If p is a non-positive number, then for what value of p does the expression |77 – 6p| holds the minimum value?
Which of the following numbers has the greatest number of unique digits?
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How many integers n are there such that −145 < −|n2| < −120?
What is the value of the square root of the square root of .00000256?
Working alone at its constant rate, pump X pumped out ¼ of the water in a tank in 2 hours. Then pumps Y and Z started working and the three pumps, working simultaneously at their respective constant rates, pumped out the rest of the water in 3 hours. If pump Y, working alone at its constant rate, would have taken 18 hours to pump out the rest of the water, how many hours would it have taken pump Z, working alone at its constant rate, to pump out all of the water that was pumped out of the tank?
In a university club of 200 people, the number of Political Science majors is 50 less than 4 times the number of International Relations majors. If one fifth of the club members are neither Political Science majors nor International Relations majors, and no club member is majoring in both Political Science and International Relations, how many of the club members are International Relations majors?
If the ratio of the present age of Anna and Paula is 3 : 4, what could be the ratio of their respective ages after 8 years?
Working together at their respective constant rates, machine R, machine S, and machine T can produce a batch of parts in 4 hours. If machine R, working alone at its constant rate, can produce the same batch of parts in 6 hours, how many hours would it take machine S and machine T, working together at their respective constant rates, to produce the same batch of parts?
From the even numbers between 1 and 9, two different numbers are to be chosen at random. What is the probability that their sum will be 8?
If the total cost of 20 pairs of shoes is equal to the total revenue generated from the sale of 25 pairs of shoes, what is the percent of profit or loss made on the sale of each pair of shoes, assuming each pair of shoes cost the same dollar amount and each pair of shoes sold for the same dollar amount?
A certain state has a sales tax of 2 percent on the purchase price of all products. In addition, a city within this state imposes its own 0.5 percent sales tax on the purchase price of all products. If the sales tax on a particular product purchased in this city was $2.80, what was the purchase price of this product?
If s and t are positive integers and s/t = 39.12, then which one of the following could t equal?
A dishonest milkman wants to make a profit on the selling of milk. He would like to mix water (costing nothing) with milk costing Rs.33 per litre so as to make a profit of 20% on cost when he sells the resulting milk and water mixture for Rs.36 In what ratio should he mix the water and milk?
Which of the following is NOT a possible value of
A sequence of numbers is defined recursively by for all n ≥ 3 Then a2019 can be written as p/q, where p and q are relatively prime positive integers. What is p + q?
If x4 – 8x3 + ax2 – bx + 16 = 0 has positive real roots, find a – b.
Clarissa spent all day on a sightseeing trip in Britain. Starting from her hotel, Clarissa boarded a bus, which traveled at an average speed of 15 miles per hour through a 30 mile section of the countryside. The bus then stopped for lunch in London before continuing on a 3 hour tour of the city's sights at a speed of 10mph. Finally, the bus left the city and drove 40 miles straight back to the hotel. Clarissa arrived at her hotel exactly 2 hours after leaving London. What was the bus's average rate, approximately, for the entire journey?
If (1 − p) is a root of quadratic equation x2 + px + (1 − p) = 0 then its roots are
A, B, and C, each of them working alone can complete a job in 6, 8 and 12 days respectively. If all three of them work together to complete a job and earn $ 2340, what will be C's share of the earnings?
If two distinct integers a and b are picked from {1, 2, 3, 4, .... 100} and multiplied, what is the probability that the resulting number has EXACTLY 3 factors?
Of the 100 athletes at a soccer club, 40 play defense and 70 play midfield. If at least 20 of the athletes play neither midfield nor defense, the number of athletes that play both midfield and defense could be any number between
Real Estate Agent: Next year, the occupancy rate for residential rental properties in Riverton will increase despite projections of decreasing population in the city. Generally, when a city’s population decreases, so does the occupancy rate for residential rental properties. However, in the continuing climate of increasing interest rates on home mortgages, an unusually large number of Riverton residents who would typically buy homes will opt to rent instead.
Q. The boldfaced statements (underlined) in the argument above play which of the following roles?
A careful review of hospital fatalities due to anesthesia during the last 20 years indicates that the most significant safety improvements resulted from better training of anesthetists. Equipment that monitors a patient’s oxygen and carbon dioxide levels was not available in most operating rooms during the period under review. Therefore, the increased use of such monitoring equipment in operating rooms will not significantly cut fatalities due to anesthesia.
Q. A flaw in the argument is that
College football recruiting services rank incoming players on a scale of 1-star (not a highly sought-after prospect) to 5-star (considered to be the best players). Recently a service attempted to validate its rankings by assigning star ratings to players upon completion of their careers to determine the accuracy of the initial rankings. The survey averaged the post-career ratings of each player and found that 5-star players’ final average was 4.46, compared with 3.98 for 4-stars and 3.11 for 3-stars. This suggests that the rankings services do not effectively judge high-end talent as well as they judge players in the middle of the range.
Q. Which of the following identifies a problem with the service’s attempt to validate its rankings?
A severe illness which affects the red blood cell count has been found to be hereditary. Fifty percent of those who are diagnosed with the illness have a parent who suffers from it. A known scientist has hypothesized that 50% of the children of carriers of the illness will also suffer from it at one point or another.
Q. Which of the following, if true, would most weaken the conclusion drawn by the known scientist?
Passage
Film scholars agree that Hollywood portrayals of America at war follow a cyclical pattern. During and immediately after a conflict, important films trumpet glory and sacrifice. Ten to fifteen years later, questioning and sometimes pacifistic movies about the conflict dominate. In the late 1960’s, “the raging bulls” of Hollywood—the young trendsetters rising to prominence—proclaimed this pattern obsolete. However, the passage of time has demonstrated this cultural pattern to be more resilient than it seemed in those days of social change.
Throughout the majority of the last century, evidence of the cyclical portrayal of war in film abounds. After America declared war against Germany during World War I, the still infant film industry glorified the fight against “the Hun.” By the early 1930’s, major releases had changed their tone; for example, All Quiet on the Western Front put forth an anti-war message by displaying the horrors of combat. After World War II began, the industry shifted gears. Suddenly, important pictures again portrayed glories and courage without the questioning or despair. For example, Guadalcanal Diary, produced during the war, showed “the ultimate sacrifice” as a noble and undoubted good. Once again, though, by 1957, films such as The Bridge on the River Kwai won awards for depicting the moral confusion of war.
Those who later declared this pattern dead based their conviction on their hearts rather than their minds. During the Vietnam War, the only major film about that conflict was The Green Berets, starring John Wayne and far closer in tone to Guadalcanal Diary than to The Bridge on the River Kwai. Similarly, years went by before more complex visions of war, such as Apocalypse Now, and then Platoon, emerged.
While today’s film industry is more diverse and its audience more culturally fragmented, this cycle largely continues. Jarhead, a layered depiction of the first gulf war, premiered more than ten years after that conflict. Further evidence of this pattern can be seen in the release of Apocalypse Now Redux, which contained additional footage that the producers originally thought would repel audiences. Thus, the famous aphorism “The more things change, the more they stay the same” certainly applies to this aspect of the film industry.
Q. According to the passage, Apocalypse Now Redux differed from Apocalypse Now in which of the following ways?
Passage
Film scholars agree that Hollywood portrayals of America at war follow a cyclical pattern. During and immediately after a conflict, important films trumpet glory and sacrifice. Ten to fifteen years later, questioning and sometimes pacifistic movies about the conflict dominate. In the late 1960’s, “the raging bulls” of Hollywood—the young trendsetters rising to prominence—proclaimed this pattern obsolete. However, the passage of time has demonstrated this cultural pattern to be more resilient than it seemed in those days of social change.
Throughout the majority of the last century, evidence of the cyclical portrayal of war in film abounds. After America declared war against Germany during World War I, the still infant film industry glorified the fight against “the Hun.” By the early 1930’s, major releases had changed their tone; for example, All Quiet on the Western Front put forth an anti-war message by displaying the horrors of combat. After World War II began, the industry shifted gears. Suddenly, important pictures again portrayed glories and courage without the questioning or despair. For example, Guadalcanal Diary, produced during the war, showed “the ultimate sacrifice” as a noble and undoubted good. Once again, though, by 1957, films such as The Bridge on the River Kwai won awards for depicting the moral confusion of war.
Those who later declared this pattern dead based their conviction on their hearts rather than their minds. During the Vietnam War, the only major film about that conflict was The Green Berets, starring John Wayne and far closer in tone to Guadalcanal Diary than to The Bridge on the River Kwai. Similarly, years went by before more complex visions of war, such as Apocalypse Now, and then Platoon, emerged.
While today’s film industry is more diverse and its audience more culturally fragmented, this cycle largely continues. Jarhead, a layered depiction of the first gulf war, premiered more than ten years after that conflict. Further evidence of this pattern can be seen in the release of Apocalypse Now Redux, which contained additional footage that the producers originally thought would repel audiences. Thus, the famous aphorism “The more things change, the more they stay the same” certainly applies to this aspect of the film industry.
Q. The passage implies that the combat depicted in All Quiet on the Western Front least resembles the depiction of combat in which of the following?
Passage
Film scholars agree that Hollywood portrayals of America at war follow a cyclical pattern. During and immediately after a conflict, important films trumpet glory and sacrifice. Ten to fifteen years later, questioning and sometimes pacifistic movies about the conflict dominate. In the late 1960’s, “the raging bulls” of Hollywood—the young trendsetters rising to prominence—proclaimed this pattern obsolete. However, the passage of time has demonstrated this cultural pattern to be more resilient than it seemed in those days of social change.
Throughout the majority of the last century, evidence of the cyclical portrayal of war in film abounds. After America declared war against Germany during World War I, the still infant film industry glorified the fight against “the Hun.” By the early 1930’s, major releases had changed their tone; for example, All Quiet on the Western Front put forth an anti-war message by displaying the horrors of combat. After World War II began, the industry shifted gears. Suddenly, important pictures again portrayed glories and courage without the questioning or despair. For example, Guadalcanal Diary, produced during the war, showed “the ultimate sacrifice” as a noble and undoubted good. Once again, though, by 1957, films such as The Bridge on the River Kwai won awards for depicting the moral confusion of war.
Those who later declared this pattern dead based their conviction on their hearts rather than their minds. During the Vietnam War, the only major film about that conflict was The Green Berets, starring John Wayne and far closer in tone to Guadalcanal Diary than to The Bridge on the River Kwai. Similarly, years went by before more complex visions of war, such as Apocalypse Now, and then Platoon, emerged.
While today’s film industry is more diverse and its audience more culturally fragmented, this cycle largely continues. Jarhead, a layered depiction of the first gulf war, premiered more than ten years after that conflict. Further evidence of this pattern can be seen in the release of Apocalypse Now Redux, which contained additional footage that the producers originally thought would repel audiences. Thus, the famous aphorism “The more things change, the more they stay the same” certainly applies to this aspect of the film industry.
Q. What is the main point made by the author?
A survey of charitable giving in the state found that the average dollar amount contributed annually by residents of urban areas to programs for the homeless was $15 greater than the amount contributed by residents of rural areas. The survey’s creators, an urban-promotion group known as Live in the City, concluded that city dwellers are on average more generous than residents of rural areas.
Q. EACH of the following, if true, casts doubt on the conclusion of the survey’s creators EXCEPT
A small percentage of dogs are believed to be able to detect the onset of seizures in their owners. A dog with this ability will display characteristic behaviors, such as staring intently at its owner, just before a seizure occurs. Observations of epilepsy patients do not reveal any noticeable change in odor, behavior, or appearance before a seizure. However, seizure-detecting dogs can predict a seizure even when the patient is in another room.
Q. If the statements above are true, which of the following is most strongly supported by them?