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Machines A, B, and C can either load nails into a bin or unload nails from that bin. Each machine works at a constant rate that is the same for loading and for unloading, although the individual machines may have different rates. Working together to load at their respective constant rates, machines A and B can load the bin in 6 minutes. Likewise, working together to load at their respective constant rates, machines B and C can load the bin in 9 minutes. How long will it take machine A to load the bin if machine C is simultaneously unloading the bin?
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The sum of the first n positive perfect squares, where n is a positive integer, is given by the formula $${n^{3}\over{3}}+cn^{2}+\frac{n}{6}$$, where c is a constant. What is the sum of the first 15 positive perfect squares?
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Save-a-Tot Corporation is a manufacturer of safety seats for bicycles and automobiles. Children often die unnecessarily in collisions because they were not properly fastened into seats that conform to their fragile bodies. Save-a-Tot has recently designed a new type of safety seat that is able to conform more closely than ever to curves in the spines and necks of small children. This new design also cushions the head in a better way. Save-a-Tot claims that the usage of these safety seats will decrease child mortality rates in serious collisions by up to 60 percent.Which of the following, if true, represents the strongest challenge to Save-a-Tot's claim?
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Lately many people in a certain post-communist country have decided to emigrate for economic reasons. The people who want to leave the county in search of a job or a better life are those who have no money, or who know many foreign languages.Of the following people, who is LEAST likely to emigrate?
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Finance Minister: Last year was disastrous for our manufacturing sector, which has traditionally contributed about 75% of our national budget. It is therefore encouraging that there is evidence that the IT sector is growing stronger. Taxes from the IT sector accounted for 15% of our national budget, up from 8% last year.On the basis of the statements above, what best supports the above conclusion?
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What is the value of $$({u}-{1})^{3}$$ if $${u}=\frac{6}{7}+\frac{18}{21}-\frac{12}{14}$$
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The population of Country S is 10 million people less than the population of Country J. If in 5 years, Country J has twice as many people as Country S, how many people will live in Country S in three years given that each country has a constant population growth of 0.5 million people per year?
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How many factors of 80 are greater than $$\sqrt{80}$$?
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Which of the following can be odd?I. The sum of 7 consecutive integersII. The sum of 10 consecutive integersIII. The product of 13 consecutive integers
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If $${N}=\frac{S}{1-pq}$$ and N,S,p, and q are positive numbers, then in terms of N,S, and q what does p equal?
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If x > 0 and y < 0, which of the following IS necessarily true?
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 If the area of rectangle ABCD is $$4\sqrt3$$, then what is the area of the square DEFG?
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$$\frac{1}{\frac{3}{4}-\frac{2}{3}}=$$
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A university professor received a government grant of M dollars to be spent on research during the year. 25 percent of the grant was appropriated by the university, so the professor used 20 percent of what was left to buy lab equipment. What percent of the original sum of M dollars was either given to the university or spent on lab equipment?
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If $$w=\frac{1+x\frac{y}{z^2}}{x+y}$$, $${x}=\frac{z}{2}$$, and $${y}={3}\frac{z}{4}$$,what is the value of w in terms of z?
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To enhance the performance of her PC, Marie-Ann purchased n megabytes of Random Access Memory (RAM). Soon thereafter, the price of memory decreased by $1.25 per megabyte. How much RAM in megabytes did Marie-Ann purchase if it became known that she could have saved $62.50. had she postponed her purchase for a short while?
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A group of tourists needed to walk 45 miles. During the first day the group walked 19 miles. To complete the required distance during the second day, the group had to cover the distance which was approximately what percent greater than the distance walked during the first day?
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A model of London's Millennium Wheel in the cubicle of Manhattan Review's CEO has supports which are 4 centimeters apart, and a reinforcement bar of 2 centimeters in length. The length of each support is 8 centimeters. If a fly sits on top of the wheel, how high does it sit above the surface on which the supports rest?
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To keep the structural integrity of a mechanical system, the horizontal co-ordinate x may be any number, whereas it vertical co-ordinate y must be such that its third power is less than or equal to the numerical value of x. Each of the following pairs satisfies this rule EXCEPT
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Which of the following is a solution of the equation $$\frac{x^2+14x-240}{x+24}$$?
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