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Week Three
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(*1)
How many prome numbers are there between 1 and a thousand that are divisible by 3?
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solution
on sunday
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Week Two
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(*2)
A package of 500 rocks weighs 48 kg. How muck does a package of 375 rocks weigh?
(consider that the packages have identical rocks)
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solution
this style of questions requires a simple proportion.
the answer will be added in a short time, today
If you didn't quite understand this solution, you should visit my arithmetic series tutorial
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Week One
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(*4)
find the sum of all three digit numbers that are divisible by seven.
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solutionIf you didn't quite understand this solution, you should visit my arithmetic series tutorial
The first three digit number that is divisible by seven is 105, that last is 994.
we need to find the sum: 105 + (105+7) + (105 + 14) +...+ 994.
This is a arithmetic series.
the formula to calculate an arithmetic series is (2a + (n-1)d)(n/2),
where: a is the first term; in this case 105, d is the common difference;
in this case 7, and n is the number of term;
we dont know n.
how to find n?
any term is a + (n-1)d (can you see why?)
so, a + (n-1)d=994→ (n-1)7=994→ 7n-7 = 994→ 7n = 994+7→
7n = 896
n=128
now we plug n =128 into our formula
we get
(2a + (n-1)d)(n/2) = (2(105) + 7(127))(128/2)= (210+ 889)64=1099(64)
=70 336
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