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Manhattan
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Is $$\frac n{14}$$ an integer?(1) n is divisible by 28.(2) n is divisible by 70.
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Manhattan
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Since the Italian government began a crackdown on the black market in the 1970's, the amount of looted antiquities smuggled out of Italy dropped by a 50 percent decline.
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Manhattan
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Company Spokesperson: This year, more than 70% of the guests who stayed with us over the past summer are planning to return to our resorts for a summer vacation. Therefore, I believe that we are well-positioned for another strong and profitable quarter.Industry Analyst: This is not necessarily true. Nearly three quarters of the company’s profits come from the attendance of its theme parks located at its major resorts, and it is not certain how this segment will perform this summer.Which of the following statements, if true, would support the criticism of the Industry Analyst?
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Manhattan
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A shirt goes on sale for 80% of its original price. One week later, the sale price is marked down 10%. The final price is what percent of the original price?
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Manhattan
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What is the minimal value of function f(x)?(1) $$f(0) = 16$$(2) $$f(x) = (x – 4)^2$$
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Manhattan
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Discouraged by new data that show increases in toxic emissions from domestic factories, searches for alternative investment opportunities are being conducted by shareholders of the nation’s leading manufacturing companies.
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Manhattan
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Parent: The city education department is unable to distinguish between annoyances and important problems. For instance, prohibiting students from having cell phones is an overreaction. If a student uses one and thus interferes with instruction, confiscate it. All in all, we need educational leadership that can solve problems, not create them.
Which of the following is an assumption made by the parent?
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Manhattan
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If, 5 years ago, Jamie was half as old as he is now, how old will he be in x years?
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Manhattan
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If x is a positive integer, is x even?(1) $$x^4$$ is even(2) $$4x$$ is even
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Manhattan
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The biathlon is one of the world’s most demanding sports, it combines the endurance of cross country skiing with the precision of expert marksmanship.
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Manhattan
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Less than 10 percent of the world’s people, and of the participants in combat sports worldwide, are left-handed. However, a majority of top-level competitors in combat sports worldwide are left-handed. Which of the following, if true, most helps to resolve the discrepancy presented in the passage?
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Manhattan
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Barry walks from one end to the other of a 30-meter long moving walkway at a constant rate in 30 seconds, assisted by the walkway. When he reaches the end, he reverses direction and continues walking with the same speed, but this time it takes him 120 seconds because he is traveling against the direction of the moving walkway. If the walkway were to stop moving, how many seconds would it take Barry to walk from one end of the walkway to the other?
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Manhattan
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If r and q are integers, what is the value of $$（5^r）（3^{q+1})$$?(1) $$(5^r)(3^q) = 729$$(2) $$r + q = 6$$
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Manhattan
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The first woman elected to Congress in the United States, many people regard Jeanette Rankin to be a role model because of her committing to peace, as shown by her legislative votes against joining both World Wars.
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Manhattan
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The young orchestral conductor Sabado Domingo is a true prodigy, able to recognize when any single instrument in his orchestra is even a bit out of tune. In a recent test, an orchestra played a hundred selections from different well-known classical pieces; in approximately half of the selections, exactly one instrument would be played slightly out of tune. In every instance in which an instrument was played out of tune, Domingo pointed out that the orchestra was out of tune, and correctly identified the instrument at fault. Which of the following, if true, most strongly supports the conclusion of the argument above?
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Manhattan
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Set S consists of integers 7, 8, 10, 12, and 13. If integer n is included in the set, the average (arithmetic mean) of set S will increase by 20%. What is the value of integer n?
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Manhattan
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Is $$xy \gt 0$$?(1) $$x^2 \gt 0$$(2) $$xy^2 \gt 0$$
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Manhattan
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The work of Byron and Shelley, like other poets of their era, explored themes of love and beauty, which gave rise to the school of poetry known as Romanticism.
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Manhattan
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Scientists have determined that an effective way to lower cholesterol is to eat three servings of whole grains every day. Studies have shown that the cholesterol levels of people who did so were significantly lower after six months than were those of people who did not, even though the cholesterol levels of the two groups had been the same before the studies began. Clearly, eating whole grains can have an appreciable effect on cholesterol levels. The answer to which of the following questions, if true, would be most useful in evaluating the claim about whole grains above?
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Manhattan
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If n is an integer, f(n) = f(n – 1) – n, and f(4) = 10. What is the value of f(6)?
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