portfolio analyst interview questions shared by candidates
You have a birthday cake and have exactly 3 slices to cut it into 8 equal pieces. How do you do it?39 Answers
Cut in half, stack, cut in half, stack, cut in half. All you have to worry about is the 45 degree rotation of one of the 4 pieces after the second cut. Blade can be kept in place, like a paper cutter, as to minimize the margin for error.
Slice it horizontally across the middle creating two equal halves top and bottom. Then simple two slice cross from above like normal.
Cut each slice into 3 slices. Then eat one of them.
This is really an easy one. First cut into half across the top, then cut the halves in half also across the top (you now have 4 equal pieces) then cut across the middle = 8.
No, Jason and Sharon, you will only wind up with 6 slices. z, too many stacks. You need to cut in half, then make another cut - to get four pieces. NOW you stack these four pieces and make the last third cut - and you get 8 pieces.
A rather easy lateral thinking question. Alina's got it.
The stacking seems to be the "right" answer. But this is a stupid question. Who stacks cake? The frosting from the bottom slice would meld with the stacked slice, thus making the cake inseparable. I wouldn't get the job because I would swear at the interviewer for asking a dumb question. What good is an answer to this question if it wrecks the cake?
Assuming the cake is square: slice 1: cut horizontally to create 2 equal pieces slice 2: cut vertically to create 4 equal pieces slice 3: line up all 4 pieces of cake side by side and cut horizontally to create 8 equal pieces. don't stack, it will ruin the frosting.
With a knife
Alina would be penalized for not being able to count past 6. But then, she could get a job at another company where they appreciate people who say someone's idea is wrong, then put forth the same idea and take credit for it.
A new solution for you: who says slices have to be a straight line and not circular? I would cut a concentric circle in the middle (would have to calculate the radius compared to the whole), and then slice an X with the remaining 2 cuts. It will look like a target. If done correctly the sizes will be the same, it says nothing about having the same shape!
I guess it's much easier if you think of two planes: first cut in half, then to quarters. That's the easy part. Now look at the cake from the side, and cut it across... Each quarter is cut into two and all pieces are equal.
I would consider the interviewer's emphasis on "equal pieces." While my first thought was to bisect across each of the three dimensions, half of the pieces would end up with less frosting than the other half. Stacking the pieces would result in frosting transfer, which would also screw up some of the pieces. Therefore, I'd go with lining the pieces up and have a large knife on hand for each bisection. Hey, people get crazy about their cake slices.
I would take a different approach to this. First of all the question asks for the cake to be cut into 8 equal pieces, not 8 identical or 8 of the exact same size. Equal doesn't always have to mean the same, just equivalent to. First I would find out who I am cutting the cake for, if its 4 old ladies and 4 young guys, equal pieces would not mean that they all needed to be the same. If everybody wanted the exact same amount of cake I would figure out a way to give everybody 12.5% of the entire cake volume, but if some wanted larger or smaller pieces I would come up with a way to satisfy each individuals desire.
If you know how to cut an arbitrary shape in half, you have the solution. After every round, plan the cuts for each individual piece. Then align them so the proposed cuts are in one straight line. Make a cut. This way you can cut any cake into 2^n equal size pieces with n cuts. An interesting question is, if you start with one connected piece, will you always be able to end up with connected pieces. Think of cutting letter S in the middle, like this: $. You end up with two equal figures that are not connected (or, in other words, with 4 pieces). It's also easy to design a cake that can be split into 8 pieces with one straight cut.
I LOVE Andrew's answer! Eat one of the freakin' pieces. That's the corporate way in America anyway. Mike is either a socialist, or works in non-profit, or government. I thought "slice them long ways" but then someone misses out on the freaking frosting, which is the best part. UNLESS, it's a layer cake.
First I'd yell at whoever cut the cake incorrectly to start with. He's ruining the party. Then I'd squish the 3 pieces of cake together and re-cut the cake into the required 8 pieces. Boom.
This is as easy as pie. Viewing the cake from the top, make 1 cut vertically down the middle of the cake and another horizontally. Viewing the cake from the side, make your third cut horizontally through the middle; QED three slices and 8 pieces of cake
with a beamsplitter and prisms it could be done in 1 (with a laser)
That's an oddly presented question that is understood 2 ways: - 3 cuts allowed to cut one cake in 8 pieces. Which yields cut in 4 parts, then split those in 1/2 again with the last cut, either by stacking, realigning the slices or making a round cut. - 3 pieces of cake must be re-cut to make 8 equal parts. Which is an impossibility unless one piece is 2/3 smaller than the other 2. That yields different answers like cutting in 3, and eat one to leave 8 pieces.
They key to answering any of the brain teaser questions is to ask a few critical questions before even attempting to answer. I would start with: Is the original cake round or square? If square, line up all three pieces and recut to be 4 equal widths of cake. If round, was the original cake cut in 6 or 8 pieces? If 6 pieces you have 1/4 of a cake = easy to redivide into 8 equal slices. If 8 pieces, you have 1/3 of a cake and a little math needs to be applied to create 8 equal slices. First slice a strip off each of the 3 slices to create a fourth slice. then divide each in 1/2 to make 8 equal slices.
Cut each slice into 8 small slices. Then give each person 3 small slices.
There are some posting above who seem to not have a good grasp of numeric's. The answer is not that difficult. First, presume the pieces are not equal size (nothing states they are). Second, presume two pieces are of equal size and the third piece is twice that size. Third, cut vertically (the most usual manner in which to cut cake) the 2 equal pieces (we now have 5 pieces -4 the same size and one larger piece). Fourth, cut the large piece in half, then those two pieces in half again. Fifth, voila, one now has eight equal pieces of cake.
Hmmm, I always assumed they meant three knife cuts by the word "slice" Kind of interesting to me that others assumed the cake was given to you in 3 parts as defined by the word "slice" I'd say that you should cut the cake horizontally using the knife as a measuring device to find the exact center of the circle, then cut vertically using the same method, then take each quarter , using the knife as a straight edge, build an alignment diagram that places each set of two quarter pieces point to point along an axis that defines their center lines, and cut all 4 quarter slices with a single cut of the knife ( defined by the word slice ).
Put it all in a blender. Pour each of the resultant mixture onto a plate or into a bowl.
1. assemble 3 sliced cakes into a big cake (original shape) 2. cut it half (don't care about the indentation) , you would get 2 piece of cake 3. cut it half again, you would get 4 pieces of cake 4. cut all of them half again, that's finish.
To those who think it means you start with 3 pieces ("slices") of cake, READ IT AGAIN. It says (emphasis added): “You have a birthday cake and have exactly 3 slices to cut IT into 8 equal pieces." Get it? "... to cut IT [the cake] into 8 equal pieces."... There is NO WAY it means to cut 3 slices of cake, otherwise it would say "...exactly 3 slices to cut into...". And Mike: "equal doesn't mean same, just equivalent". That's the funniest (and stupidest) thing I've heard all day. Anyway, since 2^3 = 8, you have to stack. Assuming a round cake: Cut (or "slice") 1 creates 2 semi-circles. Stack them. Cut 2 creates 4 quarter-circles. Stack then Cut 3 creates 8 1/8th circles.
is the 3 slices equal in size?
Great answer and explanation here: http://www.programmerinterview.com/index.php/puzzles/birthday-cake-8-pieces/
Make sure the guest of honor has Blown out candles 1st! (was not specified but hey so were many other things) If the birthday boy/girl is under the age of 10, I am not too sure you want to be messing with their cake!! Cakes come in many different sizes and shapes...ESPECIALLY Birthday Cakes!!! ACK They even come in characters and shapes you can NEVER get into equal pieces but, back to the solution! Will use 2 shapes: Round and Square! Cut 1: Parallel to cutting board and horizontal to create 2 layers of equal depth; Cuts 2 and 3: Perpendicular to cutting board once then rotate 90 degrees and repeat! Now give it to the Kid in the high chair to for quality control/assurance!
Like Andrew, I would eat one piece and then cut the 2 in four equal pieces.
Remember 1 whole cake, 3 slices with a knife = 8 equal pieces Place cake flat on table. Grab a knife big enough to cut the cake horizontally. 1st cut - Cut the cake horizontally leaving the cake flat on table as if the cake still in one single piece. Now you have 2 cakes instead of one. 2nd and 3rd cut - cut through the cake vertically in the form of a cross. Now you have 8 equal pieces of cake. As if you had cut 2 cakes in 4 pieces each.
I would state that I only eat cakes in the shape of circle. then 3 equal cuts across the middle. think of it like a pizza... or a pie.... or a pizza pie. Remember these questions are made to have you think outside the box. Not all cakes are square.
cut the diagonal portion then centre line of cake
Cut each of the 3 slices into 8 equal parts which makes the slice count 3*8 = 24, Divide the 24 between 8 people 3 each.
Cut 2 slices into 4 pieces each, cut the third one into 8 pieces.
Separate 2 of the 3 slices, dividing 2 slices for 8 people is easy (each slice in 4) Then with the left piece I divide it in 8 and offer one to each person.
One more: I could put all the 3 pieces together and re slice into 8 equal pieces.
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 Answer
I said that the advice and counsel I was offering didn't originate with me but with best practices industry wide
What are the risks to investors of currency arbitrage?1 Answer
Given the nature of the portfolio strategy, the primary risk is trade execution. Due to high leverage, a delayed or erroneous futures or sport market trade can potentially wipe out a substantial portion of the fund. Another risk, although very unlikely, would be a sudden inter-trade change in a currency's underlying interest rate due to a unanticipated central bank policy move.
You have 100 quarters, 10 heads, 90 tails up in a dark room where you can't see the quarters. How do you divide them into 2 piles where you have an even amount of heads in each pile?5 Answers
randomly split the 100 quarters into two equal piles, 50 quarters per pile. Because of probability, that'll get you fairly close to an even amount of heads in each pile
Split the 100 quarters into two piles of 90 and 10 coins respectively. Flip all the coins in the pile with 10 coins.
Simply double-count that you have 50 quarters in each pile because the interviewer did not specify "heads up", they simply asked that you ensure that you have an equal number of heads in each pile, which you most assuredly will...You're welcome America(in Stewie Griffin accent).
Take the 90 quarters that are tails and split them into two piles, 45 in each. Then take 5 heads and place into each stack, and you'll have an equal amount of heads in each stack.
It is simple you only have 10 heads in front of you because 90 tails are in a darker room which you can't see. So make a pile of 5-5 of heads.
If a bond is trading above par, the YTM is greater, less, or equal to the market's yield?4 Answers
The correct answer should be equal, given efficient market. Here is the explanation: The bond is trading above par because its coupon rate is higher than the market yield. This is the result of the market (i.e. investors) trying to adjust the pricing of the bond so that the its total return (i.e. YTM) is equivalent to what the market yields for similar bonds (i.e. bonds with similar credit risk, duration, etc.). Market should cause the YTM of the bond to equal the market yield.
Greater. If the bond has YTM higher than market interest rate, investors are willing to pay premium for the bond, which is the case in the problem description.
For a bond selling at a premium: Coupon Rate > Current Yield > Yield to Maturity It has a lower YTM compared to market's yield.
Brain Teaser: you have 7 seemingly identical looking balls, only 1 is slightly lighter than the other 6. You are given a scale. How can you find the 1 lighter ball is you are only allowed to use the scale twice.4 Answers
pick 3 random balls on one side of the scale, pick 3 more to put on the other end. if scale equals, the 1 unpicked ball is the lighter one. if one side is lighter than the other one, the lighter ball is among them. take 1 random ball out of 3 to put on one side the scale, put another on the other side...you get it by now.
can we not pick 2 on each side?
You can start with 2 or 3 on each side and still only measure twice...doesn't matter. Second step would be to measure 2 of the 3 balls from the lighter side. Regardless, it's a dumb question to ask someone on an interview.
Add one ball to the scale at a time continuously . The lighter ball will show a slight difference at the scale when you adding up the weight. Like if the first ball is 12g, then adding the next one will be 24, 36, etc and the one that was slightly off will be the lighter one. I think this count as using the scale once because I use it continuously
If you had 100 million dollars to do whatever with it you like, what would you do? Would you invest it? If so, what would be your first trade?4 Answers
My first investiment could be and 'investiment couse', the best ever. So 50% in low risk investiments, 30% in middle risk investiments and 20% in high risk investiments.
Oh Carlos, how boring. I'd buy 100 million shares of Enron, then move the rest to my bank account.
I would have a chain of liquor stores in poor neighborhoods, buy properties, put 10% in CDs, and look to invest in tech companies that deal with renewable resources (solar,wind, water).
Would Help Juanita expand her horizons! #1 Investment: Myself! (Get out of Debt! and go on vacation!) #2 Buying Foreclosures, Flipping them and Incorporating as a Rental Property Company #3 Investing Those Proceeds #4 Buy my own Land, Build my Own House to which will run on renewable resources! #5 Donate To many charities that support our environment, our animals, and nothing to do with humans! #6 Live Comfortably, Humbly, and Happily!
If you had 2 6-sided dice, what's the probability you get a 7?2 Answers
here are the different ways you can get 7 1-6 6-1 2-5 5-2 3-4 4-3 prob(7) = [Prob(1)*prob(6) + prob(6)*prob(1).......................+prob(4)*Prob(3)] = 1/6
You should ask if the dice are fair.
What are the benefits of a big bank vs small firm?3 Answers
Job security , better chances of growing within the company, a bigger company will accommodate more executive or senior level staff on it's payroll than a smaller firm. More job openings because of multiple branches and departments. Division of labor which expedites work and projects towards meeting deadlines.
Small firm is as good as their last trade.
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