Practice job interview questions (sequence & powers) I am practicing for a numerical test as part of a job interview. 
They sent me practice questions, some of which I am not able to figure out completely especially given the fact that I am NOT allowed to use a calculater (see question 2). The questions are:
1) Which one of the numbers does not belong in the following series?
2 - 3 - 6 - 12 - 18 - 24 - 48
Options to choose from as an answer: 
        6,
        12,
        18,
        24, 
        48

2)  The beer market in country XYZ has an average annual growth rhythm of 15% per year. If it reached EUR 960 m in Year 5, which was the approximate value of the market in Year 0?
Options to choose from as an answer: 
        477,
        550,
        422,
        415,
        500

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The answers are:
1)  18 
However, I don't see why, given the fact that 2 -> 3 is a multiplication of 1.5, while the rest (e.g. 6->12->24 etc) is a multiplication of 2. Can someone tell me?
2) 550
The answer is simply 960/(1.15^4). However, can someone tell me how I could have computed this without a calculator?
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EDIT: 
The answer to Q2 should be 960/(1.15^5)=477  instead of 550 as mentioned above. => however my question remains: How can you calculate 1/1.15^5 without calculator?
 A: For 1), we consider the relation $$a_0=2 \\ a_{n+1}=2^n\cdot 3$$ 
Then we get $$a_0=2, \ \ a_1=2^0\cdot 3=3, \ \ a_2=2^1\cdot 3=6, \ \ a_3=2^2\cdot 3=12 , \ \ a_4=2^3\cdot 3=24, \\ a_5=2^4\cdot 3=48$$
A: 1) Let me start out by saying that the first problem does seem weird to me. If the answer is meant to be $18$, then I would argue as follows. In the sequence, I think of the first term as being the multiplier, so that $2$ is special and not part of the sequence as such:
$$(\boldsymbol{2})\  3 , 6 , 12 , 18 , 24 , 48.$$
Then the first term times the multiplier ($3\cdot 2$) gives the next term ($6$), and the second term times the multiplier ($6\times 2$) gives the next term ($12$), and so on, and only $18$ does not fit into this.
Unless there's a better solution, I don't like this problem.
2) You have a growth of $15$% pr. year. Over four years, this is approximately $4\cdot 15$% = $60$%. Thus you need to find the number, such that if you add $60$% to this number, it is approximately $960$. Certainly the result has to be larger than $500$, so $550$ is a good candidate.
A: For (1), the only reasoning I can think of is that 18 is the only number in the given list which is not divisible by each of the numbers before it in the sequence. (For example, 6 is divisible by 2 and 3, 12 is divisible by 2,3 and 6, 18 is not divisible by 12, 24 is divisible by 2, 3, 6, 12 and 48 is divisible by 2, 3, 6, 12, 24. So 18 is the one which looks the most unfitting to me). 
For (2), my answer is a bit far-fetched, but I have not seen a better one so I will post it: 
$1.15^5 = 1.15((1+0.15)^2)^2 \approx 1.15 (1+0.3)^2 \approx 1.15(1+0.6 + 0.1) = (1+0.15)(1+0.7) \approx 1 + 0.7+ 0.15 + 0.1 = 1.95$
Which shows that $+15$% increase for five years is approximately $+100$% i.e. double, so the answer is $\approx \frac{960}{2} = 480 \approx 477$. 
edit: when I say my answer is far-fetched it is because I have used a lot of approximations. In principal, this doesn't give a bad result because most of the approximations were up to a correction of $10^{-2}$. 
