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Quantity A

x+y

Quantity B

$$\sqrt{(x^2+y^2)}$$


The diagonal of square A and B is 10 and 20, respectively.
What is the ratio of the area of square A to the area of square B?
Give your answer as a fraction.
Set A={2, 4, 6}

Set B={2, 4, 6, 8, 10, 12}

If Set A is a subset of Set M, while Set M is subset of Set B, then how many ways can Set M be constructed?
In a survey, 65 percent of respondents believe drug is effective, 48 per cent of the same group of people believe exercise is effective. If 22 percent of them believe drug is effective while exercise is ineffective, then what percentage of respondents believe the other way around?
_____%
18 students can choose from snack, staple food, vegetables or none for lunch. Each student can choose whatever types of food as they want. Among 12 students who choose vegetables, 3 also choose snack but not staple food, 2 also choose staple food but not snack, while 4 also choose snack and staple food. What`s the ratio of students who only choose vegetables to all students?
Give your answer as a fraction.
All of the 80 science students at a certain school are enrolled in at least one of three science courses: biology, chemistry, and physics. There are 60 students enrolled in physics, 50 students enrolled in chemistry, and 35 students enrolled in biology. None of the students are enrolled in all three courses. Which of the following could be the number of students enrolled in both chemistry and biology?
Indicate all such possible values.
In a group of people, 40% of like red, 50% of them like blue, while 60% of them like green. 9% of them only like red, 10% only like blue and 11% only like green. 20% of them like all the three colors simultaneously. What percent of people like both red and green, but not blue?
$$a_{1}=1$$, $$a_{2}=1$$, $$a_{n}=0.2a_{n-1}(n≥3)$$

Quantity A

$$a_{6}$$

Quantity B

$$25^{3}(0.2)^{10}$$


$$a_{1}=-5$$, $$a_{2}=4$$. If for any integer n greater than 2, $$a_{n}=a_{n-1}-a_{n-2}$$, then what`s the sum of $$a_{1}$$, $$a_{2}$$, $$a_{3}$$, $$a_{4}$$ ... to $$a_{100}$$?
A list of numbers could be summarized into $$a_{n}=(-1)^{n+1}*n$$ (n is a positive integer), and $$a_{1}=1$$
What is the sum of $$a_{1}$$, $$a_{2}$$, $$a_{3}$$,...........,$$a_{97}$$, $$a_{98}$$, $$a_{99}$$?
If $$a_{1}=2$$, $$a_{2}=3$$, $$a_{n}=a_{n-1}*a_{n-2}$$ (n≥3),then $$a_{8}$$ is?
$$a_{1}=2$$,$$a_{2}=5$$
If $$a_{n}=a_{n-1} / a_{n-2}$$,then $$a_{135} =$$?
Give your answer as a fraction.
A positive integer is a palindrome if it reads exactly the same from right to left as it does from left to right. For example, 5 and 66 and 373 are all palindromes. How many palindromes are there between 1 and 1,000, inclusive?
N equals the number of positive 3-digit numbers that contain odd digits only (the same number could be used for more than once).

Quantity A

N

Quantity B

125


Quantity A

The number of 3-digit integers all of whose digits are even (the same number could be used for more than once)

Quantity B

The number of 3-digit integers all of whose digits are odd (the same number could be used for more than once)


Set A={1, 2, 3}
Set B={1, 2, 3, 4}

Quantity A

The total number of different four-digit positive integers that can be formed by elements from Set A

Quantity B

The total number of different three-digit positive integers that can be formed by elements from Set B


A three-digit code for certain locks uses the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 according to the following constraints. The first digit cannot be 0 or 1, the second digit must be 0 or 1, and the second and third digits cannot both be 0 in the same code. How many different codes are possible?

Mark is supposed to fill three sectors of a garden with a selection of five colors of flowers. The same color could be used, but only twice at most, and not adjacent. In how many ways can the garden be decorated?
n is a positive integer

Quantity A

$$(n^{2})!$$

Quantity B

$$(n!)^{2}$$


$$\frac{X}{2}$$=n!
If n is a positive integer, then X could be?
Indicate all such numbers.
1 2 ... 16 17 18 19 20 21 22 ... 25 26

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