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Triangle T is equilateral and has a height of 20, and triangle W is isosceles and has a height of 20.

Quantity A

The area of the isosceles triangle T

Quantity B

The area of the equilateral triangle W


If $$y=\frac{x+w}{2}$$ , what is $$w-y$$ in terms of $$x$$ and $$y$$?
$$x=\frac{a+\frac{b}{d}}{\frac{d}{c}}$$

Which one of a, b, c, d doubles, so that x will also double?
k is an integer

Quantity A

$$\frac{k^{2}+1}{k^{2}}$$

Quantity B

$$\frac{k^{3}+1}{k^{3}}$$


Quantity A

(1-$$\frac{1}{100}$$)*(1+$$\frac{1}{101}$$)*(1-$$\frac{1}{102}$$)*(1+$$\frac{1}{103}$$) *(1-$$\frac{1}{104}$$)

Quantity B

1


$$\frac{2}{23}$$ < x < $$\frac{2}{21}$$

Quantity A

$$\frac{2}{22}$$

Quantity B

x


2 ≤ r < s ≤ 6

If r and s are both integers, then what`s the greatest possible value of $$\frac{r+s}{rs}$$?
$$\frac{2}{x}$$=$$\frac{y}{2}$$ (x and y are both integers)

Quantity A

x

Quantity B

y


If z=$$\frac{x}{y}$$, w= $$\frac{x}{x+y}$$, and 0 < x < y, what is w in terms of z?
$$\frac{a+1}{b-1}=\frac{5}{7}$$

Quantity A

$$\frac{a}{b}$$

Quantity B

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


1 pound tea can make 210 cups of tea and 1 pound coffee can make 40 cups of coffee. The number of cups of coffee sold by a restaurant is 12 times as many as the number of cups of tea sold. What is the ratio of the pounds of tea to pounds of coffee?

Give your answer as a fraction.
In a factory, 840 workers are on day shift, among whom 252 are female. 700 workers are on night shift. The ratio of male and female workers is the same for both workers on day shift and workers on night shift. What is the number of male workers that are on night shift?

Triangles ABC and DEF are right triangles with AB = CB = DE = EF. If the area of the inscribed square region labeled X is 441, what is the area of the inscnibed square region labeled Y?

The figure above is three congruent square. The bottom side of the left square aligns with the top side of the bottom square. The area of each square is 4, AC=BC. What's the perimeter of △ABC?

The figure shown consists of a rectangle with length 14 and width 6, together with three isosceles right triangles. What is the area of the entire figure?
The length of three sides of a triangle is 3, 4 and y. If none of the interior angles of the triangle is more than 90°, then the range of y is?

In △ABC, AE = 1/2 BE, EF is parallel with BC. If EF = 5, what is the length of BC?

The sides of the two squares is 4 and 6, respectively. What is the area of the shaded region?

The quadrilateral ABCD is a square, and EFGB is a rectangle, AE=CG

Quantity A

The area of ABCD

Quantity B

The area of EFGB



In square ABCD, the side of each side is 15, If the area of the shaded area accounts for 75% of the total area of the entire square, then what is the value of x?
Give your answer as a decimal.

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