1

Part of 2013 BMT Spring

Problems(5)

BMT 2013 Spring - Geometry 1

Source:

A rectangle with sides

a

b

24

and a diagonal of length

11

. Find the perimeter of this rectangle.

2013 BMT Team 1

Source:

A time is called reflexive if its representation on an analog clock would still be permissible if the hour and minute hand were switched. In a given non-leap day (

12:00:00.00

11:59:59.99

p.m.), how many times are reflexive?

BMT 2013 Spring - Discrete 1

Source:

A number is between

500

1000

and has a remainder of

6

when divided by

25

and a remainder of

7

when divided by

9

. Find the only odd number to satisfy these requirements.

BMT 2013 Spring - Analysis 1

Source:

Find the value of

a

satisfying \begin{align*} a+b&=3\\ b+c&=11\\ c+a&=61 \end{align*}

algebrasystem of equations

2013 BMT Individual 1

Source:

Billy the kid likes to play on escalators! Moving at a constant speed, he manages to climb up one escalator in

24

seconds and climb back down the same escalator in

40

seconds. If at any given moment the escalator contains

48

steps, how many steps can Billy climb in one second?