Question 1

Use problem solving strategies to solve the problem.
-A mouse is at the bottom of a 10-foot-tall clock. Every hour he climbs up 3 feet. But when the clock strikes at the hour, he falls back 1 foot. If the mouse starts climbing at 8 a.m., at what time to the
Nearest minute will it reach the top of the clock?
A)1:10 p.m.
B)12:40 p.m.
C)1:00 p.m.
D)12:30 p.m.

Accepted Answer

The mouse effectively climbs 2 feet every hour (3 feet up, 1 foot down). By 12:00 p.m., it will have climbed 8 feet. In the next hour, it climbs 3 feet to reach the top at 12:40 p.m.

Question 2

Solve the problem.
-A cell has at least 3 and at most 47 nucleii. How many cells must a scientist view under his microscope to be certain that at least two cells have the same number of nucleii?
A)45 cells
B)44 cells
C)47 cells
D)46 cells

Accepted Answer

The pigeonhole principle states that if n items are put into m containers, with n > m, then at least one container must contain more than one item. In this case, there are 45 possible numbers of nucleii a cell can have (from 3 to 47, inclusive). To guarantee that at least two cells have the same number of nucleii, one must view 46 cells. This is because viewing 45 cells could, in the worst-case scenario, result in each cell having a unique number of nucleii. Viewing one more (46th) cell ensures that at least two cells will have the same number of nucleii.

Question 3

Solve the problem.
-Sally and Karl work at different jobs. Sally earns $6 per hour and Karl earns $3 per hour. They each earn the same amount per week but Karl works 4 more hours. How many hours a week does Karl
Work?
A)4
B)12
C)16
D)8

Accepted Answer

The answer of Solve the problem.
-Sally and Karl work at...

Question 4

Use problem solving strategies to solve the problem.
-What's the easiest way to heat a pan of water for 9 minutes when you have only a 6-minute hour-glass timer and a 21-minute hour-glass timer?
A)Start both timers. When the 6-min one runs out, turn it over. When it runs out again, start heating the water until the 21-min timer runs out.
B)Start the 6-min timer. When it's halfway through start heating the water. When it runs out turn it over and heat the water until it runs out again.
C)Can't be done.
D)Start both timers. When the 6-min timer runs out, start heating the water. Continue until the 21-min timer runs out.

Accepted Answer

Starting both timers and flipping the 6-minute timer after its first run allows for a total of 12 minutes to pass before the 21-minute timer runs out. Starting the heating process at this point ensures the water heats for exactly 9 minutes until the 21-minute timer runs out.

Question 5

Use problem solving strategies to solve the problem.
-A boxer takes 3 drinks of water after each of the first three rounds of a championship fight. After the fourth round he increases the number of drinks by 1. If he continues to increase his drinks by 1
After each round, how many drinks will he take between the 14th and 15th rounds?
A)12 drinks
B)13 drinks
C)15 drinks
D)14 drinks

Accepted Answer

The pattern of drinks increases by 1 after the fourth round. For the first three rounds, he takes 3 drinks each, so for rounds 1, 2, 3, he takes 3 drinks. After the fourth round, he takes 4 drinks, and then increases by 1 drink after each subsequent round. Therefore, by the 14th round, he will be taking 3 drinks + (14 - 3) = 14 drinks, since he started increasing from the 4th round.

Question 6

Solve the problem.
-If you raise 4 to the 214th power, what is the units digit of the result?
A)2
B)4
C)8
D)6

Accepted Answer

The units digit of powers of 4 cycles every two numbers: 4^1 = 4, 4^2 = 16, 4^3 = 64, 4^4 = 256, etc. The units digits are 4, 6, 4, 6, and so on. Since 214 is even, the units digit of 4^214 is the same as 4^2, which is 6.

Question 7

During vacation time, two students met on a train. One asked the other how old he was. He replied, "The day before yesterday I was 15, and next year I will have my 18th birthday." On what
Date of the year did the two students meet?
A)Dec 31
B)Feb 29
C)Jan 1
D)Feb 28

Accepted Answer

The student was 15 the day before yesterday, turned 16 yesterday, and will turn 17 this year, meaning he will turn 18 next year. This scenario fits if they met on January 1st.

Question 8

Use logic to solve the problem.
-If it takes 10 minutes to hard-boil 5 goose eggs when dropped into boiling water, how long will it take to hard-boil 10 goose eggs?

Accepted Answer

The answer of Use logic to solve the problem.
-If it...

Question 9

Use problem solving strategies to solve the problem.
-Steve is older than Donna but younger than Brenda. Kelly is younger than Brandon. What is the first letter in the name of the oldest person?
A)K
B)D
C)B
D)S

Accepted Answer

Since Steve is younger than Brenda, and there's no information comparing Brenda's age to anyone else's except Steve, Brenda is the oldest.

Question 10

Solve the problem.
-An average library contains at least 50 and at most 250 books. How many library owners must be polled to be certain that at least two owners have the same number of books in their libraries?
A)200 owners
B)201 owners
C)203 owners
D)202 owners

Accepted Answer

The pigeonhole principle applies here, with 201 possible numbers of books (from 50 to 250, inclusive). To guarantee at least two owners have the same number of books, you need 202 owners.

Question 11

Use logic to solve the problem.
-Why are 1985 pennies worth almost twenty dollars?

Accepted Answer

The answer of Use logic to solve the problem.
-Why are...

Question 12

Use problem solving strategies to solve the problem.
-A rabbit grows so that every 2 months it doubles in weight. However, the rabbit will never go over 75 pounds. If a bunny is born on July 15th, weighing 2 pounds, in which month will it weigh 46 Pounds?
A)July
B)June
C)April
D)February

Accepted Answer

The rabbit doubles its weight every 2 months. Starting from 2 pounds in July, it will weigh 4 pounds in September, 8 pounds in November, 16 pounds in January, 32 pounds in March, and 64 pounds in May. Therefore, it will weigh 46 pounds in April, as it surpasses 32 pounds but hasn't reached 64 pounds yet.

Question 13

Use problem solving strategies to solve the problem.
-There is a number between 100 and 115, such that if you find the sum of the cubes of the digits, subtract this sum from 99, divide the result by 3, and add the digits once more, you get 2. What is
The number?
A)113
B)100
C)102
D)114

Accepted Answer

The answer of Use problem solving strategies to solve the...

Question 14

Solve the problem.
-A girl asks her father how many ties he has and he answers with a riddle: "Seven-eighths of my ties plus five." How many ties does her father have?
A)40
B)45
C)50
D)35

Accepted Answer

Let the total number of ties be x. According to the riddle, 7/8x + 5 = x. Solving for x, we subtract 7/8x from both sides to get 5 = 1/8x, which means x = 40.

Question 15

If the hometown baseball team scored 3 runs every inning played, and the visiting team scored 1 run every inning played, what was the final score? 
A) Home: 24
Visitors: 9

B) Home: 27
Visitors: 8

C) Home: 0
Visitors: 0

D) Home: 27
Visitors: 9

Accepted Answer

The answer of If the hometown baseball team scored 3...

Question 16

Solve the problem.
-If you raise 9 to the 387th power, what is the units digit of the result?
A)9
B)7
C)6
D)1

Accepted Answer

The units digit of powers of 9 follows a pattern: 9^1 = 9 (units digit 9), 9^2 = 81 (units digit 1), 9^3 = 729 (units digit 9), and so on, alternating between 9 and 1. Since 387 is odd, the units digit of 9^387 will be the same as the units digit of 9^1, which is 9.

Question 17

Use problem solving strategies to solve the problem.
-There is a number between 2 and 8, such that if you raise any of the remaining numbers to the power of this number, the units digit of the result will always be equal to the base. What is the
Number?
A)3
B)6
C)5
D)8

Accepted Answer

The correct number is 5. When any number (except 0) is raised to the power of 5, the units digit of the result is always the same as the units digit of the base number. This is due to the cyclical nature of powers in their units digits.

Question 18

Use problem solving strategies to solve the problem.
-The number of dogs and chickens on a farm add up to 12. The number of legs between them is 28. How many dogs and how many chickens are on the farm if there are at least twice as many
Chickens as dogs?
A)6 dogs, 6 chickens
B)2 dogs, 10 chickens
C)3 dogs, 9 chickens
D)4 dogs, 8 chickens

Accepted Answer

Let the number of dogs be $d$ and the number of chickens be $c$. We have two equations: $d + c = 12$ and $4d + 2c = 28$ (since dogs have 4 legs and chickens have 2 legs). Solving these equations simultaneously, we find that $d = 2$ and $c = 10$, which satisfies the condition that there are at least twice as many chickens as dogs.

Question 19

Use problem solving strategies to solve the problem.
-I'm thinking of a number between 4 and 10. If I square my number and find the difference of the digits, I will end up with the cube root of my number. What is my number?
A)13
B)5
C)10
D)8

Accepted Answer

The answer of Use problem solving strategies to solve the...

Question 20

A farmer had a stone weighing 40 pounds that he used to weigh pigs, but the stone broke into 4 pieces. The farmer found to his surprise that with the four pieces, he could weigh any whole
Number from 1 to 40. What did each of the 4 pieces weigh?
A)1, 4, 8, and 27 lb
B)1, 3, 9, and 27 lb
C)1, 3, 7, and 29 lb
D)1, 4, 9, and 26 lb

Accepted Answer

The correct weights are 1, 3, 9, and 27 pounds. These weights follow a pattern where each weight is a power of 3 (3^0, 3^1, 3^2, 3^3). This allows for weighing any whole number from 1 to 40 by combining these weights in various ways on opposite sides of a balance scale.

Quiz 1: The Art of Problem Solving

Solve the problem. -A cell has at least 3 and at most 47 nucleii. How many cells must a scientist view under his microscope to be certain that at least two cells have the same number of nucleii?

Solve the problem. -Sally and Karl work at different jobs. Sally earns $6 per hour and Karl earns $3 per hour. They each earn the same amount per week but Karl works 4 more hours. How many hours a week does Karl Work?

Use problem solving strategies to solve the problem. -What's the easiest way to heat a pan of water for 9 minutes when you have only a 6-minute hour-glass timer and a 21-minute hour-glass timer?

Solve the problem. -If you raise 4 to the 214th power, what is the units digit of the result?

During vacation time, two students met on a train. One asked the other how old he was. He replied, "The day before yesterday I was 15, and next year I will have my 18th birthday." On what Date of the year did the two students meet?

Use logic to solve the problem. -If it takes 10 minutes to hard-boil 5 goose eggs when dropped into boiling water, how long will it take to hard-boil 10 goose eggs?

Use problem solving strategies to solve the problem. -Steve is older than Donna but younger than Brenda. Kelly is younger than Brandon. What is the first letter in the name of the oldest person?

Solve the problem. -An average library contains at least 50 and at most 250 books. How many library owners must be polled to be certain that at least two owners have the same number of books in their libraries?

Use logic to solve the problem. -Why are 1985 pennies worth almost twenty dollars?

Use problem solving strategies to solve the problem. -A rabbit grows so that every 2 months it doubles in weight. However, the rabbit will never go over 75 pounds. If a bunny is born on July 15th, weighing 2 pounds, in which month will it weigh 46 Pounds?

Use problem solving strategies to solve the problem. -There is a number between 100 and 115, such that if you find the sum of the cubes of the digits, subtract this sum from 99, divide the result by 3, and add the digits once more, you get 2. What is The number?

Solve the problem. -A girl asks her father how many ties he has and he answers with a riddle: "Seven-eighths of my ties plus five." How many ties does her father have?

If the hometown baseball team scored 3 runs every inning played, and the visiting team scored 1 run every inning played, what was the final score?

Solve the problem. -If you raise 9 to the 387th power, what is the units digit of the result?

Use problem solving strategies to solve the problem. -There is a number between 2 and 8, such that if you raise any of the remaining numbers to the power of this number, the units digit of the result will always be equal to the base. What is the Number?

Use problem solving strategies to solve the problem. -The number of dogs and chickens on a farm add up to 12. The number of legs between them is 28. How many dogs and how many chickens are on the farm if there are at least twice as many Chickens as dogs?

Use problem solving strategies to solve the problem. -I'm thinking of a number between 4 and 10. If I square my number and find the difference of the digits, I will end up with the cube root of my number. What is my number?

A farmer had a stone weighing 40 pounds that he used to weigh pigs, but the stone broke into 4 pieces. The farmer found to his surprise that with the four pieces, he could weigh any whole Number from 1 to 40. What did each of the 4 pieces weigh?