Let n and k be positive integers with k≦n. From an n×n array of dots, a k×k array of dots is selected. The figure above shows two examples where the selected k×k array is enclosed in a square. How many pairs (n, k) are possible so that exactly 48 of the dots in the n×n array are NOT in the selected k×k array?

Even though sub-Saharan Africa often evokes images of drought and famine, researchers say that the area is the home of more than 2,000 grains, vegetables, roots, fruits, and other foods that have the possibility for feeding the continent, even other parts of the world.

The smallest prime factor of 899 is x. Which of the following is true of x?

OG2021-798Political Strategist: The domestic policies of our opponents in Party X are contrary to the priorities of many middle-class voters. Yet some of these same voters are supporters of Party X and its candidates due to the party's appeals about foreign policy. In order to win these voters back, we in Party Y must prove to middle-class voters that Party X does not represent their priorities with respect to domestic policy. Which of the following would, if true, most strongly suggest that the political strategist's plan is unlikely to succeed?

Both weakened by concern about the government's agreement with the International Monetary Fund and by growing fears of a rise in inflation, the country's currency continued its slide to a record low against the dollar, which forced the central bank to intervene for the fourth time in a week.

Three large companies and seven small companies currently manufacture a product with potential military applications. If the government regulates the industry, it will institute a single set of manufacturing specifications to which all ten companies will have to adhere. In this case, therefore, since none of the seven small companies can afford to convert their production lines to a new set of manufacturing specifications, only the three large companies will be able to remain in business.Which of the following is an assumption on which the author's argument relies?

OG2021-786Lockeport's commercial fishing boats use gill nets, which kill many of the netted fish, including some fish of endangered species. The fishing commission has proposed requiring the use of tent nets, which do not kill fish; boat crews would then throw back fish of endangered species. Profitable commercial fishing boats in similar areas have already switched over to tent nets. The proposal can therefore be implemented without economic harm to Lockeport's commercial fishing boat operators. Which of the following, if true, casts the most serious doubt on the argument made for the proposal?

Vitacorp, a manufacturer, wishes to make its information booth at an industry convention more productive in terms of boosting sales. The booth offers information introducing the company’s new products and services. To achieve the desired result, Vitacorp’s marketing department will attempt to attract more people to the boost. The marketing director’s first measure was to instruct each salesperson to call his or her five best customers and personally invite them to visit the boost.Which of the following, if true, most seriously weaken the predication that the marketing director’s first measure will contribute to meeting that goal of boosting sales?

The electronics company has unveiled what it claims to be the world's smallest network digital camcorder, the length of which is that of a handheld computer, and it weighs less than 11 ounces.

Mel: The official salary for judges has always been too low to attract the best candidates to the job. The legislature’s move to raise the salary has done nothing to improve the situation, because it was coupled with a ban on receiving money for lectures and teaching engagements.Pat: No, the raise in salary really does improve the situation. Since very few judges teach or give lectures, the ban will have little or no negative effect.Pat’s response to Mel is inadequate in that it