# Brokerage Services interview questions

## Interview Questions

How would you handle a client who told you that you don't know what you are talking about because you have no experience? 1 AnswerI said that the advice and counsel I was offering didn't originate with me but with best practices industry wide |

### Intern at Northwestern Mutual was asked...

What is it about this job that interests you? 1 AnswerMake sure you research the job description and are ready to speak to specific roles and responsibilities. |

Can you describe what your design process is? 2 AnswersTell me about a time when a senior executive or client disagreed with your design - how did you handle it? I first figure out what the needs of the customer are and determine how I can design the product to best fit those needs and make the product easy to use. I then focus on the aesthetic part of the project and make it look as good as possible. |

If given X area square footage and X length of the room, what is the room's perimeter? 13 AnswersThe answer is one. Oops. Make that four That's easy-f'rinstince, if it's a 500 square footer which is 25 feet long, you'd figure the other two sides at 20 feet. To get the room's peri, you just add the four sides-90 feet! Show More Responses Area=Length x Width But Area is given as X unit square Perimeter=2(Length+Width) But Length has been given as X The4 Width= Area/Length = X/X=1 The4 Perimeter=2(1+X)= 2X For the record, all of these above answers are incorrect. If X = Area and L = X: A = L x W X = Xw w = 1 P = 2(L+W) P = 2(X+1) P = 2X + 2 The answer is 4 Solution: If Area is X and X is the length of the room, then we are dealing with a square where X is 1, hence perimeter is 4X or 4(1)=4 Lx W = Area Given Area = X and length =X Area/L= width X/X=area = 1 width =1 Perimiter = 2L + 2W 2(X) + 2 (1)= 2X + 2 Final answer is 2X +2 , not enough info to solve for X. This is a square so all sides are same length, one side is given as 4x and multiply 4 sides by 4x equals 16x perimator 4x... 2x The answer is not quantitative in mature. It's simply a test to see if you will ask more questions in order to understand the problem. In order to find a solution ..... quantitative in nature' It's no wonder Merrill is owned by a bank. They are asking architect questions in advisor interviews |

### Summer Intern at Five Rings Capital was asked...

• Is 1027 a prime number? • How would you write an algorithm that identifies prime numbers? • 2 blue and 2 red balls, in a box, no replacing. Guess the color of the ball, you receive a dollar if you are correct. What is the dollar amount you would pay to play this game? 6 AnswersAn algorithm for testing prime numbers is trial testing, test whether whether the number is dividable by an integer from 2 to its square root. For the color guessing game, the expected number of dollars you get is the average identity between a permutation of rrbb and rrbb, which is 2. For the prime number testing, only the number 2 and then odd numbers need to be tested. If it is not divisible by 2, there is no need to test against any other even number. So start with 2, then 3, then increment by 2 after that (3,7,9,...) until you are greater than the square root (then it's prime), or you find a divisible factor (it is not prime). To test for divisibility, we are looking for a remainder of zero - use a MOD function if available. Taking the integer portion of the quotient and subtracting from the actual quotient: if the difference is zero, then the remainder is zero and we have a divisible factor. If the difference is nonzero, then it is not divisible and continue testing. In this case, we find that dividing by 13 gives 79 with no remainder, so it is not prime. For the guessing game, the minimum winnings are $2 every time with the proper strategy. I'm assuming the rules are you pay to play and you get to guess until there are no more marbles. Say you guess wrong the first attempt. (you guess blue and it was red). So now you know there are 2 blue, 1 red. Your logical choice is to choose blue again, since there are more of them. But say you guess wrong again. Now you know there are 2 blue left, so you will win on both of the last 2 draws. If you were correct on one or both of the first two trials, then you could wind up with an even chance on the third trial, so you would win that some of the time, then you'll always win on the last trial. Show More Responses David, I think we could pay more that $2 and still come out on top. You logic seems sound, but looking at the probabilities I see: 1/2+1/3*(2)+2/3*(5/2) = 17/6 = ~2.83 Choosing the first ball, we obviously have an expected value of 1/2. Then, WLOG, we are left with RRB. Clearly we then choose R as this gives us a 2/3 shot at picking correctly. If it is R, then we get that $1, have a 50% shot at the next, and are assured the last, giving us, on average, $2.5. If it is B, then we know the next two will be R, giving us $2. As you can see, with an optimal strategy, we should expect to make ~$2.83 per round. Take the square root fo 1027. You get 32.04. Need only to check if divisible by prime numbers from 1 to 32, which include 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, and 31 For algorithm, see Lucas' test on Wikipedia, where there is also pseudocode. 1027 = 1000 + 27 = 10^3 + 3^3 and you know you can factor a^3 + b^3 |

### Assistant Trader at Five Rings Capital was asked...

You are standing beside a road watching cars pass by. The probability that you see a car pass by in 1 minute is 1/4. What is the probability that you see a car pass by in 30 seconds? 8 Answers1-sqrt(3)/2 why is this let p=probability that you see a car in 30 seconds p(see car in first 30 seconds)=p p(see car in second 30 seconds)=p p(see car in the first 60 seconds)=2p-p^2=1/4 solving you get p=1-sqrt(3)/2 (reject 1+sqrt(3)/2 since it's over 1) Show More Responses I have a question on this solution: 1-(1-p)^2 is the probability of seeing at least one car, not the probability of seeing a car. You can also solve this using exponential distribution. From the question, you can deduce that the distribution has to be memoryless and hence there has to be a constant rate per unit time for the event to occur. Let the probability per unit time of a car passing by be p. Then from the given information 1/4 = 1 - e^{-p*T} The required answer is e^{-p*T/2} which gives the answer as reported above. Minor correction in above. The required answer is 1 - e^{-p*T/2} ans 1/2 as the person sees car in 15 sec of each 1 minute if we divide 1 minute into 4 parts (60/4 = 15 secs) s the probablity of seeing car now we are asked in 30 sec . the rate of moving of car will not change it will still continue to come at a rate of 1 in each 15 sec so the ans for each 30 sec would be 1/2 if we divide 30 into 2 parts . so in 15 sec one car is left .but for next 30 sec no car is going to come then itls probability would be 0 . now the ans is tricky which 30 secs are asked , the 30 sec in which car is seen or in which it is not seen by the man 1 - sqrt(3)/2 is the wrong answer |

### Equity Trader at Chimera Securities was asked...

If you have 9 marbles and one is heavier than the other 8. How can you use only a balance beam to figure out which is the heavy one if you can only use it twice. 7 AnswersWeigh 3 against 3. If they're the same weight, the heavy one's in the other group of 3. Your answer does not select the actual heaviest marble, nor does it make use of the balance beam twice as indicated in the original problem. Instead: weigh 4 against 4. IF they are the same weight then the remaining one is the heaviest. OTHERWISE IF one lot is heavier then take the lot of 4 and discard the rest. Then weigh 2 against 2. Take the heavier lot of 2 and place one in each hand. The heavier one is the heaviest marble. Your answer does not select the actual heaviest marble, nor does it make use of the balance beam twice as indicated in the original problem. Instead: weigh 4 against 4. IF they are the same weight then the remaining one is the heaviest. OTHERWISE IF one lot is heavier then take the lot of 4 and discard the rest. Then weigh 2 against 2. Take the heavier lot of 2 and place one in each hand. The heavier one is the heaviest marble. Show More Responses @qq11, I don't think your answer is right either. The question specifically says the balance beam can only be used twice, so I assume the question is asking how to find the heaviest marble by using the beam twice, not 3 times. You simply just split the 9 marbles into groups of 3. Put two sets on each side of the balance beam, and this will tell you which set has the heavy marble. After that, just take the heavy set of 3 marbles and put 2 of them on the balance beam, and you'll know which marble is the heavy marble. @qq : go kill yourself.....are you really thinking about sayng to put the marble in your hand?? c mon bro.......alex is right btw Ooo and ooo and ooo. First try: Ooo vs ooo => Ooo is heavier. Now take two of those and put one on each scale. If equal than the third is heaviest. If not equal, heavier one is heaviest. OR try ooo vs. ooo. Equal. Repeat step two for the pile that is established to be Ooo. Foolish children. Quantchi will guide and enlighten you, Alex above is 100% right. Segment 3 split breakups. Pair the marbles into 3 sections. Weight two, once you determine which set is abnormal you then weigh two of the 3 marbles of that set. Problem solved |

### Junior Trader at TransMarket Group was asked...

“Given the numbers 1 to 1000, what is the minimum numbers guesses needed to find a specific number if you are given the hint "higher" or "lower" for each guess you make.” 6 AnswersI found 1 of the questions on their test here: http://www.math.ku.dk/~rolf/teaching/mfe03/mfe03.soln.pdf Is this 10? 2^10 > 1000 and 2^9 < 1000? The answer is 1. Read the question carefully. It asks for the minimum # of guesses for a number between 1 and 1000. If you guessed the # right the first time, you don't need to guess again. Show More Responses Crazy is craziness idt 9 |

what's angle do the hands of a clock make at 1:20? 5 Answers75 degrees 80 degrees 80 is correct. you are 1/3 of the way through the 1 and 2. Each area represents 30 degrees. So you are 10 degrees past the 1. That's 20 left, plus the 30 in each of the areas between 2 and 3 and 3 and 4. = 80 Show More Responses it would be 90 degrees - there's 30 degrees between each hour, 30(3) = 90 The hands of a clock travel in a circular pattern so they cover 360 degrees on full rotation. Between each hour segment (i.e. 12 and 1) there are 30 degrees (360/12 = 30). At 1:20, the minute hand has traveled 120 degrees (30*4 = 120) which is 4/12 or 1/3 of the full rotation. This tells us that the hour hand has also traveled 1/3 of the way between 1 and 2. Since we know there are 30 degrees between 1 and 2, we can calculate that the hour hand has traveled 10 degrees from 1 to 2. This means the hour hand has traveled a total of 40 degrees past 12. Now we subtract the 40 degrees that the hour hand has traveled from the 120 degrees that the minute hand has traveled and we get 80 degrees. The angle between the hour hand and minute hand is 80 degrees. |

One thousand 1x1x1 cubes in a 10x10x10 cube. Outside spray painted. How many have no paint.\? 5 Answers1000-8^3=488 Its asking how many have no paint, so its just 512 1000....because they are placed INSIDE the 10x10x10 cube, thus the only cube getting painted is the big one. Show More Responses 1000- the number of cubes on the outside = 1000 - 2 sides - 2 other sides (not counting the cubes that were already counted by the 2 previous sides) - 2 remaining sides (not counting the cubes that were counted by the 4 previous sides) = 1000 - 200 - 160 - 128 = 512 or just count the number of cubes on the inside = 8^3 = 512 http://brainteaserbible.com/interview-brainteaser-cube-dipped-in-paint-10x10x10 |