Archive of Former Middle School Problems
Two identical rectangular sheets of paper are lying one on top
of the other exactly as shown in the diagram below.
Which of the two parts of the sheet of paper underneath is bigger,
the part that is uncovered, or the part that is covered?
Answer: the covered portion
After a mathematics test each of the twenty-five students
in the class got a peek at the teacher's grade sheet.
Each student noticed five A's.
No student saw all the grades and no student
saw her or his own grade.
What is the minimum number of students who scored
an A on this test?
Answer: 6
If a rectangular box (20 cm x 10 cm x 45 cm) is filled to 80% capacity
with water, what will be the weight of the water in pounds?
[Recall that 1 cm3 = 1 mL (milliliter), and 1 liter = 2.2 pounds]Answer: 15.84 pounds
My yearly salary is $30,000, and it will be increased by $3,000 a year.
Your yearly salary is $20,000, and it will be increased by $5,000 a year.
In how many years will we both have the same yearly salary?
Answer: 5 years
Find the total score in this figure
if triangles count 3, quadrilaterals count 4,
pentagons count 5, and hexagons count 6
Answer: 54
A merchant paid $30 for an article.
He wishes to place a price tag on it so that he can offer a
10% discount on the price marked on the tag
AND
still make a 20% profit on the cost of the item.
What price should he mark on the tag?
Answer: $40
If two "fair" dice are tossed,
what is the probability that the sum of their faces
will be a prime number?
Answer: 15/36
A 24-foot by 72-foot rectangular dance floor is completely
tiled by 1-foot by 1-foot square tiles.
Two opposite corners of the dance floor are connected by a diagonal.
This diagonal passes through the interior of exactly how many tiles?
Answer: 88
Container A is half full of water. Container B will hold 9 cups of water.
When the contents of container A is poured into container B, container B is 2/3 full.
How much water will container A hold?
Answer: 12 cups
A certain exam containing 12 questions was graded
by giving 10 points for each correct answer and
then deducting 5 points for each incorrect answer.
David attempted all 12 questions, leaving no question
unanswered, and scored a total of 75 points.
How many wrong answers did he have?
Answer: 3
Twenty students were randomly surveyed.
The survey found that 5 students took band,
6 took chorus, and 12 took art.
They also found that 3 of those students took band and art,
2 took chorus and art, 1 took band and chorus,
and 1 took all three.
How many students did not have any of these classes?
Answer: 2
If m and n are whole numbers,
49 < n < 101 and 19 < m < 51,
then what is the greatest value for (n + m) / n?
Answer: 2
A TV screen measures 24 inches by 16 inches.
If each dimension is increased by 20 percent,
by what percent is the area increased?
Answer: 44%
Jane's aquarium contains goldfish, turtles, and snails.
There are 16 legs, 10 shells, and 36 eyes in the aquarium.
How many creatures of each type are in the aquarium?
(Hint: Snails have two eyes, one shell, and one leg.)
Answer: 8 goldfish, 2 turtles and 8 snails
An end-of-season sale for winter clothes advertises
30% to 45% off the original price.
What was the lowest original price of a jersey
that is now on sale for $14.99?
Answer: $21.42
The Lord of the Rings used two wardrobes, different only in scale.
One wardrobe was made for Frodo, the 5 foot 5 inch actor,
and one wardrobe was made for his 4 foot character double.
Assume that Frodo's shirt is in the same proportion as the shirt for his character double.
If Frodo's sleeve length is 32 inches and the collar is 15.5 inches,
what sleeve and collar dimensions should the costume department
produce for the character double? (Nearest 10th of an inch)
Answer: Sleeve is 23.6 inches, Collar is 11.5 inches
A person made a purchase for D dollars and C cents
and gave the cashier a $20 bill.
The cashier incorrectly charged the person C dollars and D cents,
and returned $4.88 in change.
If the cashier had charged the correct price,
what would the correct change have been?
Answer: $7.96
Two houses on the same street are separated by a large, empty field.
The first house is numbered 29, and the other is numbered 211.
An architect is designing 13 new houses to be built between
the two existing houses.
What should the numbers of the new houses be if along with the
existing houses, the numbers need to form an arithmetic sequence?
Answer: 42, 55, 68, 81, 94, 107, 120, 133, 146, 159, 172, 185, 198
Given rectangle ABCD with length twice the width;
midpoints E, F, G, and H; and perimeter equal to 48 units.
Find the area of EFGH.
Answer: 64 units2
A certain number has exactly eight factors, of which 35 and 77 are two.
Find the value of the number.
Answer: 385
What is the largest sum of money -- all in coins and no silver dollars --
that you could have in your pocket without being able to give change
for a dollar, a half-dollar, a quarter, a dime, or a nickel?
Answer: $1.19
Which of the four numbers in the array doesn't belong? Why?
23 20
25 15
Answer: Any of these numbers could be defended as the answer to this question.
In the target shown below, the circles have radius = 1, 2, and 3, respectively.
If you throw two darts and you are assured both will hit the target,
what is the probability that your score will be exactly 150 points?
Answer: 2/27 (or 0.074 or 7.4%)
A certain examination of 12 questions was graded by giving 10 points for each
correct answer and then deducting 5 points for each incorrect answer.
David attempted all 12 questions leaving no question unanswered,
and scored a total of 75 points.
How many wrong answers did he have?
(Answer: 3)
What number belongs in the START circle of this set of instructions?
(Answer: 74)
Ms. Angelou asked her students to open their mathematics books
so that the sum of the facing pages is 93.
To which pages should the students turn?
What are the possible sums for facing pages?
What strategy will always work to fund facing pages with a given sum?
(Answer: pages 46 and 47)
What is the value of the following:
2 - 4 + 6 - 8 + 10 - 12 + 14 - ... - 100?
(Answer: -50)
Assuming the same width and type of crust and the same toppings,
which has more pizza:
one 18 inch party pizza or two large 12 inch pizzas?
These pizzas are circular and the measurements are across
the pizza - diameter.
(Answer: the first pizza with 81¼ in2 of area on top.)
You decide to take a trip with your father-in-law's only child's spouse's mother.
How is she related to you?
(Answer: The person you will take on the trip with you is your mother.)
How many different squares exist on a standard
8 by 8 checkerboard?
(Answer: 204)
Five candidates -- A, B, C, D, and E -- were in an election.
Candidate A was elected with 30 votes, B placed second, and E was last with three votes.
If 49 votes were cast and no two candidates had the same number of votes,
what is the smallest amount of votes that B could have received?
(Answer: 7 votes)
In the cells shown, place a ten-digit number such that
the digit in the first cell indicates the total number of 0's in the entire number,
the digit in cell 1 indicates the number of 1's in the number, and so on, to the last cell.
(Answer: 6210001000)
Wait in Line.
Your group of fifty is in a single line waiting to ride a roller coaster at Six Flags Amusement Park.
The coaster has eleven cars, which holds two people each. The ride lasts four minutes,
and three minutes are required to unload one group and load the next group.
What is the least amount of time from when the first member of your group
begins to load until the last member of your group unloads?
What is the greatest amount of time?
(Answer: 24 minutes minimum and 31 minutes maximum)
A bug crawls around the outside of a rectangle that measures 6.5 cm by 8.5 cm.
If the bug stays 3.5 cm from the rectangle at all times, what is the area,
to the nearest cm2, of the region bound by the path of the bug?
(Answer: 116 sq. cm)
Shown is the floor plan of a haunted house.
You enter and the front door locks behind you.
You run from room to room looking for a way out.
Each time you pass through a door, it locks behind you.
Can you get locked in a room with no way out?
(Answer: It is impossible to get locked in a room and therefore the house.)