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06 Aug 2026, 22:26
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| Problem Solving Butler: August 2026 | ||
| August 7 | PS 1 | PS 2 |
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PS 1
\(P = \frac{x^2−1}{x^2+1 }\)
If x is replaced with \(\frac{-1}{x}\) in the expression P, the expression Q is obtained. Which of the following is the correct relationship between P and Q?
A) \(PQ=1\)
B) \(P+Q=0\)
C) \(\frac{P}{Q } = 1\)
D) \(\frac{P}{Q^2} = -1\)
E) \(\frac{P}{Q^2} = 1\)
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PS 2
List A: 7, a, b, c
List B: 2, 3, 6, a, b, c
If the average (arithmetic mean) of the 4 numbers in list A is 10, what is the average of the 6 numbers in list B?
A. 22
B. 11
C. 22/3
D. 11/3
E. 11/6
06 Aug 2026, 22:28
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| Critical Reasoning Butler: August 2026 | ||
| August 7 | CR 1 | CR 2 |
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CR 1
A number of college students were recruited by the psychology department to participate in a paid, unspecified experiment, which turned out to be a menial, monotonous counting exercise. Unbeknownst to the students, half of the participants were paid a meager rate for their participation, while half received a generous rate. After the counting exercise was complete, each student was asked questions on his or her perception of the counting exercise. Surprisingly, the participants who had been paid less reported higher levels of enjoyment in completing the exercise than the higher-paid participants did.
Which of the following hypotheses, if true, best accounts for the findings of the experiment?
A. In both groups, the portion of the brain activated by counting was disrupted by the exercise and distorted perceptions of financial quantities.
B. Those who counted faster in the experiment experienced more satisfaction than those who counted more slowly.
C. The participants who were paid less had more motivation, conscious or unconscious, to justify their participation in the menial exercise.
D. The energy expenditure of counting in the human mind was associated with the cognitive load of worrying about a quantity of money.
E. Counting is most capably performed by accountants, whose level of satisfaction is highest while they are at work.
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CR 2
Wappo, a company that manufactures turbine blades for hydroelectric dams, has designed a new model of blade with a superior hydrodynamic form that will save energy and hence cost in implementation. Wappo is willing to sell these blades to a particular hydroelectric dam at no initial cost. The only payment will be the difference between, first, a percentage of the dam's improved profits, as measured by the percentage improvement of the hydroelectric dam efficiency times the value of energy sold by the plant over an 18-month period, and, second, the additional cost of installation and maintenance of the new turbines. On installation, the dam will make an estimated payment, which will be adjusted after eighteen months to equal the proper amount.
Which of the following, if it occurred, would constitute a disadvantage for Wappo of the plan described above?
A. Another manufacturer's introduction to the market of a similarly efficient turbine blade
B. The dam's need for a large number of turbine blades
C. Energy efficiency of the dam's current turbines somewhat below the industry average
D. Levels of demand for hydroelectric power that were stagnant but above predicted levels
E. Uncharacteristic weather conditions decreasing the amount of energy that can be harvested through hydroelectric means at the dam's location
06 Aug 2026, 22:30
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| Data Sufficiency Butler: August 2026 | ||
| August 7 | DS 1 | DS 2 |
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DS 1
Justin took a test of French at school and scored 72 marks out of 100. If there were 20 students who appeared for the test, within how many standard deviations from the mean did Justin’s score lie?
(1) Darren and Matthew scored 70 and 75 respectively and their scores were within one standard deviation from the mean.
(2) The mean score of 20 students was 65 and Andrew who scored 59 was within one standard deviation of the mean.
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DS 2
What is Ben’s age?
(1) Two years less than twice Ben’s age is equal to twice of Erin’s age 3 years ago.
(2) Twice of Erin’s age is 4 more than twice of Ben’s age.
