DAY 407

Tom and Tina both have some money (in dollars).  They each want to buy a gift card, but neither of them has enough money. Tina needs $2 more, and Tom needs $24 more. They decide to combine their money and buy one gift card, but they still don't have enough.  How much is the gift card?

Answer:

$25 ....................  If Tina only needs $2 more, and they still don't have enough money after Tom gives her what he has, Tom must only have $1.

DAY 406

Ten students take a test with a maximum score of 100. The average of the ten scores is 92. What is the lowest score a student could have received?

Answer:

20 ................. For the average to be 92, the ten students must have scored a total of 920 points (920/10 = 92). This is 80 points short of the 1,000 possible points.   1000 - 80 = 20.

DAY 405


A thick rope will burn its entire length in one hour when one end is set on fire. How could you use the rope to measure 1/2 hour?

Answer:

Set both ends on fire at the same time. 

DAY 404

What is unusual about the following sequence of numbers?

1, 4, 9, 6, 1, 5, 10, 4, 2

HINT:
It has to do with Roman Numerals.

Answer:

Written in Roman Numerals, these numbers form a palindrome. That is, they read the same in both directions.

I IV IX VI I V X IV II

DAY 403

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 amount of the bet - but keeps Jack's other dollar.

DAY 402

If 3 cats can catch 3 mice in 3 minutes, how long would it take the 3 cats to catch 100 mice?

Answer:

102 minutes ........... If 3 cats can catch 3 mice in 3 minutes, it takes each cat 3 minutes to catch 1 mouse.

1 cat - 1 mouse - 3 minutes

3 cats - 3 mice - 3 minutes

3 cats - 6 mice - 6 minutes

3 cats - 9 mice - 9 minutes

.

.

.

.

3 cats 99 mice - 99 minutes

(Every 3 minutes, one mouse is caught by each cat. In 99 minutes, each cat catches 33 mice ........ 3 x 33 = 99)

To catch the 100th mouse takes another 3 minutes ........ 99 + 3 = 102 minutes

OR

100 mice/3 cats = 33 - the number of mice caught by each cat

( + remainder 1 mouse)

Since it takes 3 minutes for each cat to catch one mouse,

3 x 33 =99 minutes

+ 3 minutes to catch the remaining mouse = 102 minutes

DAY 401

10 ice cream bars and 6 ice cream cones cost $13.00.

6 ice cream bars and 10 ice cream cones cost $11.00.

How much for each ice cream bar and each cone?

Answer:

Ice cream bars cost $1.00, and cones cost $.50 .

16 bars and 16 cones cost $24.00 .

1 bar and 1 cone cost 24/16 = $1.50 .

DAY 400

Three children, Peter, Jane, and Eric share a bag of peanuts. There are 770 peanuts in the bag. For every 4 peanuts Peter took, Jane took 3. For every 6 peanuts Peter took, Eric took 7. How many peanuts did Peter get?

Answer:

264 ........... For every 12 peanuts Peter took, Jane took 9 and Eric took 14. This totals 35 peanuts for each round ... 770/35 = 22 rounds ... 12 x 22 = 264

DAY 399

360 doctors and nurses work in a hospital. If the ratio of doctors to nurses is 7 to 11, how many nurses are there?

Answer:

220 .......... 7 + 11 = 18. 360/18 = 20. There are 20 groups of doctors and nurses. If the ratio is 7 to 11, there are 7 x 20 = 140 doctors, and 11 x 20 = 220 nurses.

DAY 398

A postman delivers one letter on his first day of work, three letters on his second day of work, five letters on the third day, and so on - delivering two letters more each day than he delivered the previous day. How many total letters has he delivered after fifteen days of work?

Answer:

225

DAY ................ NUMBER OF LETTERS DELIVERED

1 .................................................... 1

2 ................................................... 3

3 ................................................... 5

4 ................................................... 7

5 ................................................... 9

6 .................................................. 11

The total number of letters delivered is the square of the number of days worked. For example, after 4 days, he has delivered 1 + 3 + 5 + 7 = 16 letters.

DAY 397

Six trees stand equally spaced along the side of a straight road. The distance from the first tree to the fourth is 60 feet. What is the distance between the first and last trees?

Answer:


100 feet 

DAY 396

Use the number 23 four different times to equal 24.

Answer:

23 x 23 = 529. This means that 529 divided by 23 = 23. To get a quotient of 24, you would have to add 23 to the dividend. 

So 23 x 23 = 529
529 + 23 = 552
552/23 = 24

DAY 395

The same letter goes in all three blanks:

_ is 1,000 times _ _ .

Answer:


m ............ 1 meter (m) = 1,000 millimeters (mm)

DAY 394

At an outdoor party, six places are set at each table. There are six chairs at each table, and all the tables and chairs have four legs each. There are a total of 196 legs. How many people are invited to the party?

Answer:


42 ........... Each table and its six chairs = 28 legs (7 x4) ........... 196/28 = 7 tables ........... 7 x 6 = 42


Another way to solve this would be  196/4 = 49. This means there are a combined total of 49 tables and chairs, but we don't know how many of each. Since there are 6 chairs at each table, guessing and checking gives us 7 x 6 = 42 ......... 42 chairs and 7 tables. 

DAY 393

At a certain high school, there are twice as many girl graduates as boy graduates. If 3/4 of the girl graduates and 5/6 of the boy graduates go on to college, what fraction of the schools graduates does this represent?

Answer:


7/9 ............. Let x = boy graduates and 2x = girl graduates ........... 3x = total number of graduates. 3/4(2x) + 5/6(x) = 7/3(x) = graduates who go on to college .......... 7/3(x)/3x = 7/9

DAY 392

Before you is a bowl filled with $50, $20, $10, and $5 bills. You are blindfolded and told you may pull out the bills one at a time, but you must stop when you have four bills of the same denomination.  What is the most money you could pull out of the bowl before you had to stop?

Answer:


$305 .......... You could pull out three $50's, three $20's, three $10's, three $5's, and another $50. Another way of thinking of it is: $50 + $20 + $10 + $5 = $85 ............... $85 x 3 = $255 ...............  $255 + $50 = $305. 

DAY 391

Which three consecutive, even numbers, when multiplied together, will give the product 8xxxx2 ? The x's represent four digits, though not necessarily the same ones.

Answer:


884,352


Since 90 cubed is 729,000 and the product of the three numbers  is over 800,000,  all three numbers must begin with 9.  Since they are even, the numbers must be either 90, 92, and 94, or 92, 94, and 96, or 94, 96, and 98. The product must end with 2. Looking at the second digits of 90, 92, and 94 - 0 x 2 x 4 = 0 - ending digit 0. Looking at the second digits of 92, 94, and 96 - 2 x 4 x 6 = 48 - ending digit 8. Looking at the second digits in 94, 96, and 98 ------- 4 x 6 x 8 = 192 - ending digit 2, which is what is required.  So 94 x 96 x 98 = 884,352.

DAY 390

The difference between the squares of two consecutive positive whole numbers is 25. What are the numbers?

Answer:

12 and 13 ............ x (squared) - (x-1) squared = 25

DAY 389

Double my number, I'm less than a score,

One half my number is less than four;

Add one to my double when bakers are near,

Still the days of the week are greater, I fear.

Answer:

6

DAY 388

What would be the product of this multiplication problem?

(x - a)(x - b)(x - c)(x - d) ................ (x - z)

HINT:

You don't need to know the numerical value of any of the variables.

Answer:

Zero ......... The 24th term (x -x) would be zero, thus making the product zero.

(Credit: Andrew Robinson)

DAY 387

You have driven the first 10 miles of a 20 mile trip at an average speed of 25 miles per hour. How fast would you have to go in the second half of your trip to average 40 miles per hour over the entire distance?

Answer:

100 miles per hour .......... Using the formula D = RT, it has taken you 24 minutes to drive the first ten miles (10 = 25 T, T = 10/25 or 2/5 hr. = 2/5 x 60 = 24). To average 40 mph over 20 miles would take 30 minutes (20 = 40 T). Therefore you have 6 minutes to drive the remaining 10 miles. 6 minutes is 1/10 of an hour. So 10 = R 1/10, R =100.

DAY 386

When could these equations be true?

6 + 24 =1

5 + 5 = 2
23 + 60 =1
2 + 1 = 1
10 + 4 = 2

Answers:

6 days + 24 hours = 1 week

5 fingers/toes + 5 fingers/toes = 2 hands/feet
23 hours + 60 minutes = 1 day
2 dimes + 1 nickel = 1 quarter
10 o'clock + 4 hours  = 2 o'clock

DAY 385

Tom: Give me four and we'll each have the same.

Jane: Give me four and I'll have twice as many as you.

How many does each have?

Answer:

Tom has 20 and Jane has 28 ............ If gaining four will make Tom and Jane equal, Jane must have 8 more than Tom.

Let x = Tom

Let x + 8 = Jane

2(x-4) = x + 12

2x - 8 = x + 12

x = 20

x + 8 = 28

OR

Let x = Jane

Let x - 8 = Tom

2(x-12) = x + 4

2x - 24 = x + 4

x = 28

x - 8 = 20

DAY 384

When could these equations be true?

1 + 1 = 1

30 + 30 = 1

Answers:

1 foot + 1 foot + 1 foot = 1 yard

30 seconds + 30 seconds = 1 minute

or

30 minutes + 30 minutes = 1 hour

DAY 383

Three men eat three steaks in three days. How many steaks will six men eat in six days?

Answer:

12 ......... If three men can eat three steaks in three days, each man can eat one steak in three days .......... or two steaks in six days. Six men could eat six times that number of steaks in six days, or 12 steaks.

DAY 382

Consider the digits 1 - 9. They can be arranged in 9! ways. If you were to write down all of these possible arrangements on individual cards and then pick one, what is the possibility that the number you picked would be prime?

Answer:

Zero .......... In any nine-digit number using each of the digits once, the sum of the digits would be 45 (1+2+3+4+5+6+7+8+9 = 45). According to the rules of divisibility, any number in which the digits add up to a multiple of 9, is divisible by 9, and therefore not prime. Since 45 is a multiple of 9, the nine-digit number could not be prime.

DAY 381

How can this be true?

1/3 of 12 + 4/5 of 7 = 11

Answer:

It can be true if you use the letter words for the numbers 12 and 7.

twELve (1/3 of the six letters in TWELVE) + sEVEN (4/5 of the five letters in SEVEN) = ELEVEN

DAY 380

If

x/y = 4/7 and z/y = 3/2, what is x/z ?

Answer:

8/21 .......... x/y divided by z/y = x/y X y/z = x/z

.................. 4/7 divided by 3/2 = 4/7 X 2/3 = 8/21