Options:
1)16 2)17 3)19 4)15
How did we get that answer by solving??
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How many multiples of $6$ are there? How many multiples of $12$ are there? – Angina Seng Dec 21 '17 at 15:10
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A number that is a multiple of 6 and at the same time a multiple of 4 is a multiple of... – drhab Dec 21 '17 at 15:12
2 Answers
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A number that is multiple of $4$ and $6$ at the same time must be multiple of $lcm(4,6)=12$.
This means that there are $$\left\lfloor\dfrac{200}{6}\right\rfloor-\left\lfloor\dfrac{200}{12}\right\rfloor =33-16 =17$$ multiple of $6$ and not multiple of $4$ between 1 and 200.
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By writing out a few terms you can see the formula for the elements of the sequence:
$$6,18,30,42,... \to a_n = 6 + 12n$$
(I wrote down the first few multiples of $6$, and took out the ones that were multiples of $4$.)
The largest value of $n$ that produces a value less than $200$ is $n=16 (a_n = 6 + 12(16) = 196)$.
Hence, there are $17$ elements ($n=0...16$).
John
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