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x ≠ 0

$$(x+\frac{1}{x})^{2}$$=5

Quantity A

$$x^{2}$$+$$(\frac{1}{x})^{2}$$

Quantity B

3


x, n and k are all integers, 0 < x < $$10^{7}$$, x=$$n^{k}$$

If the units digit of x is 5, and x could be transformed into both the square of an integer and the cube of an integer, then x must be?


In a hexagon, ∠X=115°

Quantity A

∠y

Quantity B

115°




AB∥ED,△ABC and EDC are similar triangles,and the area of △EDC equals to $$\frac{1}{9}$$ of the area of △ABC. What is the ratio of AE to EC?


As shown in the figure, the centers of the two circles are respectively on the circumference of each other, and the radius is 3. What is the perimeter of this figure?
15.6 is 2 standard deviation below the mean, and 26.1 is 3 standard deviation above the mean, what is the mean?
In a kindergarten, three shorter kids sit in the first row, while four taller ones sit in the second row. In how many ways can they be arranged?
Fred`s suitcase contains 4 shirts, 3 pair of pants, and 2 pair of shoes. A matching outfit consists of any shirts, any pair of pants, and a pair of shoes, except that one of the shirts does not match one of the pairs of pants. How many matching outfits can be selected from Fred`s suitcase?
Four guests A, B, C and D have to be assigned into three different office rooms (one double room and two single rooms) such that A and B won`t have to stay in the double room at the same time. How many ways in total can they be assigned into these office rooms?
Three numbers are to be selected at random and without replacement from the five numbers 4, 5, 7, 8 and 11. What is the probability that the three numbers selected could be the lengths of the sides of a triangle?
What is the probability that the one 3-digit and one 2-digit integers that could be formed out of 1, 2, 3, 4 and 5 (each figure is used for only once) are both even integers?

Give your answer as a fraction.
The units digit of $$7^{n}$$ is r, and the units digit of $$9^{n}$$ is t, where n, r, and t are positive integers. Which of the following could be the value of r+t?

Indicate all such values.
For the positive integers less than or equal than 603, how many integers are the multiple of 3, or the multiple of 2, or the multiple of both?
How many integers between 100 and 1,000 are multiples of 7?
The sum of three different positive integers is 11.

Which two of the following statements together provide sufficient information to determine the three integers?

Indicate two such statements.
Z=$$123^{4}$$-$$123^{3}$$+$$123^{2}$$-123

What is the remainder when Z is divided by 122?
For 7 soccer ball teams, each of them has to play with all the other teams. However, to decide which team wins, every two teams have to play 3 rounds and the team that win for the most times will ultimately win. How many rounds of game do all teams have to play in total?
n is a positive integer.

Quantity A

$$\frac{1}{3^{n}}$$

Quantity B

$$3(\frac{1}{4^{n}})$$


What is the value of $$\frac{51!-50!}{50!-49!}$$?

Give your answer as a fraction.
How many positive divisors of 210 can be expressed as a product of two prime factors?

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