MikaStars39/nano-eval huggingface dataset:
A homeowner agreed to buy a neighbor's car for the fair market value of $16,000. The two-year-old car was a popular make and model in excellent condition. The contract specified that, if for any reason the homeowner failed to pay the full $16,000 on the agreed date of the sale, the homeowner would owe the neighbor $16,000 as liquidated damages. The homeowner was subsequently laid off and was unable to purchase the car on the date of the sale. The neighbor immediately sued the homeowner for breach of contract, seeking $16,000 in liquidated damages.
Is the court likely to enforce the liquidated damages provision of the contract?

Options:
A. Yes, because $16,000 was the fair market value of the car, and thus is a reasonable estimate of the neighbor's anticipated loss.
B. No, because the neighbor would be able to sell the car to another buyer if the neighbor desired to do so, making the amount of the neighbor's actual loss much lower than $16,000.
C. Yes, because liquidated damages provide a clear financial remedy when calculating actual damages is challenging.
D. No, because the fair market value and the sale price were the same, making further damages unreasonable to enforce.
E. Yes, because liquidated damages are enforceable when they represent an estimate of actual loss for a breach.
F. Yes, because $16,000 was the contract price, and thus the amount that the neighbor lost in expectation interest as a result of the homeowner's breach.
G. Yes, because the homeowner's inability to pay does not nullify the obligation to cover estimated losses.
H. No, because the homeowner's loss of a job is likely to excuse her performance of the contract.
I. No, because the contract price is not indicative of the neighbor's expectation interest in the transaction.
J. No, because the contract's liquidated damages clause explicitly covers the scenario of non-payment by the buyer.
Answer: B
A librarian agreed to sell her private book collection to her neighbor. Before the closing date, the librarian's house was intentionally damaged by arson, and the book collection was mostly destroyed in the fire. On the date of performance, the neighbor refused to pay anything for the few books remaining in the collection. In a subsequent breach of contract action brought by the librarian against the neighbor, the court found that the neighbor must still perform the contract and pay the full amount that the parties had agreed upon.
Which of the following findings, if any, would explain the court's ruling for the librarian?

Options:
A. The neighbor inherited the damaged books from the librarian.
B. The contract included a clause about book condition.
C. The librarian misrepresented the value of the book collection.
D. The neighbor was the arsonist.
E. The neighbor didn't tell the librarian why she wished to buy the collection.
F. The neighbor purchased another collection elsewhere.
G. The books were insured, and the librarian received compensation.
H. The librarian colluded with the neighbor to destroy the books.
I. The neighbor lacked the funds to complete the purchase.
J. The librarian had replacement copies of all the destroyed books.
Answer: D
A gamer agreed to purchase a friend's used smart TV for $100. When negotiating the sale, the gamer had asked the friend if the Internet function on the TV worked. The friend said, "The last time I checked, the Internet worked." The gamer never inspected the TV. The parties reduced their agreement to a writing that they both intended to serve as their final and complete agreement. The written agreement contained the disclaimer, "The seller makes no warranties about the smart TV, either express or implied, including oral representations." In addition, the written agreement stated, in large-print, bold letters, "The TV is sold as is." When the gamer attempted to set up the TV, the Internet function did not work.
If the gamer brings a claim against the friend for the faulty TV and argues that there was a warranty based on the parties' discussion about the Internet function, is the gamer likely to prevail?

Options:
A. Yes, because the friend's oral assurance that the Internet function worked created an express warranty, which was violated.
B. No, because the gamer explicitly accepted the TV "as is," assuming all risks associated with its condition.
C. Yes, because the friend's oral statement overrides the written disclaimer about the TV's condition.
D. Yes, because the friend's oral assurance that the Internet function worked created an implied warranty of fitness for a particular purpose, which was violated.
E. No, because the friend's statement likely did not create a warranty as to the Internet function, and if it did, evidence of the statement would be excluded by the parol evidence rule.
F. Yes, because the friend's oral assurance that the Internet function worked created a hidden defect warranty, which was violated.
G. No, because the gamer had a duty to examine the TV prior to purchase.
H. Yes, because the gamer reasonably relied on the friend's assurance about the Internet function, creating a reliance-based warranty.
I. No, because the disclaimer in the written agreement negates any potential warranties from oral statements.
J. No, because the verbal assurance about the Internet function has no legal effect due to the written agreement.
Answer: E
A recording company entered into a contract with a famous singer to record an album. Under the terms of the contract, the singer would receive one payment up front, followed by a much larger payment once the album was released. After the singer recorded the album, she experienced a personal scandal that greatly decreased her popularity. The recording company believed that it would lose money by releasing the album, as the payment owed to the singer upon release would likely be greater than the amount the company would earn from sales of the album. The company reviewed the terms of the contract with the singer and realized that nothing in the contract specified a date by which the album had to be released. The company decided to not release the album.
If the singer sues the company for breach of contract, how will a court likely rule?

Options:
A. It will require arbitration to determine the fair release date for the album.
B. It will void the contract because the absence of a key term means that the contract is too indefinite to be enforced.
C. It will void the contract because the absence of a key term means that there was not mutual assent.
D. It will impose a duty of good faith and require the company to release the album within a reasonable time after its recording.
E. It will require renegotiation of terms since the scandal altered the contract's fundamental assumptions.
F. It will interpret the contract based on the purpose of the recording company for entering into the contract, which was to make money, and not require the company to release the album because doing so would no longer be profitable.
G. It will impose a duty to renegotiate the contract terms to account for the scandal's impact.
H. It will declare the contract void due to the unforeseen change in the singer's public perception.
I. It will rule that the album cannot be released until the singer's reputation is restored.
J. It will hold the company responsible for lost profits due to the delay in album release.
Answer: D
A couple of days before her 18th birthday, a girl entered into a contract with an adult.
The girl understood the overall nature and consequences of entering into the contract. The adult knew that the girl was 17 at the time the contract was signed, but believed that the girl's age was not an issue since the girl would be 18 by the time her performance was due. Two weeks later, the girl informed the adult that she would not perform under the contract. The adult sued to enforce the contract, and the girl raised a defense of incapacity.
Is the girl's defense likely to succeed?

Options:
A. Yes, because the adult knew about the girl's incapacity at the time the contract was formed.
B. No, because the girl's performance was not due until she was 18 years old.
C. Yes, if the contract specified that age was irrelevant to the enforcement, which it did not.
D. Yes, because the girl was under the age of majority at the time she signed the contract, regardless of the adult's knowledge of this fact.
E. Yes, because the girl's age was not disclosed accurately to the adult by any official documents.
F. No, because the girl's infancy did not prevent her from understanding the nature and consequences of the contract.
G. No, because the contract would become voidable only if the girl had misrepresented her age intentionally.
H. No, since the girl had the capacity to comprehend the essential terms and obligations at hand.
I. Yes, provided the girl had parental consent to sign the contract, which would be a significant factor.
J. No, as the girl was capable of entering contracts owing to the anticipated age at the performance.
Answer: D
A home-appliance retailer offered in an email to purchase 100 toaster ovens of a particular model and 100 microwaves of a particular model from their manufacturer, stating that he would pay the same price that he had paid for the same items in a previous contract with the manufacturer. The manufacturer's manager replied by email that he would promptly ship 100 toaster ovens and 100 microwaves to the retailer. However, the email explained that the manufacturer was having shipping problems with its toaster ovens and that some had been arriving to customers damaged. The manager's email stated that any objections to the quality of the toaster ovens had to be sent via email by the retailer within five business days. Similar due dates for quality objections were standard in the home-appliance industry.
What is the legal status of the retailer's offer to buy 100 toaster ovens and 100 microwaves?

Options:
A. The offer was void due to quality objections on toaster ovens.
B. The offer was terminated by the manufacturer's rejection and counteroffer.
C. The offer was invalid due to differences in shipping problems.
D. The offer was accepted as to both the toaster ovens and microwaves.
E. The offer was ignored because of the damaged toaster ovens.
F. The offer was accepted as to microwaves and rejected as to toaster ovens.
G. The offer was declined due to shipping issues with toaster ovens.
H. The offer was accepted as to microwaves, and will remain open as to toaster ovens for a reasonable time.
I. The offer was rejected because the manufacturer did not agree.
J. The offer was unacceptable and needed further negotiation.
Answer: D
An attorney brought suit in federal court for a plaintiff's injuries that occurred in another state. Based on his experience with his own state's two-year statute of limitations, the attorney drafted and filed the complaint 15 months after the injuries occurred, believing the case was well within the statute of limitations. However, the other state had a one-year statute of limitations, resulting in dismissal of the suit as time-barred.
May the court sanction the attorney for his mistake in assuming that a two-year statute of limitations applied?

Options:
A. Yes, because the attorney's signature makes him strictly liable for any defects in the complaint.
B. No, because the attorney checked the local court's rules before filing.
C. No, because the attorney has the right to amend the plaintiff's pleadings once as a matter of course.
D. No, because the attorney believed the client had a good faith basis for filing.
E. No, because the attorney consulted expert legal opinion regarding filing timing.
F. Yes, because the attorney missed crucial discovery deadlines in the case.
G. No, because the attorney relied on his extensive experience in similar cases.
H. No, because the attorney thought that the plaintiff's case was warranted by existing law.
I. Yes, because the attorney should have known that the plaintiff's case was not warranted by existing law.
J. Yes, because the attorney himself assumed the case was time-barred by the law.
Answer: I
A plaintiff sued a defendant in federal district court. Ten days after being served with the complaint, the defendant filed a motion under Rule 12(f) to strike portions of the complaint. One month later, the district court denied the motion. The defendant filed an answer to the complaint five days after the district court's order denying the motion to strike. Fourteen days after being served with the defendant's answer, the plaintiff wanted to amend her complaint to add new claims.
May the plaintiff amend her complaint without the defendant's consent or leave from the court?

Options:
A. No, because the plaintiff did not respond within 10 days to the defendant's answer.
B. Yes, because each party may amend its pleading once as of right at any time.
C. Yes, because less than 21 days have passed since the plaintiff was served with the defendant's answer.
D. No, because more than 21 days have passed since the plaintiff was served with the defendant's motion to strike.
E. Yes, because the district court denied the defendant's motion to strike the complaint.
F. Yes, because the plaintiff can amend the complaint at any time before trial.
G. No, because more than 10 days have passed since the plaintiff was served with the defendant's answer.
H. No, because fewer than 14 days have passed since the plaintiff was served with the defendant's answer.
I. Yes, because more than 14 days have passed since the defendant filed the motion to strike.
J. No, because fewer than 21 days have passed since the defendant filed the motion to strike.
Answer: D
A manufacturer obtained an exclusive license from a patentee. The license granted the manufacturer the sole rights to make and sell a patented product in State A. The license agreement also stated that the patentee would refrain from licensing any manufacturer in bordering States B and C for a period of two years. One year into the license agreement, the manufacturer noticed that another company was making and selling a similar product in State B. The manufacturer believed the similar product infringed the patent under which it held the license. When the manufacturer confronted the company, the company explained that it, too, had a license from the patentee. The manufacturer sued the patentee for breach of contract in federal district court in State A. The patentee moved to dismiss the complaint under Rule 12(b)(7) for failure to join a required party.
Is the district court likely to conclude that the company is a necessary party?

Options:
A. No, because the court prefers not to complicate the action.
B. No, because the patentee's actions alone are under scrutiny.
C. Yes, because the manufacturer has no other legal recourse.
D. Yes, because the company is central to the infringement claim.
E. No, because the manufacturer may obtain complete relief from the patentee.
F. Yes, because proceeding in the company's absence would risk multiple, inconsistent liabilities for the patentee.
G. No, because the manufacturer's rights are not impacted directly.
H. No, because the company's interest may be pursued in a separate litigation against the patentee.
I. Yes, because the company's conduct triggered the lawsuit.
J. Yes, because it influences the exclusivity of the license.
Answer: F
Holding all other factors constant, a decrease in the price of a certain commodity will lead to ( ).

Options:
A. Economic capacity growth is solely determined by the number of laborers.
B. Greater governmental intervention in trade.
C. Decrease in consumer interest for that commodity.
D. Inflation
E. Unemployment
F. Increased consumer demand for luxury goods.
G. Abundance in human labor welfare.
H. Promotion of sustainable agricultural practices.
I. Increase in useful resources or technological advancement
J. Shift towards artisanal & hand-crafted products.
Answer: E
A sample of diamond has a $\mathbf{\delta}^{13}$C value relative to the lab standard.The lab standard has a $\mathbf{\delta}^{13}$C value of -6.50 relative to VPDB.What is the diamond relative to VPDB?

Options:
A. $0.9850 * \delta^{14} \mathrm{C}_{\mathrm{DMD}, \mathrm{Std}}-6.4991$
B. $0.9935 * \delta^{13} \mathrm{C}_{\mathrm{DMT}, \mathrm{Std}}-6.4990$
C. $0.9935 * \delta^{12} \mathrm{C}_{\mathrm{DMD}, \mathrm{Std}}-6.4999$
D. $0.9935 * \delta^{15} \mathrm{C}_{\mathrm{DMD}, \mathrm{Std}}-6.4993$
E. $0.9935 * \delta^{13} \mathrm{C}_{\mathrm{DMT}, \mathrm{Std}}-6.4997$
F. $0.9935 * \delta^{18} \mathrm{C}_{\mathrm{DMD}, \mathrm{Std}}-6.0000$
G. $0.9935 * \delta^{14} \mathrm{C}_{\mathrm{DMD}, \mathrm{Std}}-6.4998$
H. $1.0000 * \delta^{13} \mathrm{C}_{\mathrm{DMD}, \mathrm{Std}}-6.5000$
I. $0.9935 * \delta^{13} \mathrm{C}_{\mathrm{DMD}, \mathrm{Std}}-6.4998$
J. $0.8500 * \delta^{13} \mathrm{C}_{\mathrm{DMD}, \mathrm{Std}}-5.9998$
Answer: I
What is the balanced redox reaction coupling the reduction of selenate to the oxidation of acetate and calculating its energy yield?

Options:
A. $2 / 8 \mathrm{~ a c e t a t e} + 2 / 6 \mathrm{~ S e O_{2}^{~ 4 -}+4 / 2 5 ~ H^{+} ~}=2 / 6 \mathrm{~ S e}_{( g )}+2 / 6 \mathrm{~ H_{2} O}+2 / 4 \mathrm{~ H C O_{2}^{~ -} ~}$
$\mathrm{p e}^{\circ}=1 1. 7 8$
$$
\Delta G^{\circ}=
- 5 5. 0 2 \, \mathrm{K J / m o l ~ e l e c t r o n s}
$$
B. $2 / 8 \mathrm{~ a c e t a t e-}+3 / 6 \mathrm{~ S e O_{3}^{~ 2 -}+5 / 2 3 ~ H^{+} ~}=1 / 6 \mathrm{~ S e}_{( s )}+1 / 6 \mathrm{~ H_{2} O}+1 / 4 \mathrm{~ H C O_{3}^{~ -} ~}$
$\mathrm{p e}^{\circ}=1 1. 6 8$
$$
\Delta G^{\circ}=
- 6 5. 0 2 \, \mathrm{K J / m o l ~ e l e c t r o n s}
$$
C. $1 / 8 \mathrm{~ a c e t a t e-}+1 / 6 \mathrm{~ S e O_{4}^{~ 2 -}+5 / 2 4 ~ H^{+} ~}=1 / 6 \mathrm{~ S e}_{( s )}+1 / 6 \mathrm{~ H_{2} O}+1 / 4 \mathrm{~ H C O_{3}^{~ -} ~}$
$\mathrm{p e}^{\circ}=1 1. 5 8$
$$
\Delta G^{\circ}=
- 6 6. 0 2 \, \mathrm{K J / m o l ~ e l e c t r o n s}
$$
D. $1 / 6 \mathrm{~ a c e t a t e-}+1 / 5 \mathrm{~ S e O_{4}^{~ 3 -}+5 / 3 4 ~ H^{+} ~}=1 / 6 \mathrm{~ S e}_{( s )}+1 / 6 \mathrm{~ H_{2} O}+1 / 4 \mathrm{~ H C O_{3}^{~ -} ~}$
$\mathrm{p e}^{\circ}=1 4. 5 8$
$$
\Delta G^{\circ}=
- 7 7. 0 2 \, \mathrm{K J / m o l ~ e l e c t r o n s}
$$
E. $1 / 8 \mathrm{~ a c e t a t e-}+2 / 6 \mathrm{~ S e O_{4}^{~ 2 -}+4 / 2 4 ~ H^{+} ~}=2 / 6 \mathrm{~ S e}_{( s )}+2 / 6 \mathrm{~ H_{2} O}+2 / 4 \mathrm{~ H C O_{3}^{~-} ~}$
$\mathrm{p e}^{\circ}=1 1. 3 8$
$$
\Delta G^{\circ}=
- 5 6. 0 2 \, \mathrm{K J / m o l ~ e l e c t r o n s}
$$
F. $1 / 7 \mathrm{~ b u t y r a t e-} + 1 / 5 \mathrm{~ S e O_{3}^{~ 2 -}+5 / 4 2 ~ H^{+} ~}=1 / 5 \mathrm{~ S e}_{( s )}+1 / 5 \mathrm{~ H_{2} O}+1 / 5 \mathrm{~ H C O_{3}^{~ -} ~}$
$\mathrm{p e}^{\circ}=1 0. 4 8$
$$
\Delta G^{\circ}=
- 6 7. 0 2 \, \mathrm{K J / m o l ~ e l e c t r o n s}
$$
G. $2 / 8 \mathrm{~ a c e t a t e-}+2 / 9 \mathrm{~ S e O_{4}^{~ 3 -}+3 / 1 4 ~ H^{+} ~}=1 / 6 \mathrm{~ S e}_{( s )}+1 / 6 \mathrm{~ H_{2} O}+1 / 4 \mathrm{~ H C O_{3}^{~ -} ~}$
$\mathrm{p e}^{\circ}=1 3. 4 8$
$$
\Delta G^{\circ}=
- 6 8. 0 2\, \mathrm{K J / m o l ~ e l e c t r o n s}
$$
H. $2 / 8 \mathrm{~ a c e t a t e-}+1 / 6 \mathrm{~ S e O_{4}^{~ 3 -}+5 / 2 9 ~ H^{+} ~}=1 / 6 \mathrm{~ S e}_{( s )}+1 / 6 \mathrm{~ H_{2} O}+1 / 4 \mathrm{~ H C O_{3}^{~ -} ~}$
$\mathrm{p e}^{\circ}=1 1. 7 8$
$$
\Delta G^{\circ}=
- 5 9. 0 2 \, \mathrm{K J / m o l ~ e l e c t r o n s}
$$
I. $3 / 8 \mathrm{~ a c e t a t e-}+1 / 7 \mathrm{~ S e O_{4}^{~ 4 -}+5 / 3 4 ~ H^{+} ~}=1 / 6 \mathrm{~ T e}_{( s )}+1 / 6 \mathrm{~ H_{2} O}+1 / 4 \mathrm{~ H C O_{3}^{~ -} ~}$
$\mathrm{p e}^{\circ}=1 2. 8 8$
$$
\Delta G^{\circ}=
- 7 9. 0 2 \, \mathrm{K J / m o l ~ e l e c t r o n s}
$$
J. $1 / 8 \mathrm{~ a c e t a t e-}+4 / 5 \mathrm{~ S e O_{4}^{~ 2 -}+5 / 3 4 ~ H^{+} ~}=1 / 6 \mathrm{~ S e}_{( g )}+1 / 6 \mathrm{~ H_{2} O}+1 / 4 \mathrm{~ H C O_{3}^{~ -} ~}$
$\mathrm{p e}^{\circ}=1 0. 9 8$
$$
\Delta G^{\circ}=
- 6 3. 5 2 \, \mathrm{K J / m o l ~ e l e c t r o n s}
$$
Answer: C
Which of the following pairs of words is a minimal pair?

Options:
A. bright-sprite
B. coat-goat
C. sun-fun
D. book-look
E. cat-rat
F. light-night
G. park-bark
H. pen-pan
I. shoe-zoo
J. mop-pop
Answer: I
When the distance a point radiation source is halved, the radiation level will be

Options:
A. Reduced to one-fourth
B. Reduced to one-fifth
C. Unchanged
D. Quadrupled
E. Tripled
F. Increased eightfold
G. Reduced to one quarter
H. Reduced to half
I. Decreased to one-third
J. Doubled
Answer: D
A radiation producing device which emits radiation of one or a few discreet wavelengths is ___

Options:
A. A monochromatic laser
B. A broadband radiator
C. A thermionic diode
D. A linear accelerator
E. A cathode ray tube
F. A synchrotron generator
G. An X ray machine
H. An ultrasonic transducer
I. A betatron
J. A gamma ray source
Answer: J
The radiation pattern of a half-wave dipole has the shape of a __

Options:
A. circular
B. hemisphere
C. teardrop
D. doughnut
E. pyramid
F. triangle
G. cube
H. ellipse
I. sphere
J. parabola
Answer: D
When it comes to protection against internal exposure, the following statements are correct ()

Options:
A. Internal exposure is commonly seen with unsealed radioactive materials, and once they enter the human body, the potential harm is significant.
B. Exposure of radioactive materials at the site of a wound to the human body is called internal exposure.
C. External exposure is the major concern with unsealed materials, with internal exposure largely being non-threatening.
D. For sealed gamma sources, the potential for internal exposure is negligible, so protective measures are unnecessary.
E. When gamma rays penetrate the human body from the outside and irradiate it, this situation is called internal exposure.
F. Non-sealed radioactive materials rarely cause internal exposure because they are primarily of concern outside the body.
G. Internal exposure is predominantly linked to external radioactive sources, and the risk is minimal once they enter the environment.
H. Internal exposure involves sealed radioactive materials, and the threat significantly decreases once they interact externally.
I. For non-sealed alpha sources, due to their poor penetration ability, internal exposure does not need to be considered.
Answer: A
The following statement best describes the purpose of workplace air pollution monitoring:

Options:
A. Investigate climate change impacts, and support research on biodiversity conservation.
B. Monitor indoor air quality inconsistencies, and maintain records for future technological upgrades.
C. Satisfying the Public's Right to Know
D. Provide data for evaluating public exposure doses
E. To provide data for verifying the applicability of the environmental impact assessment model
F. Evaluate the necessity of air purification systems, and ensure public accessibility to data.
G. Enhance awareness of environmental policies, and promote safe manufacturing standards.
H. Provide information for personal dose assessment, and warnings for anomalies or incidents.
I. Ensure compliance with labor laws, and motivate companies to reduce their carbon footprint.
J. Generate statistics for governmental air quality reports, and improve city planning regulations.
Answer: H
The relative inherent error of the environmental monitoring $\mathrm{X}$ and $\gamma$ radiation air kerma (absorbed dose) rate instrument does not exceed

Options:
A. ±30%
B. ±20%
C. ±55%
D. ±50%
E. ±5%
F. ±35%
G. ±25%
H. ±40%
I. ±10%
J. ±15%
Answer: J
Radiation-induced cell death in carcinomas typically occurs immediately after attempting to traverse which phase of the cell cycle?

Options:
A. G0
B. G2
C. G1
D. M
E. Cytokinesis
F. Interphase
G. Anaphase
H. G1/S checkpoint
I. S
J. G2 checkpoint
Answer: D
Find the theoretical limiting angular resolution of a commercial 8-inch (diameter) optical telescope being used in visible (at $\lambda=5 0 0 0 A=5 0 0 \mathrm{~ n m}=5 \times1 0^{-5} \mathrm{~ c m}=5 \times1 0^{-7} \mathrm{~ m} )$

Options:
A. $$1. 7 3 \mathrm{~ a r c s e c s}$$
B. $$0. 3 9 \mathrm{~ a r c s e c s}$$
C. $$0. 4 9 \mathrm{~ a r c s e c s}$$
D. $$1. 0 9 \mathrm{~ a r c s e c s}$$
E. $$3. 0 7 \mathrm{~ a r c s e c s}$$
F. $$0. 7 6 \mathrm{~ a r c s e c s}$$
G. $$2. 2 5 \mathrm{~ a r c s e c s}$$
H. $$0. 6 4 \mathrm{~ a r c s e c s}$$
I. $$1. 2 1 \mathrm{~ a r c s e c s}$$
J. $$0. 5 8 \mathrm{~ a r c s e c s}$$
Answer: C
Which method can be used to differentiate the following amino acids?
(i) Glycine (ii) Phenylalanine (iii) Proline (iv) Aspartic acid (v) Lysine

Options:
A. Analyzing the Electrophoresis Mobility of Five Amino Acids
B. Determining the Solubility Limits of Five Amino Acids
C. Measuring the Isoelectric Points of Five Amino Acids
D. Comparing the UV Absorption Spectra of Five Amino Acids
E. Observing the Crystallization Patterns of Five Amino Acids
F. Identifying the Chromatographic Retention of Five Amino Acids
G. Studying the Enzymatic Activity of Five Amino Acids
H. Investigating the Reaction with Ninhydrin for Five Amino Acids
I. Calculating the Molecular Weights of Five Amino Acids
J. Examining the Infrared Spectra of Five Amino Acids
Answer: C
Which type of simply supported reinforced concrete slab has the worst fire resistance limit when having the same thickness of protective layer?

Options:
A. Bonded Tension Coil Panel
B. Precast Ribbed Grid Sheet
C. Prestressed Circular Hole Plate
D. Reinforced Waffle Slab
E. Unbonded Flat Panel Deck
F. Tensioned Double-Wide Beam
G. Non-tensioned Fluted Slab
H. Reinforced Precast Hollow Plate
I. Tensioned Solid Beam Segment
J. Non-Prestressed Grid Slab
Answer: C
We now define an algorithm: The definition of a(n) is the layer counting sequence for hyperbolic tessellation by cuspidal triangles of angles (Pi/3, Pi/3, 0) - this is the classical modular tessellation. Given the input x_list (a series of values): [28, 29, 30, 31, 32, 33, 34, 35, 36, 37], determine the corresponding output sequence y_list.

Options:
A. [1664080, 2692538, 4356618, 7049156, 11405774, 18454930, 29860704, 48315634, 78176338, 126491972]
B. [1660000, 2690000, 4360000, 7050000, 11400000, 18400000, 29900000, 48400000, 78200000, 126500000]
C. [1600000, 2650000, 4340000, 7030000, 11400000, 18500000, 29800000, 48500000, 78200000, 126000000]
D. [1670000, 2680000, 4350000, 7040000, 11300000, 18300000, 29800000, 48200000, 78100000, 126000000]
E. [1650000, 2690000, 4350000, 7040000, 11400000, 18500000, 29700000, 48000000, 78000000, 126000000]
F. [1670000, 2680000, 4340000, 7020000, 11300000, 18500000, 29900000, 48300000, 78100000, 126490000]
G. [1660000, 2620000, 4350000, 7050000, 11300000, 18400000, 29800000, 48300000, 78300000, 126000000]
H. [1634010, 2672500, 4326600, 7019000, 11205000, 18054000, 29460000, 47815000, 77375000, 125490000]
I. [1600000, 2600000, 4300000, 7000000, 11000000, 18000000, 29000000, 47000000, 77000000, 120000000]
J. [1700000, 2700000, 4400000, 7100000, 11500000, 18500000, 30000000, 49000000, 79000000, 130000000]
Answer: A
We now define an algorithm: The definition of a(n) is the values of m for which a regular polygon with m sides cannot be constructed with ruler and compass, based on the classical constructions in Euclidean geometry. Given the input x_list (a series of values): [57, 58, 59, 60, 61, 62, 63, 64, 65, 66], determine the corresponding output sequence y_list.

Options:
A. [71, 72, 73, 74, 76, 77, 78, 79, 80, 81]
B. [51, 52, 53, 54, 56, 57, 58, 59, 60, 61]
C. [91, 92, 93, 94, 95, 97, 98, 99, 100, 101]
D. [101, 102, 103, 104, 106, 107, 108, 109, 110, 111]
E. [31, 32, 33, 34, 36, 37, 38, 39, 40, 41]
F. [81, 82, 83, 84, 86, 87, 88, 89, 90, 91]
G. [61, 62, 63, 64, 66, 67, 68, 69, 70, 71]
H. [21, 22, 23, 24, 26, 27, 28, 29, 30, 31]
I. [41, 42, 43, 44, 46, 47, 48, 49, 50, 51]
J. [111, 112, 113, 114, 116, 117, 118, 119, 120, 121]
Answer: F
We now define an algorithm: The definition of a(n) is the number of rooted polyhedral graphs with n edges, where a polyhedral graph is a graph that can be embedded on the surface of a sphere such that all its faces (including the unbounded one if consider planar graph) are bounded by simple cycles. Given the input x_list (a series of values): [22, 23, 24, 25, 26, 27, 28, 29, 30, 31], determine the corresponding output sequence y_list.

Options:
A. [42416488, 150716770, 538421590, 1932851590, 6969847486, 25237047110, 91729488354, 334589415276, 1224445617889, 4494622109424]
B. [42416488, 150718770, 538421590, 1932856590, 6969847486, 25237057110, 91729488354, 334589415276, 1224445617889, 4494622119424]
C. [42416488, 150718771, 538421590, 1932856590, 6969847486, 25237057110, 91729488354, 334589415276, 1224445617888, 4494622119424]
D. [42416489, 150718770, 538421590, 1932856591, 6969847486, 25237057110, 91729488351, 334589415276, 1224445617889, 4494622119424]
E. [42416488, 150718770, 538421590, 1932856590, 6969847486, 25237057110, 91729488354, 334589415277, 1224445617889, 4494622119423]
F. [32416488, 160718770, 538421590, 1832856590, 6969847486, 25237057110, 91729488354, 334589415276, 1124445617889, 4494622119424]
G. [42416488, 150718770, 538421590, 1932856590, 6969847486, 25237057110, 91729488354, 334589415276, 1224445617889, 3594822119424]
H. [42416487, 150718770, 538421590, 1932856590, 6969847486, 25237057110, 91729488354, 334589415275, 1224445617889, 4494622119423]
I. [42416488, 150718770, 538421590, 1932856590, 6969847495, 25237057110, 91729488354, 334589415276, 1224445617889, 4564622119424]
J. [42416488, 150718769, 538421591, 1932856590, 6969847487, 25237057111, 91729488355, 334589415276, 1224445617889, 4494622119425]
Answer: B
We now define an algorithm: The definition of a(n) is Landau's function g(n): the largest order of a permutation of n elements. Equivalently, the largest least common multiple (LCM) of all partitions of n. This function originates from number theory and combinatorics, specifically regarding the order of permutations and their cycle structures. Given the input x_list (a series of values): [38, 39, 40, 41, 42, 43, 44, 45, 46, 47], determine the corresponding output sequence y_list.

Options:
A. [16388, 16388, 27730, 30038, 32770, 60068, 60068, 60068, 60068, 120128]
B. [16384, 16384, 27726, 30034, 32766, 60064, 60064, 60064, 60064, 120124]
C. [16381, 16381, 27723, 30031, 32763, 60061, 60061, 60061, 60061, 120121]
D. [16380, 16380, 27720, 30030, 32760, 60060, 60060, 60060, 60060, 120120]
E. [16387, 16387, 27729, 30037, 32769, 60067, 60067, 60067, 60067, 120127]
F. [16385, 16385, 27727, 30035, 32767, 60065, 60065, 60065, 60065, 120125]
G. [16389, 16389, 27731, 30039, 32771, 60069, 60069, 60069, 60069, 120129]
H. [16383, 16383, 27725, 30033, 32765, 60063, 60063, 60063, 60063, 120123]
I. [16382, 16382, 27724, 30032, 32764, 60062, 60062, 60062, 60062, 120122]
J. [16386, 16386, 27728, 30036, 32768, 60066, 60066, 60066, 60066, 120126]
Answer: D
We now define an algorithm: The definition of a(n) is: Rearrangement of natural numbers such that a(n) is the smallest proper divisor of n not included earlier but if no such divisor exists then a(n) is the smallest proper multiple of n not included earlier, subject always to the condition that a(n) is not equal to n. Given the input x_list (a series of values): [59, 60, 61, 62, 63, 64, 65, 66, 67, 68], determine the corresponding output sequence y_list.

Options:
A. [118, 121, 123, 32, 126, 129, 130, 33, 134, 138]
B. [117, 120, 121, 32, 126, 128, 130, 33, 133, 136]
C. [118, 120, 122, 31, 126, 128, 130, 33, 134, 136]
D. [119, 120, 123, 31, 125, 129, 130, 33, 133, 135]
E. [118, 119, 123, 32, 125, 127, 131, 34, 135, 137]
F. [118, 121, 123, 31, 125, 127, 131, 34, 134, 138]
G. [117, 121, 122, 32, 126, 127, 131, 34, 133, 136]
H. [119, 120, 124, 31, 126, 128, 131, 34, 134, 137]
I. [119, 120, 122, 32, 127, 128, 131, 33, 135, 137]
J. [119, 121, 122, 32, 127, 128, 131, 33, 134, 136]
Answer: C
We now define an algorithm: The definition of a(n) is the number of unitary (and also of squarefree) divisors of n!, where n! is the factorial of n. Given the input x_list (a series of values): [41, 42, 43, 44, 45, 46, 47, 48, 49, 50], determine the corresponding output sequence y_list.

Options:
A. [1024, 1024, 2048, 2048, 2048, 2048, 4096, 4096, 4096, 4096]
B. [8192, 8192, 16384, 16384, 16384, 16384, 32768, 32768, 32768, 32768]
C. [16384, 16384, 16384, 16384, 16384, 16384, 16384, 16384, 16384, 16384]
D. [4096, 4096, 4096, 4096, 16384, 16384, 16384, 16384, 65536, 65536]
E. [8192, 8192, 8192, 8192, 32768, 32768, 32768, 32768, 32768, 32768]
F. [65536, 65536, 131072, 131072, 131072, 131072, 262144, 262144, 262144, 262144]
G. [512, 512, 1024, 1024, 1024, 1024, 2048, 2048, 2048, 2048]
H. [8192, 8224, 16384, 16416, 16448, 16480, 32768, 32800, 32832, 32864]
I. [256, 256, 512, 512, 512, 512, 1024, 1024, 1024, 1024]
J. [32768, 32768, 32768, 32768, 65536, 65536, 65536, 65536, 65536, 65536]
Answer: B
We now define an algorithm: The definition of a(n) is the number of ways to partition n labeled elements into 6 pie slices, where each partition must have at least one element in each slice. Given the input x_list (a series of values): [14, 15, 16, 17, 18, 19, 20, 21, 22, 23], determine the corresponding output sequence y_list.

Options:
A. [7601213470, 50392184720, 327281085970, 2091587471450, 13201473874660, 83079783489650, 515829341355120, 3181279880119630, 19516603220111500, 119075293856227400]
B. [7612364765, 50483192765, 328191186965, 2100689987765, 13282470124685, 83169792213485, 516729467446085, 3190281535536485, 19596640721427005, 119876382958008605]
C. [8212464760, 54483192760, 348191186960, 2300689987760, 13882470124680, 87169792213480, 536729467446080, 3290281535536480, 19996640721427000, 123876382958008600]
D. [7612364760, 50483192760, 328191186960, 2100689987760, 13282470124680, 83169792213480, 516729467446080, 3190281535536480, 19596640721427000, 119876382958008600]
E. [7612364460, 50484192760, 328181186960, 2100589987760, 13282420124680, 83169772213480, 516729467146080, 3190281534536480, 19596640721417000, 119876382958006500]
F. [7652364760, 50883192760, 332191186960, 2140689987760, 13482470124680, 83569792213480, 518729467446080, 3210281535536480, 19796640721427000, 121876382958008600]
G. [3682907935, 24620641535, 161418434735, 1033389821335, 6518563089335, 41261028126735, 261252873527935, 1652202667935935, 10367225483927935, 65045529947379935]
H. [7612364761, 50483192761, 328191186961, 2100689987761, 13282470124681, 83169792213481, 516729467446081, 3190281535536481, 19596640721427001, 119876382958008601]
I. [6523797560, 43281975600, 292627486960, 1863568789960, 11802387124680, 76128788213480, 491257467446080, 3038371535536480, 18697340721427000, 113876382958008600]
J. [12154850560, 80620601260, 524033177060, 3356219125060, 21671924375760, 143371634521060, 950414810315360, 6285245877673360, 41489578102724600, 273369503976049600]
Answer: D
We now define an algorithm: The definition of a(n) is the number of 5-dimensional centered tetrahedral numbers. Given the input x_list (a series of values): [20, 21, 22, 23, 24, 25, 26, 27, 28, 29], determine the corresponding output sequence y_list.

Options:
A. [191467, 241743, 302124, 374070, 459176, 559178, 675959, 811555, 968161, 1148137]
B. [191468, 241744, 302125, 374071, 459177, 559179, 675960, 811556, 968162, 1148138]
C. [191466, 241742, 302123, 374069, 459175, 559177, 675958, 811554, 968160, 1148136]
D. [191470, 241746, 302127, 374073, 459179, 559181, 675962, 811558, 968164, 1148140]
E. [191471, 241747, 302128, 374074, 459180, 559182, 675963, 811559, 968165, 1148141]
F. [191473, 241749, 302130, 374076, 459182, 559184, 675965, 811561, 968167, 1148143]
G. [191472, 241748, 302129, 374075, 459181, 559183, 675964, 811560, 968166, 1148142]
H. [191475, 241751, 302132, 374078, 459184, 559186, 675967, 811563, 968169, 1148145]
I. [191474, 241750, 302131, 374077, 459183, 559185, 675966, 811562, 968168, 1148144]
J. [191469, 241745, 302126, 374072, 459178, 559180, 675961, 811557, 968163, 1148139]
Answer: D
We now define an algorithm: The definition of a(n) is the number of single paradiddles (a four-note drum sticking pattern consisting of two alternating notes followed by two notes on the same hand) that can be formed using n drum hits. Given the input x_list (a series of values): [86, 87, 88, 89, 90, 91, 92, 93, 94, 95], determine the corresponding output sequence y_list.

Options:
A. [0, 1, 0, 0, 1, 1, 0, 1, 1, 0]
B. [0, 0, 1, 1, 1, 0, 0, 1, 1, 0]
C. [1, 1, 1, 0, 0, 1, 0, 1, 0, 1]
D. [1, 0, 1, 1, 0, 1, 0, 1, 0, 0]
E. [1, 0, 0, 1, 1, 0, 1, 1, 0, 1]
F. [0, 1, 0, 0, 1, 0, 1, 1, 1, 1]
G. [1, 1, 0, 1, 0, 1, 1, 0, 0, 0]
H. [1, 1, 0, 1, 0, 0, 1, 0, 1, 1]
I. [1, 0, 1, 1, 0, 0, 1, 1, 1, 0]
J. [0, 1, 1, 0, 0, 1, 1, 1, 0, 1]
Answer: H
We now define an algorithm: The definition of a(n) is a variation of the Josephus problem, removing every other person in a circular arrangement, starting with person 1. The position a(n) refers to the last remaining person after repeatedly removing every second individual in this manner. Given the input x_list (a series of values): [65, 66, 67, 68, 69, 70, 71, 72, 73, 74], determine the corresponding output sequence y_list.

Options:
A. [3, 4, 5, 6, 7, 8, 9, 10, 11, 12]
B. [6, 7, 8, 9, 10, 11, 12, 13, 14, 15]
C. [3, 5, 7, 9, 11, 13, 15, 17, 19, 21]
D. [7, 8, 9, 10, 11, 12, 13, 14, 15, 16]
E. [1, 3, 5, 7, 9, 11, 13, 15, 17, 19]
F. [9, 10, 11, 12, 13, 14, 15, 16, 17, 18]
G. [5, 7, 9, 11, 13, 15, 17, 19, 21, 23]
H. [4, 5, 6, 7, 8, 9, 10, 11, 12, 13]
I. [8, 9, 10, 11, 12, 13, 14, 15, 16, 17]
J. [2, 4, 6, 8, 10, 12, 14, 16, 18, 20]
Answer: J
We now define an algorithm: The definition of a(n) is: -1 followed by infinitely many 1's. Given the input x_list (a series of values): [95, 96, 97, 98, 99, 100, 101, 102, 103, 104], determine the corresponding output sequence y_list.

Options:
A. [1, 1, 1, 1, 0, 0, 0, 0, 0, 0]
B. [1, 0, 1, 0, 1, 0, 1, 0, 1, 0]
C. [-2, -1, -1, -1, -1, -1, -1, -1, -2, ]
D. [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
E. [0, 1, 0, 1, 0, 1, 0, 1, 0, 1]
F. [1, 1, -1, 1, 1, -1, 1, 1, -1, 1]
G. [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
H. [1, -1, 1, -1, 1, -1, 1, -1, 1, -1]
I. [1, -2, 1, -2, 1, -2, 1, -2, 1, -2]
J. [1, 2, 3, 4, 1, 2, 3, 4, 1, 2]
Answer: D
We now define an algorithm: The definition of a(n) is the trajectory of the binary number 10110 under the operation 'Reverse and Add!' carried out in base 2. Given the input x_list (a series of values): [7, 8, 9, 10, 11, 12, 13, 14, 15, 16], determine the corresponding output sequence y_list.

Options:
A. [110110101, 1010101000, 1101000111, 10111110000, 11001101101, 101111010010, 110110001101, 1011111100000, 1100101011101, 10111110110000]
B. [110010101, 1011101000, 1101000101, 10111010000, 11000101101, 101111010000, 110010001101, 1011110100000, 1100001011101, 10111110100000]
C. [110011001, 1011001100, 1101010101, 10110110000, 11001100101, 101010010000, 110011011101, 1011110111000, 1100101011100, 10111000100010]
D. [111010101, 1010100000, 1101001100, 10111010010, 11011101101, 101111011000, 110100001101, 1011111100100, 1100101010101, 10101110100000]
E. [110000101, 1011001000, 1101001101, 10100010000, 11001101111, 101110010100, 110010001001, 1011100100000, 1100001010111, 10110110100000]
F. [111010001, 1011101100, 1100111101, 10100110000, 11001001101, 101000110000, 110001001111, 1011110110000, 1100011111101, 10111100100000]
G. [110011101, 1011111000, 1101100101, 10111011000, 11000111101, 101101010000, 110010100101, 1011111100000, 1100011011101, 10111111100000]
H. [101000101, 1011101010, 1111001101, 10111001000, 11010011101, 101110010000, 110000001101, 1011110010000, 1101011011101, 10111010100000]
I. [110010110, 1011101001, 1101000110, 10111010001, 11000101110, 101111010001, 110010001110, 1011110100001, 1100001011110, 10111110100001]
J. [110111001, 1011110000, 1101001111, 10101010000, 11101101101, 101111000010, 110011001101, 1011010100000, 1100001111101, 10101110100000]
Answer: B
We now define an algorithm: The definition of a(n) is Blue code for n: in the binary coding of a polynomial over GF(2), substitute x+1 for x. (Consider the binary representation of n as the coefficient vector of a polynomial over the finite field GF(2). Apply the substitution x+1 for x in this polynomial, and then convert the resulting polynomial back to a binary number.) Given the input x_list (a series of values): [57, 58, 59, 60, 61, 62, 63, 64, 65, 66], determine the corresponding output sequence y_list.

Options:
A. [24, 26, 27, 20, 21, 23, 22, 65, 64, 66]
B. [04, 06, 07, 00, 01, 03, 02, 45, 44, 46]
C. [94, 96, 97, 90, 91, 93, 92, 135, 134, 136]
D. [44, 46, 47, 40, 41, 43, 42, 85, 84, 86]
E. [74, 76, 77, 70, 71, 73, 72, 115, 114, 116]
F. [54, 56, 59, 50, 51, 53, 52, 95, 94, 96]
G. [14, 16, 17, 10, 11, 13, 12, 55, 54, 56]
H. [64, 66, 67, 60, 61, 63, 62, 105, 104, 106]
I. [34, 36, 39, 30, 31, 33, 32, 75, 74, 76]
J. [84, 86, 87, 80, 81, 83, 82, 125, 124, 126]
Answer: D
We now define an algorithm: The definition of a(n) is the number of B-trees of order 3 (a B-tree in which each internal node has between 2 and 3 children) with n leaves. Given the input x_list (a series of values): [35, 36, 37, 38, 39, 40, 41, 42, 43, 44], determine the corresponding output sequence y_list.

Options:
A. [316774, 550647, 923035, 1514864, 2451783, 3928217, 6244749, 9766479, 15414300, 24207844]
B. [426774, 660647, 1033035, 1624864, 2561783, 4038217, 6354749, 9976479, 15714300, 24497844]
C. [517774, 751647, 1133035, 1724864, 2661783, 4138217, 6454749, 10076479, 15814300, 24607844]
D. [416884, 651647, 1024035, 1615864, 2552783, 4029217, 6345749, 9967479, 15624300, 24417844]
E. [416674, 649647, 1022035, 1613864, 2550783, 4027217, 6343749, 9965479, 15604300, 24397844]
F. [516774, 750647, 1123035, 1714864, 2651783, 4128217, 6444749, 10066479, 15714300, 24507844]
G. [416774, 650647, 1023035, 1614864, 2551783, 4028217, 6344749, 9966479, 15614300, 24407844]
H. [415774, 648647, 1021035, 1612864, 2549783, 4026217, 6342749, 9964479, 15594300, 24387844]
I. [417774, 652647, 1025035, 1616864, 2553783, 4030217, 6346749, 9968479, 15634300, 24427844]
J. [316674, 549647, 922035, 1504864, 2441783, 3918217, 6234749, 9756479, 15314300, 24107844]
Answer: G
We now define an algorithm: The definition of a(n) is the n-th entry of the Riordan array (1, c(-x)), where c(x) is the generating function of the Catalan numbers. Given the input x_list (a series of values): [63, 64, 65, 66, 67, 68, 69, 70, 71, 72], determine the corresponding output sequence y_list.

Options:
A. [48, -13, -3, -4, 16800, -16800, 11938, -7076, 3644, -1642]
B. [46, -11, -1, -2, 16798, -16798, 11936, -7074, 3642, -1640]
C. [44, -9, 1, 0, 16796, -16796, 11934, -7072, 3640, -1638]
D. [40, -5, 5, 4, 16791, -16791, 11929, -7067, 3635, -1633]
E. [47, -12, -2, -3, 16799, -16799, 11937, -7075, 3643, -1641]
F. [43, -8, 2, 1, 16795, -16795, 11933, -7071, 3639, -1637]
G. [45, -10, 0, -1, 16797, -16797, 11935, -7073, 3641, -1639]
H. [44, -8, 0, 1, 16793, -16793, 11931, -7069, 3637, -1635]
I. [41, -6, 4, 3, 16792, -16792, 11930, -7068, 3636, -1634]
J. [42, -7, 3, 2, 16794, -16794, 11932, -7070, 3638, -1636]
Answer: C
We now define an algorithm: The definition of a(n) is the sum of the elements of the upward diagonals in the Eulerian triangle, which counts the number of permutations of {1, 2, ..., n} with a given number of ascents. Given the input x_list (a series of values): [17, 18, 19, 20, 21, 22, 23, 24, 25, 26], determine the corresponding output sequence y_list.

Options:
A. [707880821, 4132235182, 23925263901, 132905588441, 657807491222, 2215424018837, 83042845392105, 631622663432978, 4931915237693517, 39535826242154973]
B. [807880821, 5132235182, 43925263901, 332905588441, 1657807491222, 12215424018837, 103042845392105, 831622663432978, 6931915237693517, 59535826242154973]
C. [907880821, 6132235182, 43925263901, 332905588441, 9657807491222, 2215424018837, 93042845392105, 831622663432978, 6931915237693517, 59535826242154973]
D. [807880821, 5132235182, 23925263901, 332905588441, 1657807491222, 2215424018837, 93042845392105, 731622663432978, 4931915237693517, 49535826242154973]
E. [707880821, 2132235182, 33925263901, 132905588441, 157807491222, 2215424018837, 23042845392105, 431622663432978, 2931915237693517, 19535826242154973]
F. [807880821, 4132235182, 33925263901, 132905588441, 9657807491222, 2215424018837, 93042845392105, 131622663432978, 6931915237693517, 49535826242154973]
G. [807880821, 5132235182, 33925263901, 232905588441, 1657807491222, 12215424018837, 93042845392105, 731622663432978, 5931915237693517, 49535826242154973]
H. [607880821, 3132235182, 33925263901, 232905588441, 657807491222, 2215424018837, 93042845392105, 731622663432978, 4931915237693517, 49535826242154973]
I. [507880821, 6132235182, 23925263901, 232905588441, 1657807491222, 12215424018837, 13042845392105, 731622663432978, 4931915237693517, 59535826242154973]
J. [907880821, 3132235182, 33925263901, 332905588441, 157807491222, 12215424018837, 93042845392105, 631622663432978, 6931915237693517, 19535826242154973]
Answer: G
We now define an algorithm: The definition of a(n) is the partial sums of the Catalan numbers starting from C1, C2, C3, ..., where Cn is the nth Catalan number. These sums begin with 1, 3, 8, 22, ... Given the input x_list (a series of values): [15, 16, 17, 18, 19, 20, 21, 22, 23, 24], determine the corresponding output sequence y_list.

Options:
A. [13402736, 48760406, 178405196, 656043896, 2423307086, 8987427506, 33453694526, 124936258166, 467995871816, 1757900019140]
B. [13402996, 48760666, 178405456, 656044156, 2423307346, 8987427766, 33453694786, 124936258426, 467995872076, 1757900019400]
C. [13402886, 48760556, 178405346, 656044046, 2423307236, 8987427656, 33453694676, 124936258316, 467995871966, 1757900019300]
D. [13402666, 48760336, 178405126, 656043826, 2423307016, 8987427436, 33453694456, 124936258096, 467995871746, 1757900019070]
E. [13402696, 48760366, 178405156, 656043856, 2423307046, 8987427466, 33453694486, 124936258126, 467995871776, 1757900019100]
F. [13402686, 48760356, 178405146, 656043846, 2423307036, 8987427456, 33453694476, 124936258116, 467995871766, 1757900019090]
G. [13402636, 48760306, 178405096, 656043796, 2423306996, 8987427406, 33453694406, 124936258056, 467995871706, 1757900019030]
H. [13402726, 48760396, 178405186, 656043876, 2423307066, 8987427486, 33453694506, 124936258146, 467995871796, 1757900019120]
I. [13402706, 48760376, 178405166, 656043866, 2423307056, 8987427476, 33453694496, 124936258136, 467995871786, 1757900019110]
J. [13402596, 48760266, 178405056, 656043756, 2423306956, 8987427366, 33453694386, 124936258026, 467995871676, 1757900019000]
Answer: E
We now define an algorithm: The definition of a(n) is: If n is semiprime (or 2-almost prime, meaning it has exactly two prime factors, not necessarily distinct) then 1 else 0. Given the input x_list (a series of values): [96, 97, 98, 99, 100, 101, 102, 103, 104, 105], determine the corresponding output sequence y_list.

Options:
A. [1, 1, 0, 0, 1, 0, 1, 1, 0, 0]
B. [0, 1, 1, 1, 0, 1, 1, 0, 0, 0]
C. [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
D. [0, 1, 1, 0, 1, 1, 0, 1, 1, 0]
E. [1, 0, 0, 1, 0, 0, 1, 0, 0, 1]
F. [1, 0, 0, 0, 1, 0, 0, 0, 1, 0]
G. [0, 1, 0, 0, 0, 1, 0, 0, 1, 0]
H. [0, 0, 0, 1, 1, 0, 0, 1, 1, 0]
I. [1, 0, 1, 0, 1, 0, 1, 0, 1, 0]
J. [0, 0, 1, 1, 0, 0, 1, 1, 0, 0]
Answer: C
We now define an algorithm: The definition of a(n) is the sequence of deficient numbers, which are numbers \\( k \\) such that the sum of the divisors of \\( k \\), denoted by \\( \\sigma(k) \\), is less than \\( 2k \\). Given the input x_list (a series of values): [57, 58, 59, 60, 61, 62, 63, 64, 65, 66], determine the corresponding output sequence y_list.

Options:
A. [66, 67, 68, 70, 71, 73, 75, 76, 77, 79]
B. [82, 83, 84, 85, 87, 88, 90, 91, 92, 94]
C. [80, 81, 82, 84, 85, 87, 89, 90, 92, 93]
D. [73, 75, 76, 78, 79, 81, 83, 84, 86, 88]
E. [74, 75, 76, 77, 79, 81, 82, 83, 85, 86]
F. [68, 69, 71, 72, 74, 75, 77, 78, 80, 81]
G. [71, 72, 73, 75, 76, 78, 79, 81, 82, 84]
H. [64, 65, 67, 68, 70, 72, 73, 74, 76, 78]
I. [69, 70, 72, 73, 74, 76, 78, 79, 81, 82]
J. [77, 78, 80, 81, 83, 85, 86, 88, 89, 91]
Answer: E
We now define an algorithm: The definition of a(n) is [t], 1+[t], [2t], 2+[2t], [3t], 3+[3t], [4t], 4+[4t], [5t], 5+[5t], ..., where t = tau = (1+sqrt(5))/2 and [] denotes the floor function. Given the input x_list (a series of values): [63, 64, 65, 66, 67, 68, 69, 70, 71, 72], determine the corresponding output sequence y_list.

Options:
A. [51, 83, 53, 86, 55, 89, 56, 91, 58, 94]
B. [49, 80, 52, 83, 55, 86, 57, 89, 58, 92]
C. [52, 84, 54, 87, 56, 90, 58, 92, 60, 95]
D. [50, 83, 52, 86, 54, 89, 56, 91, 57, 94]
E. [48, 81, 51, 84, 54, 87, 56, 90, 59, 92]
F. [51, 83, 54, 86, 56, 88, 59, 91, 60, 94]
G. [50, 82, 52, 85, 54, 88, 57, 90, 59, 93]
H. [51, 82, 53, 85, 55, 88, 57, 90, 58, 91]
I. [50, 82, 53, 86, 55, 87, 57, 90, 59, 93]
J. [49, 81, 50, 84, 53, 87, 55, 89, 57, 92]
Answer: A