MathDB

3

Part of 2014 BMT Spring

Problems(5)

BMT 2014 Spring - Geometry 3

Source:

12/29/2021
Consider an isosceles triangle ABCABC (AB=BCAB = BC). Let DD be on BCBC such that AD⊥BCAD \perp BC and OO be a circle with diameter BCBC. Suppose that segment ADAD intersects circle OO at EE. If CA=2CA = 2 what is CECE?
geometry
2014 BMT Team 3

Source:

1/6/2022
Together, Abe and Bob have less than or equal to \ 100$. When Corey asks them how much money they have, Abe says that the reciprocal of his money added to Bob’s money is thirteen times as much as the sum of Abe’s money and the reciprocal of Bob’s money. If Abe and Bob both have integer amounts of money, how many possible values are there for Abe’s money?
number theory
BMT 2014 Spring - Analysis 3

Source:

1/6/2022
Emma is seated on a train traveling at a speed of 120120 miles per hour. She notices distance markers are placed evenly alongside the track, with a constant distance xx between any two consecutive ones, and during a span of 6 minutes, she sees precisely 1111 markers pass by her. Determine the difference (in miles) between the largest and smallest possible values of xx.
ratesalgebra
BMT 2014 Spring - Discrete 3

Source:

1/6/2022
The Professor chooses to assign homework problems from a set of problems labeled 11 to 100100, inclusive. He will not assign two problems whose numbers share a common factor greater than 11. If the Professor chooses to assign the maximum number of homework problems possible, how many different combinations of problems can he assign?
number theory
BMT 2014 Spring - Individual 3

Source:

1/22/2022
Suppose three boba drinks and four burgers cost 2828 dollars, while two boba drinks and six burgers cost $37.70\$ 37.70. If you paid for one boba drink using only pennies, nickels, dimes, and quarters, determine the least number of coins you could use.
algebra