How many one-digit numbers are there, including zero?
Answer:
19.......... -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Wednesday 29 June 2011
Wednesday 22 June 2011
DAY 334
Amy lives on a street with 12 houses. Every day she gets more letters than are delivered to any other house. If 57 letters are delivered to her street today, what is the smallest number of letters Amy could receive?
Answer:
6 ............. The nearest multiple of 12 below 57 is 48. This means 48/12 = 4 letters per house (including Amy's). This leaves 9 letters. Seven people get one more letter, and Amy gets two more.
DAY 333
You have 100 marbles, 50 white and 50 black, and two bowls. You may divide the marbles in any way between the two bowls, but you must use all 100 of them. You will then be blindfolded, the two bowls will be mixed up, and you will pick one marble from one of the bowls. What is the best way to divide the marbles between the two bowls to give you the best chance of picking
a white one?
Answer:
Put one white marble in one of the bowls and the 99 others in the other bowl. This gives you a 50/50 chance of getting the bowl with the one white marble. If you get the other bowl, you still have a 49/50 chance of picking a white one.
Tuesday 7 June 2011
DAY 332
You have to drive 40 miles round trip. You drove the first half at 15 mph. How fast do you have to drive the second half to average 20 mph?
Answer:
30 mph........ To drive 40 miles at an average speed of 20 mph would take 2 hours:
(D = RT ------ 40 = 20 T). The first 1/2 (20 miles) has taken you 1 hour 20 minutes
(20 = 15 T) ------ T = 1 1/3 hours). So you must drive the second 20 miles in 40 minutes or 2/3 of an hour.
20 = R 2/3
R = 30.
DAY 331
120 people are at a party. 3/5 are women. 2/3 of the 120 are married. How many unmarried women are at the party? How many unmarried men? (Assume married means one man married to one woman.)
Answer:
32 unmarried women and 8 unmarried men........
3/5 of 120 = 72 women
120 - 72 = 48 men
2/3 of 120 = 80 married people
40 married men and 40 married women
72-40 = 32 unmarried women
48-40 = 8 unmarried men
DAY 327
Which clock is better......one that doesn't run at all, or one that loses a minute every day?
Answer:
A broken clock is right twice a day - every twelve hours. A clock that loses one minute a day will will need to make up those twelve hours to be right again. Twelve hours = 720 minutes (12 X 60). At one minute per day, the clock will not show the right time again for 720 days (almost two years). Of course, it's still an individual choice as to which clock is better.
Monday 6 June 2011
DAY 324
Mary is having a birthday party. She bought two dozen paper plates. This will allow each person at the party to have two plates - one for hot dogs and chips, and one for ice cream and cake - and leave 2 extra plates. Besides her brother and sister, how many friends will Mary have at her party?
Answer:
8..........24 plates less 6 for Mary and her brother and sister and the two extras = 16.
DAY 323
A watch gains 5 seconds every 3 minutes. It is set correctly at 7:00 am. That afternoon the watch read 4:15. What was the correct time?
Answer:
4:00............ 7:00 am to 4:15 pm = 9 hours and 15 minutes, or 555 minutes. For every 3 minute and 5 second interval in that time, the time shown on the watch is 5 seconds fast. For example, at correct time 4:03, the watch shows 4:03 and 5 seconds. Five seconds = 1/12 minute.
555 divided by 3 1/12 = 180 intervals
180 X 5 = 900 seconds
900/60 = 15 minutes (fast)
DAY 321
Diophantus' youth lasted 1/6 of his life. He grew a beard after 1/12 more. After 1/7 more of his life, he married. Five years later, he and his wife had a son. The son lived exactly half as long as his father, and Diophantus died 4 years after his son. How old was Diophantus when he died?
Answer:
84........... x/6 + x/12 + x/7 + 5 + x/2 + 4 = x
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