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Two positive numbers differ by 12 and their reciprocals differ by$$\frac{4}{5}$$ What is their product?
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If a, b, and c are positive integers, what is the remainder after b-a is divided by 3?(1)$$a=c^{3}$$(2)$$b={(c+1)}^{3}$$
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If $${{1}\over{x+2}}={{1}\over{x-2}}+{{1}\over{x+1}}$$, which of the following is a possible value of x?
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If n is a positive integer greater than 1, then p(n) represents the product of all the prime numbers less than or equal to n. The second smallest prime factor of p(12) + 11 is
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Let u,v, and w denote the lengths of three separate line segments. In order for u,v, and w to represent the lengths of three sides of a triangle, what value must v exceed?1. w= u + 52. u = 2 and w = 7
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What is the value of the two-digit number z?1. The tens digit is twice the units digit.2. The sum of two digits is 6.
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How many thousands of gallons of water does a reservoir have?1. If $$\frac{1}{3}$$ of the water in the reservoir were released, then the reservoir would be filled to $$\frac{1}{2}$$ of its capacity.2. If 60 thousand gallons of water were pumped into the reservoir, it would be filled to capacity.
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Ice hockey teams R and U played against each other in the final games of numerous championships. Which of the teams won more than $$\frac{1}{2}$$ of these games?1. The total number of games teams R and U played against each other in finals is 30.2. Team R scored 128 goals in these matches, and Team U scored 203 goals in these matches.
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A software company contracted its sister network technologies firm to upgrade its network and storage equipment. The sister firm charged the software company only for equipment and labor. What fraction of the total amount paid for the upgrade was the labor charge?1. labor cost was $10,000 less than the total cost of the upgrade.2. Without the labor charge, the total cost of the upgrade would have been only $$\frac{5}{6}$$ as much.
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Does a = b?1.$$\frac{a}{b}=\frac{b}{a}$$2.$$({a}-{b})^{2}={a}^{2}-{b}^{2}$$
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The migratory paths of the California gray whale and the Pacific humpback now cross at a point roughly two thousand miles northeast of Hawaii, due to human intrusion into the Pacific Ocean along the coast of Oregon. This meeting allows scientists to gather previously unobtainable data about the communication abilities of both of these species, which normally would not come into contact with each other.Which one of the following statements, if true, would best explain why the situation described above will allow scientists to gather new data?
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Several recent studies have shown that when alcohol is consumed before driving, the incidence of automobile accidents increases significantly. On this basis, the federal government has passed strict laws prohibiting drivers from operating their vehicles after consuming specific amounts of alcohol. Surprisingly, it has since been discovered that a large number of drivers who have not been consuming alcohol in amounts that exceed the legal specifications are still becoming involved in the type of automobile accidents that the laws were designed to reduce.Which one of the following, if true, could by itself adequately explain the unexpected finding reported in the passage?
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New buildings in earthquake-prone areas must be heavily reinforced or else they may otherwise collapse in a strong quake.
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The major event of the reign of Akhenaton of Egypt was his transfer of the capital, a move that alienated members of the nobility as well as the powerful priests of Amon.
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Some researchers have suggested that stomach ulcers are caused by acute microbial infections, which suggests that physicians may soon have the option of common antibiotics being prescribed to combat ulcers in their patients.
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Since 1945. when World War II ended, the American family has become increasingly nuclearized.
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This decade has seen no end to the controversy over if state-run day care centers are a necessary response to changes in employment patterns.
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Modem research has not yet resolved the controversy over if viruses are living things, a debate arising from the fact that they cannot reproduce themselves independently.
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Refusing to take sides in any political conflict, the Red Cross goes to great lengths to maintain its commitment to neutrality.
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Pencils cost 20 cents each. The price per dozen is 10 percent cheaper. What is the cost of a dozen pencils?
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