List of practice Questions

A science teacher is selecting projects for each of two classes from a group of exactly seven projects— R, S, T, V, X, Y, and Z. The teacher will assign projects to Class 1 and Class 2 according to the following conditions:
Each project must be assigned to exactly one class.
Four of the projects must be assigned to Class 1 and three to Class 2.
R must be assigned to Class 2.
The class to which V is assigned cannot be the same class as the one to which Y is assigned.
If V is assigned to Class 1, X must be assigned to Class 1.
If Z is assigned to Class 2, Y must be assigned to Class 1.
On each of the three consecutive days Monday through Wednesday, exactly two employees are to staff a company's information booth. The three available employees — Feng, Gómez, and Hull— will staff the booth in accordance with the following conditions:
Gómez and Hull must each staff the booth on at least one of the days, but Feng must staff it on at least two the days.
The booth cannot be staffed by the same two employees on any two consecutive days.
If Hull staffs the booth on Monday, Gómez must be the other employee staffing the booth on Monday.
RESULTS OF TWO SURVEYS OF OPINIONS REGARDING THE EFFECTS OF SCIENCE ON HUMAN SOCIETY
A table shows survey responses for August 1991 and August 1992.
- Mostly beneficial: 25% (1991) \(\rightarrow\) 81% (1992)
- Equally harmful and beneficial: 37% (1991) \(\rightarrow\) 9% (1992)
- Mostly harmful: 20% (1991) \(\rightarrow\) 7% (1992)
- No opinion: 18% (1991) \(\rightarrow\) 3% (1992)
Which of the following, if true, contributes most to explaining the shift in opinions about the effects of science on human society?
Drug manufacturer: Although our company requires that patients who use our new drug also purchase from us nonreusable kits for weekly blood testing, the expense of those kits is an entirely necessary one: weekly blood testing must be done to monitor the drug's potential side effects, which can be very dangerous.
Which of the following, if true, most seriously weakens the manufacturer's argument?
Virginia and her brother William disagree over when their father was born: Virginia claims it was in 1935 and William claims it was in 1933. The hospital where their father was born has no records for 1933 but has complete records for 1935--records that do not include a birth record for their father. Therefore, he must have been born in 1933.
The argument depends on which of the following assumptions?
Politician: Each year, small businesses create more jobs than do large established businesses. Therefore, in order to reduce unemployment in the long term, we should provide incentives for starting small businesses rather than for expanding established large businesses.
Which of the following, if true, casts the most doubt on the politician's argument?
In the workplace, influenza is typically spread by infected individuals to others with whom they work in close quarters. A new medication that suppresses the symptoms of influenza therefore will actually increase the number of influenza cases, because this medication will allow people who would otherwise be home in bed to return to work while infected.
Which of the following, if true, most seriously challenges the prediction?
Editorial: Critics of nuclear power complain about the allegedly serious harm that might result from continued operation of existing nuclear power plants. But such concerns do not justify closing these plants; after all, their operation has caused no more harm than that caused by pollution generated by coal-and oil-burning power plants, the most important other sources of energy.
Which of the following is an assumption on which the argument depends?
To improve productivity, manufacturing companies have recently begun restructuring work to produce more goods with fewer assembly-line workers, and the companies have laid off many workers as a consequence. The workers laid off have been those with the least seniority (time on the job), generally the younger workers.
The statements above, if true, most strongly support which of the following as a conclusion?
During the nineteenth century, Britain's urban population increased as its rural population diminished. A historian theorizes that, rather than industrialization's being the cause, this change resulted from a series of migrations to urban areas, each occasioned by a depression in the agrarian economy. To test this hypothesis, the historian will compare economic data with population census data.
The historian's hypothesis would be most strongly supported if which of the following were found to be true?

If the area of the shaded region of the square above is 20, what is the perimeter of the square? 

 

The number of associate degrees expected to be granted in 2001 is most nearly what percent greater than the number of associate degrees expected to be granted in 1995? 

For the categories given, which category accounts for approximately \(\frac{1}{4}\) of the total number of graduates expected for each of the years shown? 

 

If the ratio of the number of personal computers sold by IBM, Compaq, and Tandy (not shown) in 1993 was 6 to 4 to 1, respectively, approximately how many personal computers were sold by Tandy in 1993? 

 

In 1992, Packard Bell accounted for what percent of the computers sold by the four companies listed? 


 

By what percent did the number of personal computers sold by Compaq increase from 1992 to 1993? 

 

\(100x < y\)
\(1000x < 2y\)

Column AColumn B
\(1,100x\)\(y\)

\(f(t) = kt\) for all \(t\), where \(k\) is a constant, and \(f(3) = \frac{1}{2}\).
 

Column AColumn B
\(k\)\(f(1)\)

\(n\) is a positive integer.
 

Column AColumn B
\(n^{100}\)\(100^n\)

ABCD is a rectangle with diagonals AC and DB.

Column AColumn B
\(r + u + v\)\(r + u + w\)

\(m = 4x + 4y\), \(x \neq -y\)
 

Column AColumn B
\(\frac{2m}{x+y}\)8

In a certain city, 20°F was the average (arithmetic mean) of the low temperatures of \(x^\circ\)F, 25°F, and 37°F on three consecutive days. 
 

Column AColumn B
\(x\)0

The three small rectangles have the same dimensions

Column AColumn B
\(\frac{PS}{RS}\)\(\frac{1}{2}\)

\(x < y < z\)
 

Column AColumn B
\(\frac{x+y+z}{3}\)\(z\)
Column AColumn B
\((0.01)(0.07)(70)\)\(0.49\)