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Jan 12, 2014
 #4
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Melody:

WoW Zamarroncis
What a great comprehensive answer!
I actually didn't understand all of what you were trying to tell me but you sound like a budding mathematician!!

It wasn't intended to be a trick question.
I wanted to know which numbers could be divided by 10 leaving no remainder.
and, you did point out that if a number has a Zero on the end then it is exactly divisable by 10.
That's the answer I was after!
Now,
Even numbers are 0,2,4,6 and 8
you also pointed out that if a number ends in an even digit then it is divisable by 2.
great now we have 2 easy ones
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What about 5, how do we tell if a big number is exactly divisable by 5? (We don't want to do the actually division)


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A number is divisible by 5 if it ends in 5 or 0.

*Note: 10/10=1 means dividing a number by 10 in base 10 requires the number to be multiplied by 1 before dividing by 10 and moving the last digit over one decimal place to the right of the decimal point. 10/5=2 means dividing a number by 5 in base ten requires the number to be multiplied by 2 before dividing by 10 and moving the last digit over to the right of the decimal point. 10/3=3+1/3 means dividing a number by 3 in base 10 requires the number to be multiplied by 3 then have 1/3 of the original value added to the multiplication before dividing by 10, shifting the decimal point one place to the left, which is the same as sending the last digit to the right of the decimal point. 10/4=5/2=2+1/2 means the same thing as above in base ten. This pattern is what makes all numbers divisible by ten in base ten. e.g. 10/7=1+3/7=7/7+3/7, 10/2=5, 10/6=5/3=1+2/3. web2.0calc is so handy...
Jan 12, 2014
 #1
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jar:

A merchant bought some goods and set the selling price higher than the cost by 60%.
He sold 70% of them in the first month and the rest at a discount of x% in the second month.It is given that the overall profit was 37.5%.
(a)Find the value of x.
(b)Find the overall profit percentage if the rest of the goods are sold at a discount of 10%.


Hi jar,
WOW! That is one difficult question.
I'll talk you through part a and you can do part b by yourself.

To get my head around it I initially put some made up numbers in.
I said that 100 units were bought for $1 each. Making a total cost of $100
It doesn't matter what numbers you choose because the whole question is based on percentages.
anyway I solved it that way first, which is probably what you should do.
That answer will be correct and I also think that the method should be acceptable, especially if you point out your logic as I have done.
HOWEVER
I will show you a general solution anyway.

Original purchase
Q units are bought for $P each. Making the cost price PQ dollars

First months sales
70% of Q are sold for 60% profit
0.7Q sold for 1.6P
Total sales revenue for 1st month = 0.7Q * 1.6P = 1.12PQ

Second months sales
30% of Q are sold for ( 100% - x% ) of the first months price
30% of Q are sold for (1 - x/100 ) of 1.6P
0.3Q are sold for 1.6( 1- x/100 ) P
Total sales revenue for 2nd month = 0.3Q*1.6( 1- x/100)P => 0.48 ( 1 - x/100 )PQ

Total Revenue for the 2 months combined = 1.12PQ + 0.48(1 - x/100)PQ => [1.12+0.48(1 - x/100)]PQ

But you were told that the profit was 37.5% which means that
Total Revenue for the 2 months combined = 1.375 of PQ
so

[1.12+0.48(1 - x/100)]PQ = 1.375PQ

1.12+0.48(1 - x/100) = 1.375
and when you solve this you end up with
x = 46.875
that is
In the second month the price is discounted by 46.875%
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Questions like this should always be checked.
1.12PQ + 0.3Q*(1-0.46875)*1.6P => [1.12+0.48*0.53125]PQ => [1.12+0.255]PQ => 1.375PQ
That is, the total profit on cost price is 37.5%
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Jan 12, 2014
 #1
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Trick question because any number in base ten is divisible by ten, because base ten is the basis of our numbering system. All you do is move the decimal point (called decimal point due to its ability to change a number by a factor of ten) to the left if you're dividing, and to the right if you're multiplying. If your number ends in zero, then dividing by ten will give you a remainder of zero. If your number IS a zero, then your remainder is your result and vice versa. Dividing a number by ten in base ten will always give you a remainder equal to the last digit in the number you are dividing.

To know if a number is divisible by another, first you check to see whether or not your divided number is a prime number. If it is, then you can only divide that number by itself or by 1. *Notice the reciprocity the of numbers: PrimeNumber / 1 = PrimeNumber and PrimeNumber/PrimeNumber=1

If the divided number is not a prime number, then look at the last digit of the number you are trying to divide, and note if it's an odd or even number. If its even, then you know it is absolutely divisible by 2 and will continue to be until you reach a prime number. If it's odd, then it's divisible by a prime number or by a product number of two prime numbers.

I found a remarkable sequence dividing prime numbers by 3 and got lost in wonder, and now I'm going to bed. So your best bet in knowing if a number is divisible by another is by memorizing prime numbers and their multiplication table.

Good night Everybody!
Jan 12, 2014

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