DAY 254
A water lily on a lake doubles in size each day. In 30 days it will cover the entire lake. How much time would it take two such lilies to cover the lake?

Answer:

29 days..............Each lily would cover half the lake on the 29th day.

DAY 253
A father gave his son 10 cents for every math problem he got right, but the son had to pay his Dad 5 cents for each problem he got wrong. At the end of the school year, 120 problems had been done, and neither Dad nor son owed anything to the other. How many problems did the boy solve correctly?

Answer:

40...............Let X = the number of problems solved correctly........ 10 X - 5(120 - X) = 0.

DAY 252
Consider the integers 0 - 99. Which digit is used the least? How often are each of the others used?

Answer:

0 is used only 10 times. Each of the other digits is used 20 times.

DAY 251
Two bicyclists are 36 miles apart and begin riding directly toward each other at a speed of 6 mph. At the same moment, a pigeon starts to fly from one bicycle to the other at 18 mph. How far has the pigeon flown when the two bikes meet?

Answer:

54 miles......The cyclists are approaching each other at a combined speed of 12 miles per hour. It will take them 3 hours to meet.

DAY 250
A snail starts at the bottom of a well 16 feet deep and crawls up 4 feet each day. Each night it slips back 3 feet. How long will it take the snail to reach the top of the well?

Answer:

13 days..............After 12 days it has climbed 12 feet. On the 13th day it climbs 4 feet and reaches the top.

DAY 249
A farmer sold 1/3 of his eggs at one store and 2/3 of the remainder at another. He still had one dozen left. How many eggs did he have to begin with?

Answer:

54 eggs

DAY 248

If I give you 5 marbles, I'll have as many as you. If you give me 5 marbles, I'll have twice as many as you. How many marbles do we each have?

Answer:

I have 35 and you have 25.............If giving you 5 marbles will make us equal, I must have 10 more than you. If X = the number of marbles I have, you have X - 10 marbles. If you give me 5 marbles, I will have 5 more and you will have 5 less: X + 5 = 2(X - 15).

DAY 247

What is the fewest number of eggs that could be in a basket such that if you count them 2 at a time, there is 1 left. If you count them 3 at a time, there are 2 left. And if you count them 4 at a time, there are 3 left?

Answer:

Eleven

DAY 246
An airplane flies 3,000 miles from LA to NY at 600 mph thanks to a strong tailwind from the jet stream. On the return trip the tailwind is now a headwind, and the plane averages only 400 mph for the return trip. What is the average speed of the plane for the entire round-trip flight?

Answer:

480 mph.............Time is distance divided by speed. The flight from LA to NY took 5 hours. The return flight took 7.5 hours. Speed is distance divided by time. The average speed for the round-trip flight is 6,000 miles divided by 12.5 hours.

Day 245
A group of 30 studemts were divided into two groups so that the first group had 8 more than the second group. How many were in each group?

Answer:

11 and 19............X + (X + 8) = 30

DAY 244
If gumdrops come in 5 colors, what is the smallest number of asorted gumdrops a child would have to buy to be sure of getting at least three of the same color?

Answer:

11............6 would assure getting two of the same color. 5 more would assure three of the same color.

DAY 243
How much would it cost to have a log cut into four pieces if each cut cost $5?

Answer:

$15..............To cut a log into four pieces requires only three cuts.

DAY 242

IT'S IN THE BAG

You have a bag of oranges. On Monday you eat 1/3 of them. On Tuesday you eat 1/2 of the remaining oranges. On Wednesday there are 2 oranges left in the bag. How many were in the bag to start?

Answer:

6.............On Tuesday, 2/3 of the oranges remain. So you eat 2/6 of them (1/2 0f 2/3)........or 1/3. 2/3 of the oranges are now gone. Since you have 2 left, 2 must be 1/3 of the original number in the bag. 2 = 1/3X, X =6.

Another solution: If you ate half the remaining oranges on Tuesday leaving 2 oranges on Wednesday, there must have been four oranges left on Tuesday. On Monday, the number of oranges less 1/3 of them should equal 4......X - 1/3X = 4.

DAY 241

3 is to 9 as 4 is to:

A) 10
B) 12
C) 16

Answer:

A, B, and C

3 + 6 = 9...........................4 + 6 = 10
3 X 3 = 9...........................4 X 3 = 12
3 squared = 9...........4 squared = 16

DAY 240
What number must be added to 1/45 to get 2/9?

Answer:

1/5.........2/9 = 10/45. You must add 9/45, which is 1/5.

DAY 239
Solve for x:

1/x + 1/x + 1/x = 1/5

Answer:

x = 15...........1/x + 1/x +1/x = 3/x
3/x = 1/5 solves to x = 15.

DAY 238
Credit: Yvonne Parietti in Parade Magazine--Ask Marilyn--by Marilyn Vos Savant

Sat that a bag contains 100 marbles: 30 red, 30 blue, 30 green, plus a mix of 10 yellow and orange marbles. To be certain that you have 10 marbles of the same color, what is the minimum number you would need to remove (without looking) from the bag?

HINT: Consider the worst case.

Answer:

38...........In the unluckiest case, you would remove (in whatever order) 9 red marbles, 9 blue , 9 green, and all 10 of the yellow and orange marbles. So far, you have removed 37 marbles, but still do not have 10 of the same color. If you remove one more marble, it will be either red, blue, or green---giving you 10 of the same color.