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题目内容
For every positive even integer n, the function h(n) is defined to be the product of all the even integers from 2 to n, inclusive. If p is the smallest prime factor of h(100)+1, then p is?
Let S be the set of all positive integers n such that $$n^{2}$$ is a multiple of both 24 and 108. Which of the following integers are divisors of every integer n in S?

Indicate all such integers.
In a certain medical group, Dr. Schwartz schedules appointments to begin 30 minutes apart, Dr. Ramirez schedules appointments to begin 25 minutes apart, and Dr. Wu schedules appointments to begin 50 minutes apart. All three doctors schedule their first appointments to begin at 8:00 in the morning, which are followed by their successive appointments throughout the day without breaks. Other than at 8:00 in the morning, at what times before 1:30 in the afternoon do all three doctors schedule their appointments to begin at the same time?

Indicate all such times
In a factory, machine A operates on a cycle of 20 hours of work followed by 4 hours of rest, and machine B operates on a cycle of 40 hours of work followed by 8 hours of rest. Last week, the two machines began their respective cycles at 12 noon on Monday and continued until 12 noon on the following Saturday. On which days during that time period was there a time when both machines were at rest?

Indicate all such days.
If x and y are positive integers, and 1 is the greatest common divisor of x and y, what is the greatest common divisor of 2x and 3y?
y > 4

Quantity A

$$\frac{3y+2}{5}$$

Quantity B

y
If y=1- ($$\frac{1}{x}$$) where x is an integer, then which of the following numbers could be y?

Indicate all such numbers.
Set K consists of all fractions of the form $$\frac{x}{x+2}$$ where x is a positive even integer less than 20. What is the product of all the fractions in Set K ?
The harmonic mean of x and y is the reciprocal of the average of the reciprocal of x and of y. What is the harmonic mean of 10 and 20?

Give your answer as a fraction.
If 0 < a < 1 < b, which of the following is true about the reciprocals of a and b?
$$-3 \lt x \lt 0$$

Quantity A

$$\frac{1}{x}$$

Quantity B

$$-3$$
If n is a positive integer then n+ denotes a number such that n < n+ < n +1.

Quantity A

$$\frac{20+}{4+}$$

Quantity B

5+
If three integers x, y and z all lie between -10 and 10 (inclusive), then the least value of $$\frac{(x-y)}{z}$$ is?
m, n are integers, 15 ≤ m ≤20 , 30 ≤ n ≤35, what is the greatest possible average of ($$\frac{1}{n}$$) and ($$\frac{1}{m}$$)?
2 ≤ r < s ≤ 6

If r and s are both integers, then what's the greatest possible value of $$\frac{(r+s)}{rs}$$?

Give your answer as a fraction.
$$\frac{1-x}{x-1}$$ = $$\frac{1}{x}$$

Quantity A

x

Quantity B

-$$\frac{1}{2}$$
$$y \neq k \neq 0$$

$$\frac{\sqrt{y}}{4}=\frac{\sqrt{k}}{5}$$

Quantity A

$$\frac{y}{k}$$

Quantity B

$$\frac{25}{16}$$
The ratio of the number of apples to the number of pears is 2 to 3 at first. If 2 more apples are added, how many pears need to be added such that the ratio of the number of apples to the number of pears remains the same?
If a square region with side x and a circular region with radius r have the same area, then x must be how many times as great as r?
A bottle of water can be divided into either five full bowls or eight full cups (of the same size). If Mark fills up a cup with water from a full bowl, then what`s the ratio of the water left to the original full bowl of water?

Give your answer as a fraction.

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