Horologist: "Mechanical watches with an Elaboré grade movement are man

Question

Horologist: "Mechanical watches with an Elaboré grade movement are manufactured to a tolerance of  \pm 20  seconds per day. However, our internal testing shows that if such a watch is worn for only a short interval - such as a single afternoon - and loses precisely one second, it is a fallacy to assume the watch is operating outside its specified range. Because the rate of a mechanical movement is inherently variable based on the position of the watch and the state of the mainspring's tension, any short-term measurement is statistically decoupled from the established 24-hour mean."

Which of the following, if true, most undermines the horologist's claim that a short-term measurement is decoupled from the 24-hour mean?

(A) Among Elaboré movements tested individually, the rate deviation observed during the first two hours after being wound shows no consistent directional trend across different units, yet each individual unit tends to maintain its own characteristic deviation pattern throughout the remainder of the 24-hour cycle.

(B) In a large sample of Elaboré movements, the average deviation calculated over a four-hour window shows a strong, positive correlation with the deviation calculated over a subsequent twenty-four-hour period.

(C) The mainspring tension in an Elaboré grade movement remains essentially constant throughout the power reserve cycle until the movement ceases to operate.

(D) Watches that lose time during the first half of a day are statistically more likely to gain time during the second half of the day.

(E) Laboratory analysis of Elaboré movements reveals that position-induced rate variation - the second pillar of the horologist's argument - follows a systematic and repeatable pattern across orientations, such that a movement's short-term positional bias can be reliably extrapolated to predict its net daily rate.

nikhilkaps · Answer

For the  short-term measurement  to be statistically decoupled from the established 24-hour mean, both measurements must be  uncorrelated .

A -  no consistent directional trend ... this seems to suggest that seconds gained in one period can be lost in another and thus strengthens the argument.
B - This explicitly  states a correlation . The measurements cant be decoupled...so this  weakens the argument 
C - We are not aware of how the tension in the spring effects the deviation measurement ...irrelevant
D - Time lost during one period, can be gained in another...strengthens
E -  "short-term positional bias can be reliably extrapolated to predict its net daily rate" ... in other words it says that both measurements are coupled

Hence the answer is B

ArmaanBajaj · Answer

Can someone please explain this question?

guddo · Answer

Horologist: Mechanical watches with an Elaboré grade movement are manufactured to a tolerance of ±20 seconds per day. However, our internal testing shows that if such a watch is worn for only a short interval, such as a single afternoon, and loses precisely one second, it is a fallacy to assume the watch is operating outside its specified range. Because the rate of a mechanical movement is inherently variable based on the position of the watch and the state of the mainspring's tension, any short-term measurement is statistically decoupled from the established 24-hour mean. 
 
Which of the following, if true, most undermines the horologist's claim that a short-term measurement is decoupled from the 24-hour mean?

The horologist says a short-term result does not reliably tell us the watch’s 24-hour average rate.  To weaken that claim, we need evidence that short-term deviation is actually connected to the daily deviation . In other words, a short measurement should have predictive value for the  24-hour mean .

(A) Among Elaboré movements tested individually, the rate deviation observed during the first two hours after being wound shows no consistent directional trend across different units, yet each individual unit tends to maintain its own characteristic deviation pattern throughout the remainder of the 24-hour cycle.

This weakens somewhat. It suggests each watch may have a stable pattern, but it does not directly say that a short-term measurement predicts the 24-hour mean.

(B) In a large sample of Elaboré movements, the average deviation calculated over a four-hour window shows a strong, positive correlation with the deviation calculated over a subsequent twenty-four-hour period.

This is correct. If a four-hour deviation strongly correlates with the 24-hour deviation, then the short-term measurement is not statistically decoupled from the daily mean. It is meaningfully connected to it.

(C) The mainspring tension in an Elaboré grade movement remains essentially constant throughout the power reserve cycle until the movement ceases to operate.

This weakens one part of the horologist’s explanation, but it does not directly show that short-term measurements predict the 24-hour mean.

(D) Watches that lose time during the first half of a day are statistically more likely to gain time during the second half of the day.

This supports the horologist. It suggests short-term loss may be offset later, so short-term measurement may not reflect the daily average.

(E) Laboratory analysis of Elaboré movements reveals that position-induced rate variation follows a systematic and repeatable pattern across orientations, such that a movement's short-term positional bias can be reliably extrapolated to predict its net daily rate.

This also weakens the horologist’s claim, but it focuses specifically on position-induced bias. B is stronger because it directly establishes a statistical relationship between short-term deviation and the 24-hour deviation.

Answer: (B)

egmat · Answer

Hi ArmaanBajaj,

The fastest way into this one is to lock onto the  exact claim  you're asked to attack, which nikhilkaps flagged well: the horologist says any short-term measurement is  "statistically decoupled from the established 24-hour mean."

What "decoupled" really means:  the short reading tells you  nothing  about the full-day rate - the two are uncorrelated. So to  undermine  it, you just need one piece of evidence showing the short reading  does  predict the daily rate. That's it. The whole question reduces to:  find the choice that links a short window to the 24-hour result.

Why (B) wins:  it says the deviation over a  four-hour window  is  "strongly, positively correlated"  with the deviation over the  subsequent 24-hour period.  That is the direct opposite of "decoupled" - a short measurement that reliably tracks the daily mean. Argument broken.

Why the tempting ones fail:

(A)  actually leans the horologist's way -  "no consistent directional trend"  early on suggests the short reading isn't a clean predictor. The "characteristic pattern" part is mixed at best, not a clean link.

(D)  says early losses tend to be offset later. That's regression to the mean - it  supports  decoupling, not undermines it.

(C)  only disputes one supporting premise (mainspring tension). It never connects a short measurement to the daily mean.

(E)  is the trap. It fixes only the  position  pillar and shows  that  is predictable - but it addresses just one of two mechanisms and never ties a full short-term reading to the  24 -hour rate the way (B) does. Narrower, so weaker.

The takeaway:  "decoupled" = no correlation. The cleanest weakener is simply direct evidence of correlation - don't get pulled into a choice that only repairs one sub-mechanism.

Quick gut check to lock it in: if I claim  "a person's mood at noon tells you nothing about their mood all day,"  which fact kills that fastest - (i)  "noon mood strongly predicts full-day mood,"  or (ii)  "their noon mood is influenced by lighting" ? You'd pick (i) instantly. That's exactly (B) over (E)/(C).

Answer: B

Horologist: "Mechanical watches with an Elaboré grade movement are man

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Horologist: "Mechanical watches with an Elaboré grade movement are man

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