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In the $$xy$$-plane, the slope of line $$l$$ is $$p$$, the slope of line $$n$$ is $$q$$, the $$y$$-intercept of line $$l$$ is $$f$$, and the $$y$$-intercept of line $$n$$ is $$j$$. $$0 \lt q \lt p$$, $$0 \lt f \lt j$$.

Quantity A

The $$x$$-intercept of line $$l$$

Quantity B

The $$x$$-intercept of line $$n$$
If a set S has a total of 6 subsets that consist of 2 members each, then S consists of how many members?
What's the number of integers that are neither multiple of 3 nor multiple of 7 from 1 to 1000, inclusive?
In a class, there are 3/4 of people taking chemistry class, and there are 5/6 of people taking biology class. It is possible that a student takes neither of them. What is the minimum ratio of people taking both these classes?
Give your answer as a fraction.
There are 210 students in a class. 160 of them take physics, 80 of them take chemistry, and 60 of them take biology. Each student has to take at least one courses. but cannot take all the three classes simultaneously. The number of students who take two classes is what percent of all the students?
Give your answer as a fraction.
Dr. Mosher call the roll ten days in a row. If Candy attended 8 times, Sam attended 7 times, and Amy attended 6 times. If they show in class simultaneously in only one day, and at least 1 student attend each day`s course, how many days in which exactly two of them attended?
The height a plant every day increased by $$\frac{1}{2}$$ than that of the preceding day. What is the ratio of the overall height in the fourth day to that of the seventh day? Give your answer as a fraction.
At 12:55 in the afternoon,there are 250 people in a certain stadium for a game scheduled to begin at 2:15 in the afternoon.If the number of people in the stadium will double every 20 minutes until the game is scheduled to start, how many people will be in the stadium at the time the game is scheduled to start?
A computer identification code on a certain machine consists of 2 letters from an alphabet of 26 letters, followed by 2 digits from the digits 0 to 9. The two digits must be different. How many identification codes are possible?
Joe remembers the first 8 digits of a 10-digit telephone number. If he uses the digits he remembers,what is the maximum number of telephone numbers that he may have to enter in order to reach the correct telephone number?
Three groups of people have 8, 6 and 10 people, respectively. How many ways can you select two people from all these groups such that they are from different groups?
How many three-digit numbers could be formed out of 2, 7 and 5 such that at least one figure is used for at least twice?
There are 5!, or 120, ways of arranging 5 different solid-colored flags side by side. If the colors of the flags are red, blue, yellow, green, and orange, how many of those arrangements have either the red flag or the blue flag in the middle position?


In how many ways can letter a b and c be assigned into a nine palace such that no letter is used more than once in each column and each row?
In how many more ways can you select 4 books out of 8 books than when you select 4 books out of 6 books?
How many different products can be formed when selecting 2 different numbers from 0, 2, 6, 8 and 12 and multiplying them together?
In how many ways can you select one Product A and two Product B out of 8 types of Product A and 6 types of Product B?
The budget of 5 countries are 0.7 billion, 1.3 billion, 1.7 billion, 2.7 billion and 3.2 billion, respectively. In how many ways can you select 3 countries from all the countries such that the total budget of these 3 countries is over 4 billion?
40 DVDs (17 are about psychology, 14 are about biology, and 9 are about history) need to be arranged in a bookshelf such that the 9 history-related DVDs are, on the whole, arranged in chronological order. In how many ways can these DVDs be arranged?
Among 50 spare parts. 2 are broken. What is the probability that both are broken when you select two spare parts from the total?
Give your answer as a fraction.

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