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a and b are consecutive positive integers and a is less than b.

Quantity A

$$a^{b}$$

Quantity B

$$b^{a}$$


Three machines, working independently, can make a production lot of widgets in 4, 6, and 8 hours, respectively. If the machines work simultaneously at their respective uniform rates to make a single lot, what fraction of the lot will be made by the fastest machine?
Three different television models - $$K$$, $$N$$, and $$P$$ - are for sale at a local store. The cost of model $$K$$ is $$20$$ percent greater than the cost of model $$N$$, and the cost of model $$N$$ is $$25$$ percent greater than the cost of model $$P$$. The cost of model $$K$$ is what percent greater than the cost of model $$P$$?

_____%
If $$\frac{1}{2}$$ is one solution of the equation $$8x^{2}+2x-k=0$$, where k is a constant, what is the other solution of the equation?
Though the art of writing was well established in Egypt and Mesopotama long before Shang period, the Chinese writing that appeared then seems to have been an entirely ______________ development.


For how many of the categories shown was the dollar amount of the expenditures in 1995 less than $1 billion?
Pine stumps have been found in discrete layers in peat deposits throughout western Europe and thus represent brief but distinct episodes of bog colonization by pine. Their occurrence implies conditions on the bog surface suitable for colonization, followed by inhospitable conditions for trees that nevertheless facilitated preservation of stumps. Thus, the (i)____________ of pine stumps can (ii)____________ climate change, by (iii)____________ the inference that bog surfaces had dried sufficiently to allow colonization and then became too wet to support the trees.


Quantity A

RS

Quantity B

ST


Although boredom is ____________, recent research indicates that excessive amounts of it can be harmful to health.
By 1600, France's sense of itself as a nation bound by a shared destiny was____________, but over the course of the seventeenth century French culture regained the strength it had had in the Middle Ages.
Like all mollusks, slugs have bodies that are very soft and far from (i)________, a prerequisite for most terrestrial animals. They get around the constant danger of desiccation by seeking out (ii)________microhabitats.
The primary purpose of the passage is to
r is the remainder obtained when dividing $$7^{995}+7^{50}-4$$ by 7

Quantity A

r

Quantity B

4


When a certain stock exchange closed on Tuesdays, $$\frac{1}{5}$$ of the stocks closed at the same price as on the previous day. Of the remaining stocks, 3 stocks closed at a higher price for every 4 stocks that closed at a lower price. What fraction of all the stocks on this exchange closed at a higher price than on the previous day?


The table above lists the rainfall, in centimeters, for June, July, and August in selected cities. Based on the information given,which of the following statements are true?

Indicate all such statements.
$$k$$ is a positive integer, and $$n=15k$$.

Quantity A

The number of different prime factors of $$n$$

Quantity B

4


A caterer has 20 liters of fruit punch that is 12 percent grape juice, by volume. How many liters of fruit punch that is 20 percent grape juice, by volume, must be added to the original 20 liters of fruit punch in order to create fruit punch that is 15 percent grape juice, by volume?
What percent of all the integers between 1 and 2,000, inclusive, are squares of an integer?
In the xy-plane, circle C is centered at (0, 3) and passes through the point (2, 0).

Quantity A

The area of circle C

Quantity B

13π


While there is no evidence that Bigfoot is real, several well-known species were once thought to be________; the okapi, for instance, was known as the “African unicorn" until explorers obtained proof of its existence.

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