MathCounts 2019-2020 Round 3

A new pair of shoes is on sale for $45. If the cost represents a 40% discount, what was the original cost of the shoes?

Tags

CCSS.6.RP.A.3C

The sum of two numbers is 7 and their product is 12. What is twice the sum of their reciprocals?

• 4/3

• 5/7

• 7/6

• 8/9

What is the largest prime factor of:

8x7x6x5x4x3 - 6x5x4x3x2x1 ?

Tags

CCSS.6.EE.A.1

The price of a pizza is directly proportional to its area. If a 12-inch pizza costs $12.00, how much does a 14-inch pizza cost? Express your answer to the nearest dollar.

A town has some strange streets that are one-way only between the hours of 7:00am and 8:00am. They run either south or east during that hour. If Joe wishes to go from A to B at 7:20am, how many different ways can he travel?

 $if\ \frac{3}{x-1}=\frac{2}{x+7}$  what is the value of x?

Tags

CCSS.HSA.REI.A.2

Given that a, b and c are positive integers and abc=20, what is the least possible sum for a+b+ c?

Tags

CCSS.8.EE.C.7B

The students from Brooks Middle School sat in 20 rows in such a way that each row after the first had 3 more students sitting in it than the previous row. If 16 students sat in the first row, how many students sat in the 19th row?

Tags

CCSS.HSF.BF.A.2

What is the area of the polygon whose vertices are (0,0), (3,4), (0,8), (5,8) and (5,0), connected in that order?

Tags

CCSS.HSG.GPE.B.7

Andrew and Lindsey are seated at a round table with four other people. If everyone is randomly seated, what is the probability that Andrew and Lindsay are seated next to each other?

• 2/5

• 6/11

• 3/4

• 5/7

Tags

CCSS.HSS.CP.B.9