MATHS QUIZ NO. 24 LOGIC

[magpie in the 80's]

1. First of all we have to find my friends Alice and Bill, who live in two different houses on Algebra Avenue. Each of the houses on Algebra Avenue is numbered with a two-digit number from 10 to 99. I can't remember where Alice and Bill live, but I remember that their house numbers are the reverse of each other (in the sense that "21" is the reverse of "12".) I also remember that the sum of their two house numbers is a perfect square. The difference between their two house numbers is also a perfect square. Alice lives in the house with the smaller house number. What is the number of Bill's house?
65

2. Now we have to find my friends Charlie and Debra, who live in two different houses on Algebra Avenue. I can't remember their house numbers either, but I remember that they are the reverse of each other. The sum of their house numbers is a perfect square, and the difference between their house numbers is a perfect cube. Charlie lives in the house with the smaller house number. What is the number of Debra's house?
74

3. Now that we've found everybody, we need to go back to my house to get some money. I keep it in a rectangular box. Unfortunately, I own a lot of rectangular boxes, and I can't remember which one I put my money in. I remember that the three dimensions of the box (height, width, and length) are all whole numbers of inches, that they are all different, and that none of the dimensions is a prime number. I also remember that the volume of the box in cubic inches is the same as the total surface area of all six sides of the box in square inches. What is this volume or surface area?
288

4. Now we've found the right box, but I forgot it has a lock on it. It's one of those locks where you have to punch in a certain number to open it. I can't remember what the number is, but I remember that it's a four-digit number. I also remember that the sum of all four digits is equal to the product of all four digits, and that the four-digit number is evenly divisible by this sum or product. By the way, I also remember that the four-digit number is not "0000". What is it?
4112

5. Now I have my money. I'll let you choose whatever toppings you want on your pizza if you can figure out how much I have. I have a certain number of one-dollar bills (more than zero) and a certain number of ten-dollar bills (more than zero.) The number of one-dollar bills multiplied by the number of ten-dollar bills is equal to the total amount of money I have in dollars. The number of ten-dollar bills is not a prime. How much money do I have?
72

6. During the lunch hour at school, a group of five boys from Miss Jones home room visited a nearby lunch wagon. one of the five boys took a candy bar without paying for it. When the boys were questioned by the school principal, they made the following statements in respective order:
1. Rex: "Neither Earl nor I did it."

2. Jack: "It was Rex or Abe."

3. Abe: "Both Rex and Jack are lying."

4. Dan: "Abe's statement is not true; one of them is lying and the other is speaking the truth."

5. Earl: "What Dan said is wrong."

When Miss Jones was consulted, she said, "Three of these boys are always truthful, but everything that two of them say will be a lie."Assuming that Miss Jones is correct, can you determine who took the candy bar?
ABE

7. A mother is four times as old as her daughter. In 20 years she will be twice as old as her daughter.
How old are mother and daughter now?
40 and 10

8. A butcher goes to the market with $100 cash. He has to buy exactly 100 animals. There are cows, geese and chicken for sale. A cow costs $15, a goose is $1 and a chicken costs $0.25. He has to buy at least one of each animal and has to spend all his money.

What does the butcher buy?
3 COWS, 41 GEESE AND 56 CHICKENS

9. 4. Four people combined have $1,000. If the only person lying is the only person with no money, then what is Andrew's money plus Kris's money?

Kris: I have twice as much as Trony
Ethan: I have $100 more than Andrew
Trony: I have $200 more than Ethan
Andrew: My dollar amount is a square number
$800

10. A clock strikes '6' in 5 seconds.
How long does it take to strike '12'?
11 SECONDS

[Q.]

A few tough ones in here M80, I won't guess this time, might take me a few lunch breaks to nut 'em out though...

(1) 65

(2) 74

[Dissident]

7. mother is 40 and the daughter is 10

[magpie in the 80's]

A few tough ones in here M80, I won't guess this time, might take me a few lunch breaks to nut 'em out though...

(1) 65

(2) 74

BOTH CORRECT Q

and here i thought your lunch hour was to do work and the work hours for quiz and metro postings

[magpie in the 80's]

7. mother is 40 and the daughter is 10

correct D

[Q.]

You'de be about right there M80

(3) 288

(4) 4112

[magpie in the 80's]

You'de be about right there M80

(3) 288

(4) 4112

both correct Q now go and have lunch

[Q.]

(5) 72

(6) Abe

(8) 3 cows, 41 goose, 56 chicken

[magpie in the 80's]

(5) 72

(6) Abe

(8) 3 cows, 41 goose, 56 chicken

all correct Q how's lunch going

[Q.]

Got a bit of lunch done this morning, decided to have some work with a cuppa just now

(9) $600

(10) 10 seconds

[magpie in the 80's]

Got a bit of lunch done this morning, decided to have some work with a cuppa just now

(9) $600

(10) 10 seconds

both close but incorrect Q

[magpie in the 80's]

1. First of all we have to find my friends Alice and Bill, who live in two different houses on Algebra Avenue. Each of the houses on Algebra Avenue is numbered with a two-digit number from 10 to 99. I can't remember where Alice and Bill live, but I remember that their house numbers are the reverse of each other (in the sense that "21" is the reverse of "12".) I also remember that the sum of their two house numbers is a perfect square. The difference between their two house numbers is also a perfect square. Alice lives in the house with the smaller house number. What is the number of Bill's house?
65

2. Now we have to find my friends Charlie and Debra, who live in two different houses on Algebra Avenue. I can't remember their house numbers either, but I remember that they are the reverse of each other. The sum of their house numbers is a perfect square, and the difference between their house numbers is a perfect cube. Charlie lives in the house with the smaller house number. What is the number of Debra's house?
74

3. Now that we've found everybody, we need to go back to my house to get some money. I keep it in a rectangular box. Unfortunately, I own a lot of rectangular boxes, and I can't remember which one I put my money in. I remember that the three dimensions of the box (height, width, and length) are all whole numbers of inches, that they are all different, and that none of the dimensions is a prime number. I also remember that the volume of the box in cubic inches is the same as the total surface area of all six sides of the box in square inches. What is this volume or surface area?
288

4. Now we've found the right box, but I forgot it has a lock on it. It's one of those locks where you have to punch in a certain number to open it. I can't remember what the number is, but I remember that it's a four-digit number. I also remember that the sum of all four digits is equal to the product of all four digits, and that the four-digit number is evenly divisible by this sum or product. By the way, I also remember that the four-digit number is not "0000". What is it?
4112

5. Now I have my money. I'll let you choose whatever toppings you want on your pizza if you can figure out how much I have. I have a certain number of one-dollar bills (more than zero) and a certain number of ten-dollar bills (more than zero.) The number of one-dollar bills multiplied by the number of ten-dollar bills is equal to the total amount of money I have in dollars. The number of ten-dollar bills is not a prime. How much money do I have?
72

6. During the lunch hour at school, a group of five boys from Miss Jones home room visited a nearby lunch wagon. one of the five boys took a candy bar without paying for it. When the boys were questioned by the school principal, they made the following statements in respective order:
1. Rex: "Neither Earl nor I did it."

2. Jack: "It was Rex or Abe."

3. Abe: "Both Rex and Jack are lying."

4. Dan: "Abe's statement is not true; one of them is lying and the other is speaking the truth."

5. Earl: "What Dan said is wrong."

When Miss Jones was consulted, she said, "Three of these boys are always truthful, but everything that two of them say will be a lie."Assuming that Miss Jones is correct, can you determine who took the candy bar?
ABE

7. A mother is four times as old as her daughter. In 20 years she will be twice as old as her daughter.
How old are mother and daughter now?
40 and 10

8. A butcher goes to the market with $100 cash. He has to buy exactly 100 animals. There are cows, geese and chicken for sale. A cow costs $15, a goose is $1 and a chicken costs $0.25. He has to buy at least one of each animal and has to spend all his money.

What does the butcher buy?
3 COWS, 41 GEESE AND 56 CHICKENS

9. 4. Four people combined have $1,000. If the only person lying is the only person with no money, then what is Andrew's money plus Kris's money?

Kris: I have twice as much as Trony
Ethan: I have $100 more than Andrew
Trony: I have $200 more than Ethan
Andrew: My dollar amount is a square number
$800

10. A clock strikes '6' in 5 seconds.
How long does it take to strike '12'?
11 SECONDS

QUESTIONS ANSWERED ARE IN RED.
QUESTIONS UNANSWERED ARE IN BLUE.

END OF QUIZ