, then Larger Pupils)

For the critic to be right, it must be true that listening to the lullaby causes pupils to become larger.

Option C provides exactly the evidence required to weaken the claim. Option C shows that when L was true, P was false. In fact, Option C shows something even stronger: the opposite of P occurred.

Symbolically, Option C demonstrates that L → ¬P. Hence, I believe that the correct answer must be C and not A.

Could someone use formal logic (if necessary) to verify whether the correct answer is A or C?

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  • Are you sure you copied the question correctly and that you doublechecked the answer key? Commented Sep 6, 2025 at 15:59
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    Yes, I don’t think anything is incoherent here, so it makes sense that the question is fine as is. As for the answer key, it could potentially be wrong; hence, I was seeking clarification. Commented Sep 6, 2025 at 16:13
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    Well then if blinking was some kind of indicator for attention, then there being no difference between the 2 groups would mean no effect for the putative cause. What was the critic criticizing and what was the hypothesis being tested? Commented Sep 6, 2025 at 16:39
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    Why overpass comment on your other SAT question, asking you to cite? see meta. did you cross post to english? is this from Digital SAT test questions administrated on June 3, 2023? Commented Sep 8, 2025 at 7:53
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    Who told you the answer is A? Based on this and the other SAT question you asked, I think you have the wrong answer key. Commented Sep 8, 2025 at 10:43

5 Answers 5

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Could someone use formal logic (if necessary) to verify whether the correct answer is A or C?

The concept of blinking came out of nowhere in the list of options. That precludes a formal approach with which to justify option A. The correct option is C.

A and B are similar in the sense that both depict a condition of steadiness: frequency of blinking and unacquaintance with the music, respectively. The difference between A and B is that A contains a clause (namely, "indicates attention") that constitutes noise. Neither that clause has support in the description of the scenario, nor is it an obvious premise: low frequency of blinking could stem from staring at something that intrigues/shocks the person (paying much attention) or simply from spacing out (lack of attention). By contrast, option C involves a variable that the description presents as relevant.

Incidentally, the formulation of A renders the test question ("Which finding, if true, would most directly weaken the critic's claim?") ambiguous as to whether "blinking [...] indicates attention" is part of what needs to be ascertained (in addition to "equally frequent blinking") versus being taken at face value. The proper way to establish the latter would be in the description of the scenario just like the remark regarding pupil size.

Option C is the correct option because not only it departs from the steadiness depicted in A [and B], but it actually goes in the opposite direction of what one would expect for consistency with the critic's assertion. A finding of A or B are inconsequential or inconclusive, whereas C most directly works against the critic's claim.

One of the answers purports to select A on the basis that it is consistent with a correlation regardless of whether that correlation is positive or negative. That argument is flawed because the adjectives in the clause "reduced heart rate can also be associated with increased attention" imply that the association is to be construed as positive correlation between "reduced heart rate" and "increased attention". To preserve admissibility of a negative correlation the statement would have to omit the adjectives reduced and increased.

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  • This does appear to be the only correct answer. Thank you for clarifying! Commented Sep 27, 2025 at 14:42
  • please - can you simplify, or expound on, your last paragraph? as this is a SAT question, kindly explain it like i'm 15 years old? what do you mean by "To preserve admissibility of a negative correlation"? Dale M's answer didn't contend "a negative correlation" by the bye, doesn't your last paragraph overcomplicate the correlation? isn't "positive correlation between "reduced heart rate" and "increased attention" the same as NEGATIVE correlation between "heart rate" and "increased attention"? if so, clearer to frame this correlation as NEGATIVE between "heart rate" and "increased attention"? Commented Nov 30, 2025 at 7:33
  • @user196764 "Dale M's answer didn't contend "a negative correlation"". Exactly. It did not, and it cannot. Evidencing a negative correlation between certain condition and the claimed effect would weaken the critic's claim more directly than evidencing that a condition is irrelevant to (i.e., compatible with) said claim. The statement "To preserve [...]" explains how the description does not support a finding of negative correlation. "clearer to frame this correlation as NEGATIVE between "heart rate" and "increased attention"?" I phrased my rationale in terms of researchers' propositions. Commented Dec 6, 2025 at 21:50
  • doesn't your last paragraph overcomplicate the correlation? isn't "positive correlation between "reduced heart rate" and "increased attention" the same as NEGATIVE correlation between "heart rate" and "increased attention"? if so, clearer to frame this correlation as NEGATIVE between "heart rate" and "increased attention"? Commented Dec 13, 2025 at 2:48
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    @user196764 The point of that statement isn't merely to summarize the correlation between heart rate and attention, but to explain why the phrasing of the scenario falls short of supporting the critic's rationale. Commented Dec 13, 2025 at 22:06
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Yeah, this question is brutal. I was stumped for a bit.

According to the critic, infants pay more attention to lullabies than non-lullabies. Now, there are two ways to refute the critic:

  1. showing that infants pay equal attention to lullabies and non-lullabies; and
  2. showing that infants pay less attention to lullabies than non-lullabies.

Before we analyze the answers, let's get some terminology on the table:

  • A's pupil-size effect on S = how much A causes S's pupils to change in size
  • A's blinking-rate effect on S = how much A causes S's blinking to change in frequency

If A has a positive pupil-size effect, then A causes your pupils to increase in size (relative to a baseline). By contrast, if A has a negative pupil-size effect, then A causes your pupils to decrease in size (relative to a baseline).

Answer (A) supports (1). That is, Answer (A) implies that infants pay equal attention to lullabies and non-lullabies. To see how, just consider this argument:

  • P1 If A has the same blinking-rate effect as B, then A captures just as much attention as B.
  • P2 And lullabies have the same blinking-rate effect as non-lullabies.
  • C So, lullabies capture just as much attention as non-lullabies.

P1 and P2 are both stated in Answer (A). Or at least the problem's author apparently intends as much.

Now for the nasty trick. Answer (C) seems to support (2). That is, Answer (C) seems to imply that infants pay less attention to lullabies and non-lullabies. To see how, just consider this argument:

  • P1 If A has a smaller pupil-size effect than B, then A captures less attention than B.
  • P2 And lullabies have a smaller pupil-size effect than non-lullabies.
  • C So, lullabies capture less attention than non-lullabies.

P2 is stated in Answer (C). Or at least the problem's author apparently intends as much. P1 seems to be stated in the passage—namely, in this quote:

[P]upils typically become larger when a stimulus captures a person's attention.

But there's a problem. This quote doesn't really state P1. That is, it doesn't really state:

  • If A has a smaller pupil-size effect than B, then A captures less attention than B.

Instead, that quote actually says:

  • If A captures attention at all, then A's pupil-size effect is positive.

This premise isn't the one we need to get (2).

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  • "If A captures attention at all, then A's pupil-size effect is positive" is not the right interpretation of the pupil size quote. It's ambiguous exactly what the right interpretation is, but it's also ambiguous what "blinking indicates attention" means. The most we should say is that there's some positive causal effect between attention and blinking, and also some positive causal effect between attention and pupil size. And then (C) is making a stronger statement to refute the critic. I'd say OP's answer key is just wrong, like it was in the other question he asked. Commented Sep 8, 2025 at 10:51
  • Neither pupil-size nor blinking show that the critic is wrong, because neither pupil-size nor blinking are perfect indicators of attention. We cannot make deductive inferences here. They just make it more likely the critic is wrong. The pupil-size indicator is stronger, because it suggests the babies were paying less attention to the lullaby, while the blinking indicator is weaker, because it doesn't show any difference. Commented Sep 8, 2025 at 10:54
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The statements are independent

The question is “Which finding, if true, would most directly weaken the critic’s claim?”. Remember what the claim is: “the lullaby relaxed the infants” (more than the other song).

A. Blinking indicates attention. It was equally prevalent. Therefore the infants paid equal attention to both songs. This weakens the claim.

B. Neither song was familiar. This doesn’t impact the claim either way.

C. Infants’ pupils are smaller when listening to lullabies. The size of the infants’ pupils are irrelevant to the claim. Or anything else (apart from the size of their pupils) for that matter.

D. The parent’s choices are irrelevant to the claim.

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  • I agree with this answer, but I bet this will still be confusing to the OP. The pupil size does have some relevance (indicating relative lack of attention while listening to the lullabies). It's just that this cannot as directly serve as evidence against the claim (reduced heart rate because of relaxation). Commented Sep 6, 2025 at 13:58
  • A doesn't end up weakening the critic's claims. Makes attention a non-factor, meaning we can't solely attribute the difference in heart rate to attention. The critic could present a counterexample where both lullaby and non-lullaby captured attention, and there was some additional factor causing the difference. Commented Sep 6, 2025 at 15:42
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    The entire text is comparative between lullaby and non-lullaby, so when the critic claims the lullaby simply attracted the attention, it necessitates that the lullaby attracted more attention than the non-lullaby. Greater decrease in heart rate during lullabies relative to non-lullabies Commented Sep 6, 2025 at 15:43
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    "the lullaby relaxed the infants" is not the critic's claim. That was the hypothesis of the researchers, the critic said that the lullaby attracts the infants' attention rather than relaxing them. Commented Sep 7, 2025 at 21:06
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    "pupils typically become larger when a stimulus captures a person's attention" -- why do you say pupil size is irrelevant to the claim? Commented Sep 7, 2025 at 21:10
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When you want to test a causal hypothesis, you do an experiment. An experiment consists of 2 groups, a test group and a control group. The suspected cause (e.g. music) is present im the test group but not in the control group; everything else is same between control and test groups. After that you look for a measurable difference between test and control groups (blinking. If there's a difference (more/less blinking in test group than in the control group) then that difference can only be because of the music, and hence a causal link is established between music and attention, as measured by blinks.

If there's no difference in the blinks then there is no causality i.e. music doesn't affect attention (measured by blinks).

We start off with the null hypothesis: there is no causal link between music and attention.
Our alternative hypothesis: there is a causal link between music and attention.

We do an experiment (sketch provided above) and look for a difference between blinks in control and test groups. If there is a difference then we have to determine if that is statistically significant (unlikely to be due to random chance). If yes, the difference is statistically significant we reject the null hypothesis and accept the alternative hypothesis. If no, we fail to reject the null hypothesis.

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  • This answer eludes what the OP is asking. Since the exact same outline of hypothesis testing can be applied to pupil size, this answer offers no actual rationale for selecting A over C. Commented Sep 15, 2025 at 10:14
  • The OQ isn't complaining Commented Sep 15, 2025 at 11:19
  • "The OQ isn't complaining". That doesn't mean the OP thinks this answer at least addresses the question. Commented Sep 15, 2025 at 11:52
  • @IñakiViggers it raises the possibility that you could be hallucinating Commented Sep 17, 2025 at 6:15
  • "you could be hallucinating". Try articulating actual, concrete ideas instead of coming up with bot-style responses. I explained the issue with your answer, and so far you've proved unable to establish why your answer isn't applicable to option A too. Commented Sep 17, 2025 at 10:24
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You are trying to understand why A prevails over C as an answer to explaining calmness:

A. Blinking [BL], which indicates attention, was equally frequent whether infants were listening to the song in Scottish Gaelic or song in Seri.

C. The infants' pupils were smaller [PS] when the infants were listening to lullabies [L] than when they were listening to non-lullabies [L*].

The authors concluded it was decreased heart rate [-HR] caused by relaxation:

The team found that the infants' heart rates decreased more during the lullaby than during the non-lullaby. Since a decrease in heart rate is associated with relaxation, the team concluded that the lullaby relaxed the infants.

The critic claims that increased attention [+A] also decreases heart rate, and not tempo is the dominant variable.

Noting that reduced heart rate can also be associated with increased attention, one critic argues that instead, the lullaby simply attracted the infants' attention. Bainbridge and colleagues also measured pupil size, as pupils typically become larger when a stimulus captures a person's attention.

Since blinking and pupil size are both proportional to attention, if measured blinking does not differ between lullabies and non-lullabies, then babies paid equal attention to both, and therefore attention cannot explain the decreased heart rate recorded with playing lullabies since a decrease in heart rate might be caused by an increase in attention and therefore blinking (inverse proportionality).

+A_BL -> -HR and -A_BL -> +HR from L to L*.

Instead, from L to L*, we see a change in D without a change in A:

0A_BL -> -HR and 0A_BL -> +HR from L to L*.

Therefore, if there is no change in A, we cannot attribute the change in D to it, and B is an irrelevant variable, and the critic must be wrong entirely. On the other hand we have:

-A_PS -> -HR and +A_PS -> +HR from L to L*.

Here, we do see a change in A correlates with a change in D. So the critic may be right that A correlates to D rather than R, though the proportion is not an inverse. Here the critic is only partially wrong, the mistake being whether or not there is a proportion or inverse proportion.

So, there you have it. In the question of whether it is relaxation or attention, only when attention can be shown not to vary from lullaby to non-lullaby when heart rate changes, can we conclude that the critic's claim has no merit since there is no difference in lullabies and non-lullabies. Only heart rate changes vary and therefore relaxation is the stronger hypothesis. When attention does vary, even if it is an inverse rather than straight proportion, we are still left with the competing claim that attention rather relaxation is at play even though the critic may have gotten it wrong that it is actually a decrease in attention that calms the infant. That is why A is superior to C in the reasoning.

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  • The use of adjectives reduced and increased in "reduced heart rate can also be associated with increased attention" suggests that the correlation between "reduced heart rate" and "increased attention" is to be construed as positive. The only way to preserve the ambiguity that would result in option A being correct is to state that "heart rate can also be associated with attention". The act of blinking is not even brought up in the description. Commented Sep 14, 2025 at 13:31

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