Закину-ка я пару-тройку задачек для вас:
1. A community of 3 people is to be selected from 5 married couples, such that the community does not include two people who are married to each other. How many such communities are possible?
2. From (1, 2, 3, 4, 5, 6), one number is picked out and replaced and one number is picked out again. If the sum of the 2 numbers is 8, what is the probability that the 2 numbers included the number 5?
3. The new contract
forbids a strike by the transportation union.
(A) forbids a strike by the transportation union
(B) forbids the transportation union from striking
(С) forbids that there be a strike by the transportation union
(D) will forbid the transportation union from striking
(E) will forbid that the transportation union strikes
4. The odds are about 4 to 1 against surviving a takeover offer, and many business consultants therefore advise
that a company’s first line of defense in eluding offers like these be to even refuse to take calls from likely corporate raiders.
(A) that a company’s first line of defense in eluding offers like these be to even refuse
(B) that a company’s first line of defense in eluding such offers be to refuse even
(С) a company defending itself against offers of this kind that, as a first line of defense, they should even refuse
(D) companies which are defending themselves against such an offer that, as a first line of defense, they should even refuse
(E) that the first line of defense for a company who is eluding offers like these is the refusal even
5. An ancient Pavonian text describes how an army of one million enemies of Pavonia stopped to drink at a certain lake and drank the lake dry. Recently, archaeologists discovered that water-based life was suddenly absent just after the event was alleged by the text to have occurred. On the basis of reading the text and an account of the archaeological evidence, some students concluded that the events described really took place.
When one of the following is a questionable technique used by the students to reach their conclusion?
(A) making a generalization about historical events on the basis of a single instance of that type of event
(B) ignoring available, potentially useful counterevidence
(С) rejecting a hypothesis because it is seemingly self-contradictory
(D) considering people and locations whose existence cannot be substantiated by modern historians
(E) taking evidence that a text has correctly described an effect to show that the text has correctly described the cause
6. Samples from the floor of a rock shelter in Pennsylvania were dated by analyzing the carbon they contained. The dates assigned to samples associated with human activities formed a consistent series, beginning with the present and going back in time, a series that was correlated with the depth from which the samples came. The oldest and deepest sample was dated at 19,650 years before the present, plus or minus 2,400 years. Skeptic, viewing that date as too early and inconsistent with the accepted date of human migration into North America, suggested that the samples could have been contaminated by dissolved old carbon carried by percolating groundwater from nearby coal deposits.
Which one of the following considerations, if true, argues most strongly against the suggestion of the skeptics?
(A) No likely mechanism of contamination involving percolating groundwater would have affected the deeper samples from the site without affecting the uppermost sample.
(B) Not every application of the carbon-dating procedure has led to results that have been generally acceptable to scientists.
(С) There is no evidence that people were using coal for fuel at any time when the deepest layer might have been laid down.
(D) No sample in the series, when retested by the carbon-dating procedure, was assigned an earlier date than that assigned to a sample from a layer above it.
(E) No North American site besides the one in Pennsylvania has ever yielded a sample to which the carbon-dating procedure assigned a date that was comparably ancient.
7. A certain square is to be drawn on a coordinate plane. One of the vertices must be on the origin, and the square is to have an area of 100. If all coordinates of the vertices must be integers, how many different ways can this square be drawn? (нашел и не сумел удержаться, чтобы не добавить
)
Сообщение отредактировал crosswall: 05.02.2009, 10:51:14
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