Um grupo de amigos formado por três meninos - entre eles Caio e Beto - e seis meninas - entre elas Ana e Beatriz - , compram ingressos para nove lugares localizados lado a lado, em uma mesma fila no cinema. Ana e Beatriz precisam sentar-se juntas porque querem compartilhar do mesmo pacote de pipocas. Caio e Beto, por sua vez, precisam sentar-se juntos porque querem compartilhar do mesmo pacote de salgadinhos. Além disso, todas as meninas querem sentar-se juntas, e todos os meninos querem sentar-se juntos. Com essas informações, o número de diferentes maneiras que esses amigos podem sentar-se é igual a:

Em determinada universidade, foi realizado um estudo para avaliar o grau de satisfação de seus professores e alunos. O estudo mostrou que, naquela universidade, nenhum aluno é completamente feliz e alguns professores são completamente felizes. Uma conclusão logicamente necessária destas informações é que, naquela universidade, objeto da pesquisa,

Todo amigo de Luiza é filho de Marcos. Todo primo de Carlos, se não for irmão de Ernesto, ou é amigo de Luiza ou é neto de Tânia. Ora, não há irmão de Ernesto ou neto de Tânia que não seja filho de Marcos. Portanto, tem-se, necessariamente, que:

Your answers to question must be based on the text below which is entitled “The Knowledge Race”:

The Knowledge Race
Source: Newsweek Special Edition
Dec 2006 – Feb 2006 (Adapted)

There are losers in every race, but let not the worries over who is winning and losing the knowledge race obscure the more powerful underlying dynamic: knowledge is liberating. It creates the possibility for change and improvement everywhere. It can create amazing devices and techniques, save lives, improve living standards and spread information. Some will do well on one measure, others on another. But on the whole, a knowledge-based world will be a healthier and richer world.

The caveat I would make is not about one or another country’s paucity of engineers or computers. These problems can be solved. But knowledge is not the same thing as wisdom. Knowledge can produce equally powerful ways to destroy life, intentionally and unintentionally. It can produce hate and seek destruction. Knowledge does not by itself produce good sense, courage, generosity and tolerance. And most crucially, it does not produce the farsightedness that will allow us all to live together – and grow together –on this world without causing war, chaos and catastrophe. For that we need wisdom.

The author intends to make a caveat in relation to the distinction between knowledge and wisdom. Thus, he is posing

Your answer to question must be based on the text below which is entitled “The politics of power”:

The politics of power
Source: www.economist.co.uk
Feb 9th 2006 (Adapted)

There is an intense debate over the future of energy and its impact on Europe’s economy. On the one hand is a longstanding project for lower prices led by the European Commission designed to liberalize the market and enable producers and distributors to compete freely within and across national borders. On the other is a camp that argues with growing confidence against further freeing the market. In its view, long-term security and stable prices can best be preserved in managed national markets that are dominated by strong quasi-monopolistic companies which can withstand bullying producers and sudden shifts in demand and supply.

This tension has implications for businesses across Europe. Today business customers in different countries pay prices that vary as much as 100% across what is supposed to be a single European market. A freer market in energy promises to reduce prices back to something like a Europe-wide clearing level. Energy is a critical input to businesses, especially manufacturing, and rising prices are putting unwelcome pressure on already tight margins, as companies try to compete with emerging low-wage economies in Asia.

The author

Your answer to question must be based on the text below which is entitled “The politics of power”:

The politics of power
Source: www.economist.co.uk
Feb 9th 2006 (Adapted)

There is an intense debate over the future of energy and its impact on Europe’s economy. On the one hand is a longstanding project for lower prices led by the European Commission designed to liberalize the market and enable producers and distributors to compete freely within and across national borders. On the other is a camp that argues with growing confidence against further freeing the market. In its view, long-term security and stable prices can best be preserved in managed national markets that are dominated by strong quasi-monopolistic companies which can withstand bullying producers and sudden shifts in demand and supply.

This tension has implications for businesses across Europe. Today business customers in different countries pay prices that vary as much as 100% across what is supposed to be a single European market. A freer market in energy promises to reduce prices back to something like a Europe-wide clearing level. Energy is a critical input to businesses, especially manufacturing, and rising prices are putting unwelcome pressure on already tight margins, as companies try to compete with emerging low-wage economies in Asia.

In paragraph 2, the author refers to a single European market whose prices

Your answer to question must be based on the text below which is entitled “The politics of power”:

The politics of power
Source: www.economist.co.uk
Feb 9th 2006 (Adapted)

There is an intense debate over the future of energy and its impact on Europe’s economy. On the one hand is a longstanding project for lower prices led by the European Commission designed to liberalize the market and enable producers and distributors to compete freely within and across national borders. On the other is a camp that argues with growing confidence against further freeing the market. In its view, long-term security and stable prices can best be preserved in managed national markets that are dominated by strong quasi-monopolistic companies which can withstand bullying producers and sudden shifts in demand and supply.

This tension has implications for businesses across Europe. Today business customers in different countries pay prices that vary as much as 100% across what is supposed to be a single European market. A freer market in energy promises to reduce prices back to something like a Europe-wide clearing level. Energy is a critical input to businesses, especially manufacturing, and rising prices are putting unwelcome pressure on already tight margins, as companies try to compete with emerging low-wage economies in Asia.

Paragraph 1 reports a debate on the future of energy and its impact on Europe’s economy which

Your answers to question must be based on the text below which is entitled “And the winners are…”:

And the winners are…
Source: The Economist/ Technology Quarterly
(Adapted) Dec 8th 2005

This newspaper was established in 1843 to take part in “a severe contest between intelligence, which presses forward, and an unworthy, timid ignorance obstructing our progress”. One of the chief ways in which intelligence presses forward is through innovation, which is now recognized as one of the most important contributors to economic growth. Innovation, in turn, depends on the creative individuals who dream up new ideas and turn them into reality.

The Economist recognizes these talented people through our annual Innovation Awards, presented in seven fields, including energy and the environment - whose winner is:

Stanford Ovshinsky, president and chief scientist and technologist, Energy Conversion Devices, for developing the nickel-metal-hydride battery. This is the battery technology found in hybrid cars, laptop computers and many other devices, and is just one of the many innovations devised by Mr Ovshinsky , a self-taught inventor who pioneered the field of amorphous materials in the 1950s. He is now focusing on solar panels and hydrogen-powered cars.

The text mentions Stanford Ovshinsky,