#### 题目列表

Two different prime numbers are greater than 2 and less than 50. If the product of them is less than 100, then how many combinations of them will there be?
0 < P*Q < 100, P and Q are both prime numbers,and P < Q, how many combinations of P and Q are there?
How many positive integers no greater than 20 can be expressed as the sum of two different prime numbers?
1575=$3^{x}$*$5^{y}$*$7^{z}$,What`s the value of x+y+z?

#### Quantity A

The number of different prime factors of 12

#### Quantity B

The number of different prime factors of 9

#### Quantity A

The number of prime factors of 27

#### Quantity B

The number of prime factors of 18

m is an odd number and greater than 1

#### Quantity A

The greatest prime factor of 2m

#### Quantity B

The greatest prime factor of $m^{2}$

k and n are consecutive positive odd integers.

#### Quantity A

The least common multiple of k and n

#### Quantity B

kn

y=105n (n is a positive integer)

y is both the square of an integer, and a multiple of 30

What is the least possible value of n?
n is an integer between 10 and 100. The remainder is 2 when n is divided by 4, 6, 7.

#### Quantity A

The remainder when n is divided by 11

#### Quantity B

9

How many positive two-digit integers have a remainder of 3 when divided by both 10 and 6?
If a, b and c are integers such that 0 < a < b < c < 2a, what is the greatest common factor of $84^{a}$, $126^{b}$, and $98^{c}$?
In a pile of books, $\frac{1}{3}$ are biography books, $\frac{1}{4}$ are chemistry books, while another $\frac{1}{5}$are math books. What ratio of all books are books other than the three subject of books listed above?

Give your answer as a fraction.
For integers x, y, and z, where 1 ≤ x < y < z ≤ 10, what is the least possible value of the expression $\frac{x-y}{z}$?

Give your answer as a fraction.
Each of the 1,800 households that participated in a survey owned either one car, two cars, or no cars. If 740 of the households owned only one car and at least $\frac{1}{3}$ of the households owned two cars, what is the greatest possible value of the ratio of the number of households that owned no cars to the number of households that owned two cars?

Give your answer as a fraction.
If x and y are positive numbers and the ratio of x to y is 5 to 4, which of the following ratios must be equal to 6 to 5?
$o.\overline {cd}$ is a repeating decimal

What is the sum of all the possible decimals o.cd that satisfy the following requirements?

1) c and d are both integers

2) c+d=5

3) c < d

Give your answer as a fraction.
b < 0

#### Quantity A

|$-b^{3}$|

#### Quantity B

$-b^{3}$

k > m

|m| - |-k|

|k| - |-m|

|2+k|=|2-k|

k

#### Quantity B

0

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