Math Problem of the DayMay 2013

5/1 Going On Vacation

The floor plan of a vacation cottage is shown. Both bedrooms have the same dimensions. What is the total area of the cottage, in square feet?

5/2 That’s Complex!

Simplify the complex fraction.

5

6−

13

38

−14

5/3 Goomats and Zignots

Five goomats plus a zignot is 87. A goomat plus five zignots is 99. What is the sum of two goomats and two zignots?

+ = 87+ = 99

5/6 Angles in a Clock

What is the number of degrees the minute hand of a clock moves from 6:04 pm and 6:21 pm?

5/7 Wire Weight

A wire of uniform diameter and composition that weighs 32 lb is cut into two pieces. One piece is 90 yd long and weighs 24 lb. What is the length, in yd, of the original wire?

5/8 Shaded Regions

Square WXYZ is partitioned into four smaller congruent squares, and then portions of those squares are shaded, as shown. What fractional part of the square is shaded?

5/10 Printing Business

If 45 business cards can be printed in 30 seconds, how long will it take to print 555 business cards at the same rate?

5/13 Sums and Products

What integer can be added to 13/12 or multiplied by 13/12 to give the same result?

5/14 Find the Number

If one-half of a number is eight less than two-thirds of the number, what is the value of the number?

5/15 Minimize the ProductFind the least possible product of two integers whose sum is 16?

a+b=16

5/16 Simply Perfect!

A perfect number is a number whose proper factors add to equal the number. For example, 6 is a perfect number because 1 + 2 + 3 = 6. Find another perfect number.

5/17 How odd!

What is the smallest odd integer with exactly six positive factors?

5/20 Picture this!

What is the minimum number of square tiles needed to exactly cover a rectangle whose length is 50% greater than its width?

5/21 How Many Numbers?How many different four-digit numbers can be formed if the digits 2, 3, 4 and 5 must be used in each of the integers?

___, ___ ___ ___

5/23 Perimeter Puzzle

A regular polygon has a total of 9 diagonals. If each side measures 2.5 inches, what is the perimeter of the polygon?

5/24 Area: Holding SteadyThe length of a rectangle is three times its width. A new rectangle is created by decreasing the length of the original rectangle by half. By what factor must the original width be multiplied, if the area remains unchanged?

5/27 Sweet Treats

The Sachem singers earned $273 by selling a combined total of 440 brownies and cookies during their concert. If each brownie sold for $0.75 and each cookie sold for $0.50, how many brownies did they sell?

5/28 Guess the Number

If twice a number is equal to 6 more than half the number, what is the number?

5/29 Solve this one

In the figure shown, the distance between adjacent dots in each row and column is 1 unit. Find the area of the shaded region in square units.

5/30 Dollars to Dollars

The ratio of John’s allowance to Bill’s allowance is 3:7. The ratio of John’s allowance to Mary’s allowance is 2:5. What is the ratio of Mary’s allowance to Bill’s allowance?

5/31 Squares and Ratios

The difference of the squares of two distinct positive numbers is equal to twice the square of their difference. What is the ratio of the smaller number to the larger?

??

Problems adapted from Math Counts School Sprint Round 2012