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Quantity A

4!

Quantity B

5!-4!



In a circle, the area of the shaded area is 16π

Quantity A

The radius of the circle

Quantity B

5.5


There are two right circular cylinder oil drums. In the first cylinder, the base area is 4π and the oil height is 5, while in the second cylinder, the base area is 10π, and the oil height is 6. Mark gradually pours oil from the second cylinder into the first one, so that the oil height in both cylinders will become the same. What will be the oil height at last?
Give your answer as a fraction.


What is the ratio of the number of people in Group 2 with the ailment sneezing and itchy eyes to the total number of people in both groups with the ailment sneezing and itchy eyes?
Give your answer as a fraction.
If there are more students in Class A than in Class B, then which of the following statements alone can sufficiently determine the average height in Class A is higher than that of Class B?
Indicate all such is/are true.
20 numbers ranging from 0 to 1 are included in Set Q. Set R also has 20 numbers inside and is composed in a way as follows:
If any number X in Set Q is less than $$\frac{1}{2}$$, then X is also included in Set R;
If any number X in Set Q equals to or is more than $$\frac{1}{2}$$, then (2X-1) is also included in Set R

Quantity A

The standard deviation of all the numbers in Set Q

Quantity B

The standard deviation of all the numbers in Set R


The random variable X is normally distributed. The values 650 and 850 are at the 60th and 90th percentiles of the distribution of X, respectively.

Quantity A

The value at the 75th percentile of the distribution of X

Quantity B

750


What is the tens digit of $$\frac{39!}{29!}$$?
n and k are integers, n > k > 1

Quantity A

(n-k)!

Quantity B

n!-k!


How many positive integers less than 10,000 are such that the product of their digits is 210?
In how many ways can 5 paintings be put into 3 different frames (one painting for each frame)?
How many odd 5-digit integers can be formed out of 3, 4, 6, 7, 9 such that each is used for only once?
A, B, C, D, E need to take seats in a row such that beween A and B, one sits at one end and the other at the other end. In how many ways can the five people arrange their seats?
How many different five-digit even integers can be formed out of 1, 2, 3, 4 and 5 such that none are selected for more than once?
How many three-digit integers can be formed out of 8 different integers (5 odd ones, 3 even ones) so that the tens and hundreds digit are both odd integers, while the units digit is an even integer (no integers could be used by more than once)?
C and M have to take pictures together with five other people. C has to stand in one of the three positions in the middle, M has to stand besides C, while the other five people can stand as they want. In how many ways can they stand in total?
Five gift cards (one 100-dollar card, one 50-dollar card, one 25-dollar card and two 10-dollar card) have to be assigned to ten kids such that each kid receives no more than one card. In how many ways can these five cards be distributed?
A knockoff website requires users to create a password using letters from the word MAGOSH. If each password must have at least 4 letters and no repeated letters are allowed, how many different passwords are possible?
In how many ways can a 5-person committee can be formed out of 6 professors, 3 managers and 4 coordinators such that Dr. W, one of the professors, and Ms. M, one of the managers, are both selected?
From a group of 8 people, it is possible to create exactly 56 different k-person committees. Which of the following could be the value of k ?
Indicate all such values.
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