What it means to “explain” something in science often comes down to the application of mathematics. Some thinkers hold that mathematics is a kind of language—a systematic contrivance of signs, the criteria for the authority of which are internal coherence, elegance, and depth. The application of such a highly artificial system to the physical world, [...]

In the years since the city of London imposed strict air-pollution regulations on local industry, the number of bird species seen in and around London has increased dramatically. Similar air-pollution rules should be imposed in other major cities. Each of the following is an assumption made in the argument above EXCEPT: A. In most major [...]

If d represents the hundredths digit and e represents the thousandths digit in the decimal .4de, what is the value of this decimal rounded to the nearest tenth? (1) d – e is equal to a positive perfect square. (2) sqrt (d) > e*e A. Statement 1 alone is sufficient but statement 2 alone is [...]

Tom, Jane, and Sue each purchased a new house. The average (arithmetic mean) price of the three houses was $120,000. What was the median price of the three houses? (1) The price of Tom’s house was $110,000. (2) The price of Jane’s house was $120,000. {democracy:7}

A supermarket sells both a leading brand of laundry detergent and its own brand of laundry detergent. On all sizes of the leading brand it makes a profit of 15 percent of the cost per jug. On all sizes of its own brand it makes a profit of 10 percent of the cost per jug. [...]

It is widely assumed that a museum is helped finan- cially when a generous patron donates a potential exhibit. In truth, however, donated objects require storage space, which is not free, and routine conser- vation, which is rather expensive. Therefore, such gifts exacerbate rather than lighten the demands made on a museum’s financial resources. Which [...]

A proposal has been made to trim the horns from rhinoceroses to discourage poachers; the question is whether tourists will continue to visit game parks and see rhinoceroses after their horns are trimmed. (A) whether tourists will continue to visit game parks and see rhinoceroses after their horns are (B) whether tourists will continue to [...]

In Aristophanes’ Lysistrata women are seen as the means of bringing peace and good sense to a wartorn world. (A) as (B) as if they are (C) that they will be (D) that they are (E) for being

When catastrophe strikes, analysts typically blame some combination of powerful mechanisms. An earthquake is traced to an immense instability along a fault line; a stock market crash is blamed on the destabilizing effect of computer trading. These explanations may well be correct. But systems as large and complicated as the Earth’s crust or the stock [...]

The surface area of a square tabletop was changed so that one of the dimensions was reduced by 1 inch and the other dimension was increased by 2 inches. What was the surface area before these changes were made? (1) After the changes were made, the surface area was 70 square inches. (2) There was [...]

Is xy > x2y2? (1) 14×2 = 3 (2) y2 = 1 A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D. EACH statement ALONE is [...]

Color X ink is created by blending red, blue, green, and yellow inks in the ratio 6 : 5 : 2 : 2) What is the number of liters of green ink that was used to create a certain batch of color X ink? (1) The amount of red ink used to create the batch [...]

I) If x is in S, then 1/x is in S. II) If both x and y are in S, then so is x + y. Is 3 in S? (1) 1/3 is in S. (2) 1 is in S. A) Statement 1 alone is sufficient but statement 2 alone is not sufficient to answer [...]

A recent national study of the public schools shows that there are now one microcomputer for every thirty-two pupils, four times as many than there were four years ago. (A) there are now one microcomputer for every thirty-two pupils, four times as many than there were (B) there is now one microcomputer for every thirty-two [...]