题目列表

题目内容
Each of the numbers m, n, and p is greater than 0 and less than 1..

Quantity A

m(n+p)

Quantity B

mn+p


$$1 \lt x \lt 2$$

Quantity A

$$\frac{1}{x}+\frac{2}{x}+\frac{3}{x}$$

Quantity B

$$x+\frac{x}{2}+\frac{x}{3}$$


The product of the positive numbers x and y is less than the sum of x and y.

Quantity A

The sum of the reciprocal of x and the reciprocal of y

Quantity B

1


0 < x < y < $$\frac{1}{2}$$, $$\frac{1}{2}$$ < r < t < 1

Quantity A

(x+y)(r+t)

Quantity B

r+t(x+y)


If 2x+y=5, then what is the value of ($$9^{x}$$)($$3^{y}$$)?
$$a=\frac{x}{x+y+z}$$ , $$b=\frac{y}{x+y+z}$$ , $$c=\frac{z}{x+y+z}$$


Quantity A

The average of a, b and c

Quantity B

$$\frac{1}{2}$$


y=$$2^{-r^{2}}$$, where r is a positive integer, which of the following could be the value of y?

Indicate all such values.
If a=$$(-\frac{1}{37})^{12}$$, which of the following equals to $$37^{-12}$$?
$$r^{3}$$-r=r-$$r^{3}$$

Quantity A

r

Quantity B

0


$$m$$ and $$v$$ are negative integers and $$m \lt v$$.

Quantity A

$$7+10^{m}$$

Quantity B

$$5+10^{v}$$


$$a \gt 0$$

$$x \neq 0$$

Quantity A

a$$x^{4}$$

Quantity B

$$(ax)^{4}$$


n is an integer

Quantity A

$$(\frac{1}{2})^{n}$$

Quantity B

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


A number can be transformed into both a perfect square and a perfect cube. If its units digit is 5, and is less than 100,000, then the number must be?

Quantity A

$$\sqrt[3]{250}$$

Quantity B

6$$\sqrt[3]{2}$$


N family have 2 boys and 1 girl each, M family have 1 boy and 2 girls each. In total, there are 11 boys and 10 girls among these M+N family. What is the sum of N+M?
The equation a$$x^{2}$$+5x-6=0 has two solutions. One is 3 and the other one is c.

Quantity A

a

Quantity B

c


x= $$\frac{3y}{5}$$= $$\frac{2z}{3}$$ (x≠0)

Quantity A

The average of x, y and z

Quantity B

x


a and b are two roots of the equation $$x^{2}-x-20=0$$

Quantity A

$$(a-b)^{2}$$

Quantity B

$$(a+b)^{2}$$


The equation $$x^{2}$$+kx+1=0 has two solutions t and r, and t < r. k is a constant.

Quantity A

t

Quantity B

1


If x and y are integers, and 1 < -x < 4, 2 < y < 5, what is the least possible value of xy?

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