DAY 379

The sun is 93,000,000 miles from earth. Light travels at a speed of 186,000 miles per second. How long does it take light from the sun to reach the earth?

Answer:

8 minutes 20 seconds ........ 93,000,000 divided by 186,000 is (exactly) 500. 500 seconds divided by 60 = 8.33333333 or 8 1/3 minutes.

DAY 378

Think of a proper fraction in which both the numerator and denominator are prime numbers. If you subtract 19 from the product of the numerator and denominator, the answer is 16. What is the fraction?

Answer:

5/7 ........... Let a/b represent the fraction. (a X b) - 19 = 16. a X b = 35.

DAY 377

Fred says to Jack: "I'll bet you $1 that if you give me $2, I'll give you back $3. Should Jack take the bet?

Answer:

No........... If Jack takes the bet, he gives Fred $2. Fred can then say, "You win. I lose the bet." He then gives Jack $1 - the mount of the bet - but keeps Jack's other dollar.

DAY 376

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 circle is greater.

DAY 375

A horse weighs 600 pounds plus 1/3 of its own weight. How much does the horse weigh?

Answer:

900 pounds .......... 600 pounds = 2/3 of its weight.

DAY 374

A storage bin is 1/3 full of grain. After 100 kg of grain are added, the bin is 1/2 full. How much can the bin hold?

Answer:

600 kg .......... 1/2 - 1/3 = 100 ......... or 3/6 - 2/6 = 100 ........... so 1/6 = 100 kg.

DAY 373

There are 10 types of people in the world: Those who understand binary and those who don't.

DAY 372

THE CAR WASH

Three cars go into a car wash. For each car to complete the cycle, it must go through all three of the following steps, in the right order. Each stage takes one minute to complete.

Step 1: Rinse

Step 2: Wash

Step 3: Dry

How long does it take for all three cars to complete the cycle?

Answer:

5 minutes ........... It is not necessary for the second car to wait until the first car has completed the cycle. The third car enters the Rinse step at the beginning of minute three.

DAY 371

If you count 20 houses on your right as you walk to school, and 20 houses on you left as you walk home (following the same route), how many houses have you counted?

Answer:

20 (The houses on your right on the way to school are the same houses on your left as you walk home.)

DAY 370

In a normal square room, there are 2 cats in each corner. Opposite each cat are 2 cats, and next to each cat is 1 cat. How many cats are in the room?

Answer:

There are 8 cats in the room.

DAY 369

Every resident of Sponge City owns one, and only one, car. Every license plate is different and consists of one letter (A - Z) and one single-digit number (0 - 9). Either the letter or the number can come first. If every possible combination is used, how many people live in Sponge City?

Answer:

520 ........... 26 X 10 = 260 / 260 X 2 = 520 (since the letter and number can come in either order)

DAY 368

John and Mary each have a number of widgets. Mary said to John, "If you give me one widget, I'll have twice as many as you, but if I give you one widget, we'll each have the same number." How many widgets did each one have?

Answer:

Mary had 7 and John had 5 ....... If giving one widget to John will make their numbers equal, Mary must have two more widgets than John. If x = the number of John's widgets, then x + 2 = the number of Mary's widgets ........... (x + 2) + 1 = 2(x - 1)

DAY 367

Bill filled the tank of his car with 12 gallons of gas. The tank immediately sprang a leak. Bill drove at 50 miles per hour and ran out of gas 4 hours later. His car gets 25 miles per gallon.

How much gas did Bill lose?

Answer:

4 gallons ....... 50 mph for 4 hours = 200 miles.

At 25m/gal. = 8 gallons. 12 - 8 = 4

DAY 366

Two in a whole and four in a pair,

And six in a trio you see;

And eight's a quartet,

But what you must guess

Is the name that fits just one of me.

Answer:

one-half

DAY 365

There are 6 players on a coed volleyball team. After a game, each girl drank 5 cups of water, and each boy drank 7 cups. The coach drank 9 cups, and 43 cups were consumed in all. How many girls and how many boys are on the team.

Answer:

2 boys, 4 girls ....... Let x = the number of boys and (6 - x) = the number of girls. The boys and girls drank 34 cups together (43 - 9) ........ 7x + 5(6 - x) = 34

DAY 364

Glenn and Steve took turns driving on a trip to Boston. Glenn drove the first 40 miles, and Steve drove the rest of the way to Boston. On the way back, Glenn started to drive, and then Steve drove the last 50 miles. Who drove more, and how much more?

Answer:

Steve drove 20 miles more than Glenn ........ It does not matter how far the trip is to Boston. Assume the distance is 60 miles each way. Glenn drives 40 miles on the way there and 10 miles on the way back for a total of 50 miles. Steve drives 20 miles on the way there and 50 miles on the way back for a total of 70 miles. The 20 mile difference does not change no matter how long the distance.

DAY 363

Two typists type two pages in two minutes. How many typists would it take to type 18 pages in 6 minutes.

Answer:

6 typists ......... One typist types one page in two minutes. One typist types 3 pages in 6 minutes. 6 typists type 18 pages in 6 minutes.

DAY 362

Your favorite candy bar maker is having a special - ten candy bar wrappers gets you a free candy bar. What fraction of a bar is each wrapper worth?

Answer: The intuitive answer of 1/10 is not correct. This is because the free candy bar also has a wrapper. So you are getting the free bar for only nine wrappers. Each wrapper is worth 1/9 of a bar.

Algebra:

Let w = wrapper

Let b = bar

10w = b +w

9w = b

w = b/9

DAY 361

This expression uses the digits 1 -9, once each:

58 x 3 = 174 = 29 x 6

DAY 360

120 people are at a party. 2/3 of them are married. 3/5 of them are women. How many single women are at the party? How many single men? (Married means one man married to one woman.)

Answer:

32 single women .......... 2/3 x 120 = 80 people are married. 40 men and 40 women

...................................... 3/5 x 120 = 72 women at the party .................... 72 - 40 = 32

8 single men................. 120 - 72 = 48 men at the party ............... 48 -40 = 8

DAY 359

What is the only two-digit number that is both a perfect square and a perfect cube?

Answer:

64 (8 squared and 4 cubed)

DAY 358

I am a two-digit number. The sum of my digits is 11, and I am evenly divisible by both 4 and 7. Who am I?

Answer:

56

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

DAY 345

Haretown and Tortoiseville are 27 miles apart. The hare can run 7 mph and the tortoise can walk 2 mph. If they both start out together from their respective homes and run/walk toward each other, how many miles will the hare have traveled when they meet?

Answer:

21 miles ............ The hare and the tortoise are moving toward each other at a combined speed of 9 mph (7+2). It will take 3 hours for both of them to cover the 27 miles (27/9 = 3). In 3 hours the hare will have run 21 miles, and the tortoise will have walked 6 miles.

DAY 344

Jones is 28 years older than his son. In 11 years, he will be 3 times as old as his son. How old are Jones and his son today?

Answer:

Jones is 31 and his son is 3.

Let x = the son's age and (x+28) = Jones' age

3(x+11) = (x+28)+11

DAY 343

Joe King divided up his coin collection as follows:

1/2 to Hal Apenyo

1/4 to Ann Arky

1/5 to Ray Beeze

49 coins to Zoe Zumi

How many coins were in Joe's collection?

Answer:

980

DAY 342

Without using 8, write an equation using the same digit three times to equal 24.

Answer:

22 + 2 = 24

DAY 341

This problem can be solved with a simple mental calculation:

If it takes you 2 minutes 13 seconds to run one lap around a track, how long will it take you to run 60 laps (assuming you maintain the same speed)?

Answer:

2 hours 13 minutes

Any number of minutes X 60 will be that many hours.
Any number of seconds  X 60 will be that many minutes.

DAY 340

Bob can wash a car in 8 minutes. Joe can wash the same car in 12 minutes. How long will it take to wash the car if Bob and Joe work together?

Answer:

4 minutes 48 seconds .......... In one minute, Bob can wash 1/8 of the car and Joe can wash 1/12 of it. Together, they can wash 5/24 of the car in one minute. This means they can wash the whole car in 24/5 minutes or 4.8 minutes.

DAY 339

Six times my age six years from now plus seven times my age seven years from now will equal fourteen times my current age. How old am I?

Answer:

85 .......... 6(x + 6) + 7(x + 7) = 14x

DAY 338

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

DAY 337

A pole is embedded in a lake bed. 1/2 the pole is in the ground, 1/3 is covered by water, and 9 feet of the pole rises above the water. How long is the pole?

Answer:

54 feet........... 1/2 + 1/3 = 5/6. 1/6 = 9 feet. 6/6 = 54 feet

DAY 336

It costs $5 to get a log cut into 2 pieces. How much will it cost to get the log cut into 4 pieces?

Answer:

$15..........$5 per cut. (It only takes one cut to make two pieces.)

DAY 335

True or False? The digits 1 -9 are randomly arranged into a nine-digit number. That number will always be divisible by nine.

Answer: True ........ Any number whose digits add up to a sum that is a multiple of nine, is divisible by nine. The digits 1 - 9 add up to 45.

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.

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 330

What does this mean?

RO

OT

Answer:

Square root

DAY 329

A fan turns 60 right angles in 10 seconds. How many full circles will the fan turn in one minute?

 

Answer:

 

90.......... It takes 4 right angles to make a circle.

60/4 = 15 circles in 10 seconds

6 X 15 = 90 circles in 1 minute

DAY 328

Find a number whose double exceeds its half by exactly 99.

Answer:

66.......... 2x - 99 = 1/2 x

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.

DAY 326

How many animals do I have?

All but 2 are horses.

All but 2 are pigs.

All but 2 are cows.

Answer:

3 - one of each

DAY 325

186 X 39 = 7254

58 X 3 = 174 = 29 X 6

These equations use all the digits 1 - 9 once each.

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 322

How many months each year will have a 5th Sunday?

Answer:

4........ There are 52 Sundays in a year. Every month has at least 4, which accounts for 48 and leaves 4.

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

DAY 320

Add nine 8's to get 9,000.

Answer:

8888 + 88 + 8 + 8 + 8 = 9000

DAY 319

What is the 1,000th prime number?

Answer:

7, 919

DAY 318

A 20-question test had a possible score of 200 points. 10 points were given for each correct answer and 5 points were deducted for every wrong answer. Your score was 140. How many questions did you get wrong?

Answer:

4..........A score of 140 means you lost 60 points. For every wrong answer, you lose 10 points plus the 5-point penalty, or 15 points. 60/15 = 4

DAY 317

You have two magic pills. One increases your life span by 10% and the other decreases it by 10%. You don't know which pill is which. You take one of the pills. But then you start to worry, so you take the other one to counteract it. Will you now have a normal life span?

Answer:

No......... 1.1 X 0.9 = 0.99

You've lost 1%.

DAY 316

Jim worked overtime and earned an extra $700. This tripled his normal pay. What was his normal pay?

Answer:

$350

Let x = normal pay

x + 700 = 3x

DAY 315

Friends A, B, and C have 100 baseball cards between them. A has twice as many as B, and 10 more than C. How many cards does each person have?

A = 44

B = 22

C = 34

A = A

B = A/2

C = A -10

A + B + C = 100

A + A/2 + (A-10) = 100

2A + A + 2A - 20 = 200

5A = 220

A = 44

B = 22

C = 34

DAY 314

Why do so many alarm clocks have a 9-minute "snooze" interval?

Answer:

After nine minutes, the last digit of the time will be one less that it was nine minutes before (6:15 + 9 minutes = 6:24). Having to monitor only one digit must somehow simplify the electronics of the clock.

DAY 313

A pet store owner sells canaries and cages. If he puts one canary per cage, he has an extra canary. If he puts two canaries in each cage, he has an extra cage. How many canaries and how many cages does he have?

Answer:

4 canaries and 3 cages

x = canaries

y = cages

x = y +1 (one canary per cage)

x = 2y -2 (two canaries per cage)

y + 1 = 2y -2

y = 3

x = 4

DAY 312

In a contest to guess how many gumballs are in a jar, the guesses are 45, 41, 55, 50, and 43. All these guesses are wrong. They are off by 3, 7, 5, 7, and 2 (but not in that order). How many gumballs are in the jar?

Answer:

48.........Since two guesses were off by 7, and no other guesses were repeated, these values must refer to numbers at the opposite sides of the spread. The two extreme are 41 and 55.

41 + 7 = 48

55 - 7 = 48

DAY 311

Add six ones to get 24.

Answer:

11 + 11 + 1 + 1 = 24

DAY 310

Use eleven 8's to make 10,000, using any math operations you want.

Answer:

88888/8 - 8888/8 =

11111 - 1111 =

10,000

DAY 309

How can you change ELUSIVE to EXCLUSIVE using math?

Answer:

Add 90 (XC in Roman numerals)

DAY 308

What are the two non-zero factors of 1,ooo,ooo,ooo?

Answer:

1,000,000,000 = 10 to the ninth power = (2 X 5) to the ninth =

2 to the ninth X 5 to the ninth =

512 X 1, 953,125

(This could also be solved using prime factorization.)

DAY 307

The same letter can go in all three blanks to make this statement true. What's the letter?

1 _ = 1000 _ _

Answer:

M..... 1 Meter = 1000 Millimeters

DAY 306

What digit is in the ones' place in the product of the first 1000 prime numbers?

Answer:

Zero..............This colossal number would have to end in zero because 2 and 5 are prime numbers, and any number multiplied by 10 will have a zero in the ones' place.

DAY 305

The same three digits, when added together, equal 12.

There are two solutions.

One is: 4 + 4 + 4 = 12.

Can you determine the other?

Answer:

1 + 11 = 12

DAY 304

If a clock strikes the number of the hour in the usual way (i.e. nine strikes for nine o'clock), and just once on the half-hour, what time is it if the clock has struck three single times?

Answer:

1:30...........The clock struck once at 12:30, once at 1:00, and once at 1:30

DAY 303

A farmer grew a delicious apple which he wanted to take to the king. The castle was surrounded by seven gated walls, with a guard at each gate. At the first gate, the farmer asked if he could go through to see the king.

GUARD: You may go through if you give me 1/2 of you apples.

FARMER: I will, but you must give back one.

GUARD: Agreed

This was repeated with each of the seven guards. When the farmer got to the king, he had the same number of apples he started with. How many?

Answer:

Two

DAY 302

What is unusual about the following subtraction problem?

954 -459 = 495

Answer:

The minuend, subtrahend, and difference are all made up of the same digits, but in a different order. In each, two of those digits (4 and 5) add up to the third digit (9).

DAY 301

Two men starting at the same point walk in opposite directions for 4 feet. Each turns left and walks another three feet. What is the distance between them?

Answer:

10 feet

When the men turn left, one is walking "up" and one is walking "down" ------------- creating two right triangles with legs of 3 and 4 feet. This is a Pythagorean triple, so the hypotenuse of each triangle is 5 feet. The men are separated by the distance of two 5-foot hypotenuses.

DAY 300

Split 34 into two parts such that 4/7 of one part equals 2/5 of the other.

Answer:

14 and 20.........Let x and y be the two parts:

x + y = 34

4/7 x = 2/5 y

x = 14/20 y

14/20 y + y = 34

14 y + 20 y = 680

34 y = 680

y = 20

It follows that x= 14

Check:

4/7 of 14 = 8

2/5 of 20 = 8

DAY 299

Add two lines to make this equation valid:

25 = 410

Answer:

2/5 = 4/10

DAY 298

In a certain three-digit number, the digits add to 18. If you add 10 to the number, the sum of the digits is 1. What is the number?

Answer:

990

DAY 297

1/3 of the candles on your birthday cake are white, 1/6 are black, and 24 are yellow. How old are you?

Answer:

You're 48. (Half the candles are black and white.)

DAY 296

1/2 + 1/4 + 1/8 + 1/16 of a number = 480. What is the number?

Answer:

512

DAY 295

Using only 4's, can you add to 10,000?

Answer:

4,444 + 4,444 + 444 + 444 + 44 + 44 + 44 + 44 + 44 + 4 = 10,000

DAY 294

In a tug-of-war, 1 Boy = 1 Girl + 1 Dog. If it's 3 Boys against 2 Girls and 3 Dogs, who would win?

Answer:

The 3 Boys would win.

3B vs 2G + 3D

Since 1B = 1G + 1D

3G + 3D vs 2G + 3D

DAY 293

111,111,111 X 111,111,111 = 12,345,678,987,654,321

11 X 1.1 = 11 + 1.1

DAY 292

An electrician charges a basic fee plus an hourly rate. For 2 hours of work, he charged $74. For 4 hours of work, he charged $118. What is his basic fee and what is his hourly rate? This problem can be solved without algebra.

Answer:

His hourly rate is $22/hour and his basic fee is $30.

4 hours + fee - 2 hours + fee = 2 hours

$118 - $74 = $44 (2 hours of work without the fee)

$22 = hourly rate

$74 --- $44 = $30 (basic fee)

Using algebra:

Let x = fee

(74 - x) = 2 hours of work without fee

x + 2(74 - x) = $118

DAY 291

A $1 coin costs $.08 to make and will last 30 years. A $1 bill costs $.04 to make and will last 20 months. Over a 30-year period, how much more will it cost to replace the $1 bill than to produce the coin?

Answer:

$2.44

DAY 290

20 vehicles---cars and motorcycles---56 wheels. How many cars, how many motorcycles?

Answer:

8 cars and 12 motorcycles

Let n = cars ............ 4n + 2(20 - n) = 56

DAY 289

PIZZA PARTY

Fred's survey of 72 students found that 3 out of 8 preferred pepperoni pizza and 1 out of 8 preferred mushroom pizza. How many more students preferred pepperoni to mushroom?

Answer:

18 ........ 1/8 = 9/72 ......... 3/8 = 27/72 ........ 27 - 9 = 18