DAY 357

On a 99 year lease, 2/3 of the time past equals 4/5 of the time remaining. How much time is left on the lease?

Answer:

45 years ......... Let x = time left - (99-x) = time past

2/3 (99-x) = 4/5 x

DAY 356

How many 5th Sundays are there in a year? (Ignore the possibility of 53 Sundays.)

Answer:

4 ......... There are 52 Sundays in a year. Each month has at least four, which is 48. The remaining 4 are fifth Sundays.

NOTE from JA: 
September 3, 2016 

I have been thinking about this problem for some time. The above statement about 48 Sundays is also true of every other day of the week. So 48 x 7 = 336. This leaves 29 more days (365-336). 29 divided by 7 = 4 remainder 1. This means there are 4 fifth Mondays, Tuesdays, Wednesdays, Thursdays, Fridays, and Saturdays - as well as 4 fifth Sundays. What about the extra day? It must mean that every year has one day that occurs 53 times - cycling through the week every seven years.

DAY 355

What do these rebus puzzles mean?

1. DECIMAL.

2. DECIMAL DECIMAL DEIMAL DECIMAL DECIMAL

Answers:

1. Terminating decimal (1/4 = .25)

2. Repeating decimal (1/3 = .33333.......)

DAY 354

Ten students took a test with a maximum score of 100 points. The average of the ten scores was 92. What is the lowest score a student could have earned?

Answer:

20 ........ (9 x 100) + 20 = 920 ....... 920/10 = 92

DAY 353

A woman has 3 children, and the product of their ages is 17. Their ages are in whole numbers (no fractions or decimals). How old are the children?

Answer:

The oldest is seventeen and the twins are 1.

DAY 352

What a pair we are,

Our sum is 100;

Our product tells you more,

For it is our sum times 24.

Who are we?

Answer:

40 and 6o .......... X(100 - X) = 2400

DAY 351

When could this equation be true?

1 + 1 + 1 = 1

Answer:

1 foot + 1 foot + 1 foot = 1 yard

DAY 350

When could this equation be true?

30 + 30 = 1

Answer:

It could be true if you are adding seconds to get 1 minute, or minutes to get 1 hour.

DAY 349

The area of a square is (x + y) squared. What is the perimeter of the square?

Answer:

4(x + y) .......... The area of a square is the side squared. So the side must be (x + y).

DAY 348

A horse walks a certain distance each day. On one day the horse's inside legs walked 30 miles, but its outside legs walked nearly 31 miles. How is this possible?

Answer:

The horse walks in a circle. The diameter of the circle is greater for the outside legs than for the inside ones. Therefore the circumference of the outside circle is greater.

DAY 347

If you could count to 200 in 1 minute, and got 1 day off every 4 years (to account for leap years),

how long would it take you to count to 1 billion?

Answer:

9 years, 187 days, 5 hours, 20 minutes

DAY 346

1. What number is equal to 9 times the sum of its digits?

2. Write 8 using three nines.

3. Write 12 using six ones.

Answer:

1. 81

2. 9 - 9/9

3. 11 11/11