1. multiplying any two numbers together that both have 1 in the "ones" position will always have a 1 in the "ones" position of the result. Therefore when dividing by 10, the remainder will always be 1. If you start simple and do 631^2, 631^3 and so on
you'll see the pattern form.
2. Let's make the problem a bit more simple. adding 7 days to the 24th makes it sunday again. Therefore if the number of days between july 24th and sept 24th is evenly divisible by 7 (0 remainder), then the day of the week is Sunday. To calculate the number
of days between july 24th and sept 24th take the remaining days in july (7) plus 31 days in august plus 24 days in september. That equals 62. Unfortunately, 62 is not evenly divisible by 7, so it's not sunday. Let's go back to an easy example. Let's add 8
days to july 24th. If we divide 8 by 7, we get 1 remainder of 1. Remainder of 1 makes it monday. Let's add 9 days. If we divide 9 by 7 we get 1 remainder of 2. Remainder 2 makes it tuesday. The pattern we have thus far is remainder 0 = sunday, remainder 1
= monday, remainder 2 = tuesday. When dividing 62 by 7 you get 8 remainder 6 (62 modulus 7 equals 6). Using the pattern you should be able to take it from here.
3. You cannot compare apples to oranges. The rate of operation for the printing machine is stated per minute. The rate of operation for the folding machine is stated per second. The first step is to make the units of measure match. You need to get both rates
of operation in either minutes or seconds, it doesn't matter which you pick so long as they are consistent (that being said it is easier to deal in whole numbers rather than fractions). The folding machine folds at a rate of 5 per second. Since there are 60
seconds in a minute, we multiply 5 by 60 to get the rate in minutes. Now we know the folding machine folds 300 per minute. If one printing machine prints 250 per minute that means 6 printing machines will print 6 * 250 = 1500 sheets per minute. The question
asks how many folding machine we'll need to keep up, that means we need to fold the same number of sheets per minute as 6 printing machines will print. Therefore:
total sheets printed per minute = total sheets folded per minute
total sheets folded per minute = number of folding machines * number of sheets 1 machine folds per minute
now let's substitute what we know.
1500 = number of folding machines * 300
4. Let's start with what we know. All the golf balls cost the same. The total number of balls bought was 300. Everyone is going to pay the same amount, thus the same number of gold balls. To calculate each person's share we divide the total number of golf balls(300)
by the total number of people(3).
300 / 3 = 100.
Charlie's share of the cost is $250 on 100 golf balls Therefore to calculate the cost of each ball is
x = $250/100
x = $2.50
To calculate how much charlie needs to give ben (b) we need to multiply the number of extra balls ben bought (180 minus 100) times the cost per ball ($2.5).
(180 - 100) * $2.5 = b
$200 = b
To calculate how much charlie needs to give al (a) you do the same, just substituting the number of balls al bought.
(120-100) * $2.5 = a
$50 = a
5. This problem is much easier if you draw a line on a piece of paper and plot the points as you go along. Since the towns form a straight line, the easiest thing to do is find the two towns that are furthest from each other. If you look at the chart, that's
towns b and c at 10 miles. Draw a line that places them at the end points and make 10 hash marks on the line between the two towns. Then, looking at row B, just plot the points on the line for the remaining towns. Count 5 hash marks from B for town A. Count
4 hash marks from B for town D. If you look at your line you should see:
B - D - A - C
C - A - D - B
(depending on how you ordered your end points).