Bonus Puzzle #23?

Question

1) What is 25% of 50% of 100.

2) what percent of 4 hours is 8 seconds?

3) Each of a certain type of tire on a 4 wheel car last exactly 10,000 miles. How many spare tires of this same variety must be carried so that a trip of 15000 miles can just be completed(assuming no tires are defective)?

4) The sum of the first 100 positive whole number is 5050. What is the sum of the first 100 positive odd whole numbers?


Show work pleasee

Answer 1

1. 50% of 100 is 50
25% of 50 is 12.5

2. This one is 8/14,400 which you will have to figure out on your own......

60 minutes in an hour, 60 seconds in a minute = 3,600 seconds per hour. Times this by 4 hours and you will get 14,400 seconds.

3. 3 tires must be carried. This will work if you rotate the tires every 5,000 miles.

Ex: Tire A, B, C, D (and spare is E F G)
first 5,000 you use tire A B C D
second you use tire B C D E
third five thousand you use A E F G

Each tires is used no more than twice (10,000 miles).

4. The easiest way to do this is as follows:
100 times 49

This works because if 1+99=100
3+97=100
and so forth, you only need to add 100 as many times as there are odd numbers before 50. In this case, there are 49

SO 49 times 100=4900

The reason you have 5050 with the positive numbers is because 50 cannot add to another number (46+54, 48+52, 50+nothing).

Hopes this helps a bit!

Answer 2

1) 12.5
Just multiply .25 x .5 x 100

2) 1 / 1800 or .055%
8 / (4 x 60 x 60)

3) 2
4 x (15,000/10,000)
This is a bit of a trick question. At first you may think 8 because you can't drive on only 2 tires. However, if you change your tires after 5,000 miles, putting on two of your new ones, and change them again after 10,000 miles when the 2 original tires fail, you will be able make it there.
Edit: Sorry, the question was how many _spare_ tires, so you only have 2 spares. My original answer said 6, because you need a total of 6 tires.

4) 2500
The easy way to get 5050 is to take 0 + 100, 1+99, 2+98, etc. until you reach 49+51. Then you add +50 to (50)(100) = 5050. Taking out the even numbers will give you exactly half of 5000, so 2500. We don't take half of 5050 because 50 is an even number, and is thrown out.

Answer 3

Previous couple are right on the first 3, but not on the 4th.

The first 100 odd whole numbers are 1..199, so you need to find the sum 1 + 3 + ... + 199

Notice
1*2 - 1 = 1
2*2 - 1 = 3
3*2 - 1 = 5
...
100*2 - 1 = 199

So you want to sum these up. This gives you 2*(sum of numbers from 1 to 100) - 100. The sum is 5050, we are given, so 2*5050 - 100 = 10000.

*edit*: You can use the formula that this is n^2 if you know it, but I restricted myself to information given in the statement of the problem.

Answer 4

1) 1/2 of 100 is 50.
50 divided by 4... 0.125
12.5

2) 4 x 60 = 240
240 x 60 = 14400
8/14400 is 0.05555555555%

3) 4 tires, not counting the ones on the car

4) 1 + 3 = 4 + 5 = 9 + 7 = 16 + 9 = 25 + 11 = 36 + 13 = 49 + 15 = 64 + 17 = 81 + 19 = 100 + 21 = 121 + 23 = 144.... Notice the pattern!
1st 2 odd numbers added becomes 2^2....
3 odd numbers = 3^2
N odd numbers = N squared
10,000

Answer 5

1) 50% of 100 = 50, 25% = 25

2) 4 hr = 240 min = 4000 secs, 8/4000 = 1/500

3) 15,000 / 10 = 1,500 tires

4) 25 = halfway, 101 = halfway, answer 202