October ProblemsMP2 Reason abstractly and quantitatively

Mrs. Hernandez’ Change

Mrs. Hernandez bought several items, all the same

price. The number of items was equal to the cost of

each item in cents. The change that Mrs. Hernandez

received from $10 was $1 and 7 coins totaling less than

$1. How much did each item cost?

10/1

Watching Water Evaporate

Alice has just finished washing clothes in a 20-gallon tub and must now throw out the wash water. She pours half the water on the ground to evaporate. After it evaporates, she will again pour out half the water that is left in the tub. How many times will she pour out the water before the tub is empty?

10/2

Raise-Cut ~ or ~ Cut-Raise?

Suppose your salary could be raised 10% and then a

month later reduced by 10%. Or suppose that you may

choose to have the cut first, followed by the raise one

month later. Which option is better? Why?

10/3

Will Wants His Watch Back

Two boys are discussing money.

Will:“How about lending me $10?”

Tyler: “I can’t; I spent some of it.”

Will:“How much did you spend?”

Tyler:“Exactly 1/4 of what I have left.”

Will: “Good. That leaves you with just what I need

to get my watch back from the watchmaker.”

How much money did Tyler have left?

10/4

What Are The Rules, Anyway?10/5

Reel It In!

Jake caught a fish. To win a contest, his fish had to

weigh more than the biggest one, which weighed 4

pounds. Jake’s fish was hard to weigh. See if you can

figure out its total weight. The tail weighed 9 ounces,

the head weighed as much as the tail and half the

body, and the body weighed as much as the head and

tail together. What was the weight of the fish?

10/9

Keep'n It Real!

Using only the digits 2, 3, 4, and 5 and the two

mathematical symbols “+” and “–” each once and

only once, create a true mathematical sentence.

For example, 2 + 3 = 45 uses all the digits and

symbols once and only once, but it is not a true

mathematical sentence. You may not use any other

mathematical symbols or digits.

254

3+ -10/10

Minimize it!

Let A, B, and C represent different digits greater than 0.

Determine the minimum value of the expression below.

(Note: for ABC, A simply signifies a number that is the hundreds digit,

B is the tens digit, and C is the ones digit—they are not multiplied.)

10/11

Pocket Change

I have 6 coins in my pocket

totaling $1.15, but I cannot make

change for a dollar, half dollar,

quarter, dime, or nickel. What

coins do I have in my pocket?

10/12

Counting Rectangles

The figure below is composed of congruent squares.

How many rectangles are in the figure?

10/15

Circumference River and Square Root Bridge

The width of the Circumference River is 3100 meters.

The Square Root Bridge spans the Circumference

River. If 1/8 of the bridge stands on land on one side of

the river, and 1/10 of the bridge stands on land on the

other side, how long is the Square Root Bridge?

10/16

A Paint Predicament

A box (shown here as a rectangular

prism) is 3 units by 4 units by 5 units.

If the box is composed of unit cubes

and completely dipped in paint, how

many unit cubes will have no paint on

any of their faces?

10/17

What’s the Relation?

If the radius of a circle is

doubled, what happens to

the area? What happens

to its circumference?

10/18

Sports Confusion

There are 40 kids in gym.

• 10 play football, soccer and basketball

• 15 play football and soccer

• 24 play football only

• 22 play soccer only

• 14 play football and basketball

How many kids are only on the basketball team?

10/19

The Prime Difference

Which of the following numbers:

1, 2, 7, 8, or 10 cannot be the

difference of two prime numbers?

Explain your reasoning, and

provide a counterexample for

each number that can be the

difference between two primes.

10/22

Tennis, Anyone?

Think about a typical can containing three

tennis balls. Which is greater, the height of

the can or the circumference of the base of

the can? (Ignore the thickness of the plastic.)

Make an estimated guess first. Then use

mathematics formulas and/or actual

measurement to verify your guess.

10/23

Prime Number Constraints

Find the sum of the least and

greatest two-digit prime numbers

whose digits are also prime.

Hint: 0 and 1 are not prime numbers.

10/24

Extend the Sequence

Find the next three numbers in the special

sequence of numbers.

3, 1, 4, 1, 5, 9, 2, 6, 5, ___, ___, ___

10/25

Decoding the Riddle

Remove “twelve letters”

to reveal two hidden

numbers. What are the

two hidden numbers? You

may have to reorder the

letters.

10/26

(Hint: In this puzzle, “twelve letters” ≠ 12)

These Shoes Were Made for Walking

You begin walking on a road. You travel

78 feet during the first minute, 85 feet the

second minute, 92 feet the third minute,

increasing by 7 feet each minute. If the

total time you traveled is 8 minutes, how

far did you walk?

10/29

Find the Missing Number

Based on the numbers in the first three 2 ×2 grids,

determine the missing number in the fourth number grid.

10/30

Fraction Frustration

Find the value of the expression

above. Your answer must be in

simplified fractional form.

10/31