A man chooses an outfit from 3 different shirts, 2 different pairs of shoes, and different pants. If he randomly selects 1 shirt, 1 pair of shoes, and 1 pair of pants each morning for 3 days, what is the probability that he wears the same pair of shoes each day, but that no other piece of clothing is repeated?the answer is (1/3)^4
I’m not sure how to reach this answer from the question. Could someone explain?
In the xy-plane, does the line with equation y=3x+2 contain the point (r,s)?
1) (3r+2-s)(4r+9-s)=0
2) (4r-6-s)(3r+2-s)=0
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 sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
A man is known to speak truth 3 out of 4 times. He throws die and reports that it is a 6. The probability that it is actually a 6 is
A) 3/4
B) 5/8
C) 2/5
D) 3/5
E) 4/5
What is the standard deviation (SD) of the four numbers p, q, r, s?
1. The sum of p, q, r and s is 24
2. The sum of the squares of p, q, r and s is 224
A. Statement 1 alone is sufficient but statement 2 alone is not sufficient to answer the question asked.
B. Statement 2 alone is sufficient but statement 1 alone is not sufficient to answer the question asked.
C. Both statements 1 and 2 together are sufficient to answer the question but neither statement is sufficient alone.
D. Each statement alone is sufficient to answer the question.
E. Statements 1 and 2 are not sufficient to answer the question asked and additional data is needed to answer the statements.
John traveled 80% of the way from Yellow-town to Green-fields by train at an average speed of 80 miles per hour. The rest of the way John traveled by car at an average speed of v miles per hour. If the average speed for the entire trip was 60 miles per hour, what is v in miles per hour?
(a) 30
(b) 40
(c) 50
(d) 55
(e) 70
If n is an integer divisible by 6 but not by 4 then which of the following can not be an integer ?
A) n/10
B) n/12
C) n/2
D) n/6
E) None of these
If each of the 8 employees working on a certain project received an award, was the amount of each award the same?
(1) The standard deviation of the amounts of the 8 awards was 0.
(2) The total amount of the 8 awards was $10,000.
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 sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
If #X =3X for all odd numbers and #Y = Y/2 for all even numbers. What will be the value of #9*# 6
A) 81
B) 27
C) 64
D) 51
E) 279
A recent generation of historians of science, far from portraying accepted scientific views as objectively accurate reflections of a natural world, explain the acceptance of such views in terms of the ideological biases of certain influential scientists or the institutional and rhetorical power such scientists wield. As an example of ideological bias, it has been argued that Pasteur rejected the theory of spontaneous generation not because of experimental evidence but because he rejected the materialist ideology implicit in that doctrine. These historians seem to find allies in certain philosophers of science who argue that scientific views are not imposed by reality but are free inventions of creative minds, and that scientific claims are never more than brave conjectures, always subject to inevitable future falsification. While these philosophers of science themselves would not be likely to have much truck with the recent historians, it is an easy step from their views to the extremism of the historians.
While this rejection of the traditional belief that scientific views are objective reflections of the world may be fashionable, it is deeply implausible. We now know, for example, that water is made of hydrogen and oxygen and that parents each contribute one-half of their children’s complement of genes. I do not believe any serious-minded and informed person can claim that these statements are not factual descriptions of the world or that they will inevitably be falsified.
However, science’s accumulation of lasting truths about the world is not by any means a straightforward matter. We certainly need to get beyond the naive view that the truth will automatically reveal itself to any scientist who looks in the right direction; most often, in fact, a whole series of prior discoveries is needed to tease reality’s truths from experiment and observation. And the philosophers of science mentioned above are quite right to argue that new scientific ideas often correct old ones by indicating errors and imprecision (as, say, Newton’s ideas did to Kepler’s). Nor would I deny that there are interesting questions to be answered about the social processes in which scientific activity is embedded. The persuasive processes by which particular scientific groups establish their experimental results as authoritative are themselves social activities and can be rewardingly studied as such. Indeed, much of the new work in the history of science has been extremely revealing about the institutional interactions and rhetorical devices that help determine whose results achieve prominence.
But one can accept all this without accepting the thesis that natural reality never plays any part at all in determining what scientists believe. What the new historians ought to be showing us is how those doctrines that do in fact fit reality work their way through the complex social processes of scientific activity to eventually receive general scientific acceptance.
1) It can be inferred from the passage that the author would be most likely to agree with which one of the following characterizations of scientific truth?
(A) It is often implausible.
(B) It is subject to inevitable falsification.
(C) It is rarely obvious and transparent.
(D) It is rarely discovered by creative processes.
(E) It is less often established by experimentation than by the rhetorical power of scientists.
2) According to the passage, Kepler’s ideas provide an example of scientific ideas that were
(A) corrected by subsequent inquiries
(B) dependent on a series of prior observations
(C) originally thought to be imprecise and then later confirmed
(D) established primarily by the force of an individuals rhetorical power
(E) specifically taken up for the purpose of falsification by later scientists
3) In the third paragraph of the passage, the author is primarily concerned with
(A) presenting conflicting explanations for a phenomenon
(B) suggesting a field for possible future research
(C) qualifying a previously expressed point of view
(D) providing an answer to a theoretical question
(E) attacking the assumptions that underlie a set of beliefs
4) The use of the words “any serious-minded and informed person’ serves which one of the following functions in the context of the passage?
(A) to satirize chronologically earlier notions about the composition of water
(B) to reinforce a previously stated opinion about certain philosophers of science
(C) to suggest the author’s reservations about the “traditional belief”
(D) to anticipate objections from someone who would argue for an objectively accurate description of the world
(E) to discredit someone who would argue that certain scientific assertions do not factually describe reality
5) It can be inferred from the passage that the author would most likely agree with which one of the following statements about the relationship between the views of “certain philosophers of science” (lines l2-13) and those of the recent historians?
(A) These two views are difficult to differentiate.
(B) These two views share some similarities.
(C) The views of the philosophers ought to be seen as the source of the historians’ views.
(D) Both views emphasize the rhetorical power of scientists.
(E) The historians explicitly acknowledge that their views are indebted to those of the philosophers.
6) Which one of the following best characterizes the author’s assessment of the opinions of the new historians of science, as these opinions are presented in the passage?
(A) They lack any credibility.
(B) They themselves can be rewardingly studied as social phenomena.
(C) They are least convincing when they concern the actions of scientific groups.
(D) Although they are gross overstatements, they lead to some valuable insights.
(E) Although they are now popular, they are likely to be refused soon.
7) In concluding the passage, the author does which one of the following?
(A) offers a prescription
(B) presents a paradox
(C) makes a prediction
(D) concedes an argument
(E) anticipates objections
If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 5-letter code words to the number of 4-letter code words?
A) 5 to 4
B) 3 to 2
C) 2 to 1
D) 5 to 1
E) 6 to 1
Four staff members at a certain company worked on a project. The amounts of time that the four staff members worked on the project were in the ratio 2 to 3 to 5 to 6. If one of the four staff members worked on the project for 30 hours, which of the following CANNOT be the total number of hours that the four staff members worked on the project?
A) 80
B) 96
C) 160
D) 192
E) 240
Each participant in a certain study was assigned a sequence of 3 different letters from the set {A, B, C, D, E, F, G, H}. If no sequence was assigned to more than one participant and if 36 of the possible sequences were not assigned, what was the number of participants in the study? (Note, for example, that the sequence A, B, C is different from the sequence C, B, A.)
A) 20
B) 92
C) 300
D) 372
E) 476
On the real number line, there are four points P, Q, S, and T, with coordinates p, q, s, and t, respectively. Suppose p < q < s < t, p = -1, s = 2. If the distance between P and Q is twice the distance between Q and S, and S is the midpoint of Q and T, then T has coordinate
A) 0
B) 1
C) 2
D) 3
E) 4
It takes 6 technicians 10 hours to build and program a new server, with each working at the same rate. If six technicians start to build the server at 11:00 AM, and one technician per hour is added beginning at 5:00 PM, at what time will the server be complete?
A) 7:00 PM
B) 8:00 PM
C) 7:40 PM
D) 7:20 PM
E) 6:40 PM
A certain culture of bacteria quadruples every hour. If a container with these bacteria was half full at 10:00 a.m., at what time was it one-eighth full?
(A) 9:00 a.m.
(B) 7:00 a.m.
(C) 6:00 a.m.
(D) 4:00 a.m.
(E) 2:00 a.m.
How many positive integers exist between 10^6 and 10^7, the sum of whose digits equal to 2 ?
A) 5
B) 6
C) 7
D) 8
E) 18
If r>t and r<1 and rt=1, then which one of the following must be true ?
A) r>0 and t<-1
B) r>-1 and t<-1
C) r<-1 and t<-1
D) r<1 and t>1
E) r>1 and t<0
A gardner sets 180 plants in row. Each row contains the same number of plants. If there were 40 more plants in a each row the gardner would need 6 fewer rows. How many rows are there ?
A) 5
B) 6
C) 8
D) 9
E) No solution
What is the value of (4x^3-x)/(2x+1)(6x-3), when x=9999 ?
A) 999999
B) 111111
C) 33333
D) 3333
E) 333
There are seven empty seat on a bus and four people entre . In how many ways can be seated ?
A) 3024
B) 840
C) 720
D) 120
E) 24
A crate measures 8 feet by 16 feet by 24 feet on the inside. A stone pillar in the shape of a right circular cylinder must fit into the crate for shipping so that it rests upright when the crate on at least one of its six sides. what is the radius, in feet, of the pillar with the largest volume that could still fit in the crate? (Contributed by: EastHaven)
a) 4
b) 8
c) 12
d) 16
e) 24
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