1

Part of 1985 National High School Mathematics League

Problems(2)

Source: 1985 National High School Mathematics League, Exam One, Problem 1

a,b

are real numbers (neither is

0

).Given two conditions: A:

a>0

a>b

a^{-1}>b^{-1}

. Then, which one of the followings are true?

(\text{A})

A is sufficient but unnecessary condition of B.

(\text{B})

A is necessary but insufficient condition of B.

(\text{C})

A is sufficient and necessary condition of B.

(\text{D})

A is insufficient and unnecessary condition of B.

Analytic Geometry Problem

Source: 1985 National High School Mathematics League, Exam Two, Problem 1

In rectangular coordinate system

xOy, A(x_1,y_1), B(x_2,y_2)

x_1,y_1,x_2,y_2

are 1-digit-numbers. Intersection angle between

OA

x

-axis positive direction is larger than

\frac{\pi}{4}

, intersection angle between

OB

x

-axis positive direction is smaller than

\frac{\pi}{4}

. Projection of

A

y

A'

, projection of

B

x

B'

\triangle OBB'

33.5

\triangle OAA'

. Find all 4-digit-number

\overline{x_1x_2y_1y_2}

analytic geometrygeometry