Let x be the income. Net income is x - x/100. Take first order derivative of that and set it 0 and solve for x for the optimal salary. The answer is 100.
I think this solution is incorrect. The net income is the gross pay less the gross pay multiplied by the tax rate: Net = Gross - Gross * Gross/100 Net = Gross - Gross^2 / 100 Calling the net pay N, and the gross pay G, N is maximized when dN/dG = 0, or: 1 - G /50 = 0. Solving for G yields an optimal pay of 50 rupees. I knew your answer was incorrect because a pay of 100 rupees corresponds to a 100 percent tax, that is, ZERO net pay! IBKR remember my name, I will submit my application upon graduating from college. Mike Mancini firstname.lastname@example.org
Technically answer is 50/50 but they want out of the box thinking. Perhaps suggest that the coin must not be fair or that there is an outside factor playing a role.
It's 50/50, and the thing to understand is that 99 heads in a row is no more likely or unlikely than a sequence of, say, H,T,H,T,T,T,T,H,H,T,H,H,T,T... and so on up to 99. Each particular "random"sequence of heads & tails is equally unlikely. If we take the averages of all possible sequences then heads comes up as many times as tails does, but for a particular string of 100 flips, there's no knowing until we are finished whether it's going to be H(99) & T(1) or H(100) & T(0). Could go either way, and the odds are 50/50.
they were looking for answer that tells them that you are looking for something that could clearly help you. NOT GIVE YOU EXPERIENCE.
Since this is a job in the financial sector, you can also spin this in similar language: RETURN ON INVESTMENT. I plan on making this a long term relationship, investing years of hard work and energy. I would hope that the company sees that, recognizes that, and helps build that relationship with me.
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Lowest multiple of 16 that only contains 1s and 0s...I couldn't come up with an efficient solution besides multiplying by stuff until I ended up with 10000 (took too long, interviewer asked me to move on).
16=2^4. So the number should be divisible by 2 four time over. Start from least significant digit: Digit 1: It can only be 0, because number ending with 1 is odd and therefore not multiple of 16. Digit 2: It can only be 0, because X...X10/2 = X...X5 which is odd. (But X...X10 is indeed multiple of 2.) And so on. You'll get 10000 as the lowest number (4 zeros = 4 embedded 2's = 16)
last digit has to be 0, so this number is 8*2*5*X = 8*10*X. By common sense, 8*125=1000, so X = 10*1000 = 10000
What angle does that clock make at 4:15? If you have 100 red and white marbles and had to place them in two separate jars - how would you distribute the marbles to give you the highest chance (EV) of getting a red marble when you are blindfolded? You have to use all the marbles.