Interview Question for Business Analyst at McKinsey & Company:

Assuming the plane is a 747. and the diameter of the golf balls is 40mm. 23.5 million balls would fit in the plane.

What kind of aircraft. Would the plane be empty or full (seats etc). I would need a lot more detail before I could answer that. Not to mention what sort of golfball.

If I asked this question in an interview. I would weed out whoever had an 'answer' with taking time to delve into the question\problem.

"Without" taking the time...

The people who require more info are missing the point. In real life decisions, you are often working on too little data to make an "easy" decision. There is no right answer to this question. What they are looking for is your ability to think the problem though, make estimates and arrive at an answer. My advice with a problem like this is to take a sheet of paper and think out loud as you work through it. Let the interviewer in on your thought process. The WORST thing you could do is ask "what sort of golf ball?"!

Too many too count, that's for sure. To make an estimate, I'd hop on the internet and see if I could find the internal volume of a 757, and just convert that to square inches. Golf balls aren't too much larger than an inch in diameter, and there's no point in wasting time shooting for any kind of precision, since the question doesn't not specify what type of plane, and why anyone would even care about the answer.

Just answer "5". It's out of the box, shows you like to get things done and can ward off dumb questions.

I would take a golf ball and put it in a cup of water. measure out this displaced water.
Golf Ball = 2.7727498 oz. of displaced water
128 = oz per gal
128 / 2.7727498 = 46.163559366229149128421179581367 (roughly 46 golf balls in a gallon)
7.48 = Gallons per cubic foot
46.163559366229149128421179581367x7.48 = 345.30342405939403548059042326863 (golf balls per cubic foot)

My answer: 345.30342405939403548059042326863 per cubic foot of free space on the plane. (Mind you the golf balls would be ground up, but then again they didn't ask how many whole golf balls would fit, now did they?)

I would take a golf ball and put it in a cup of water. measure out this displaced water.
Golf Ball = 2.7727498 oz. of displaced water
128 = oz per gal
128 / 2.7727498 = 46.163559366229149128421179581367 (roughly 46 golf balls in a gallon)
7.48 = Gallons per cubic foot
46.163559366229149128421179581367x7.48 = 345.30342405939403548059042326863 (golf balls per cubic foot)

My answer: 345.30342405939403548059042326863 per cubic foot of free space on the plane. (Mind you the golf balls would be ground up, but then again they didn't ask how many whole golf balls would fit, now did they?)

I would answer that there are say 300 passengers on the plane. Let's say that 10% are actually golfers, so that's 30 people who might even own golf balls. Then I'd say another 10% of them might actually be bringing their bags with them (on vacation, cool business trip, etc), so that's 3 people with bags. Now I usually have about 3 balls in my bag (cause I lose them all the time) - so that's the low end. On the high end, if i went to wal-mart the night before to get ready for my trip, i might have bought 2 dozen. So, I would estimate that there are between 9 (3x3) and 72 (3x24) golf balls on an airplane. Why did I work it this way? Because who the hell besides Captain Kangaroo's Evil Twin Brother would want to fill an airplane with golf balls? So I went with a realistic answer. If my percentages are off, they are easily adjusted in the formula with real life facts. Or you could call Titlest and ask them.

As many as will fit.

That's a trick question. Everyone knows that golf balls are now banned by TSA. This question is devised to see if you can go on a business trip without ending up being branded a terrorist.

42

Can you answer the question with a question?: Is this an abstract math problem or a real-world common sense problem? Then: In either case we don't have enough information.

For what it's worth, the volume of the golf ball alone doesn't help you because you need to account for the space between golf balls in the hexagonal closest packing arrangement, which I believe is the most compact way to arrange spheres. Also, the displacement method of measuring the volume isn't nearly as good as just calculating it from the diameter which you can easily Google.

Why are we flying to Augusta?

100 of them will fit.

The question never asked the "MAXIMUM" number.

I don't know that many of you guys would get the job.

I came up with an estimate of 20 million, myself. Probably an underestimate. I decided to approximate the plane as a cylinder 10 feet in diameter (too small, but lots of unusable space - seats, bulkheads, etc.), and I totally guessed at 150 feet long. Golf balls pack, I think, at just about 1 ball per cubic inch. So then I estimated a 10-foot diameter circle would hold a single layer of about 10,000 golf balls (pi*60^2 is closer to 12, 000). There would be 150*12~=2000 disks like this, if 150 feet is close.

I agree that doing this in such a way that interviewers can see your thinking is important. If you are off because some numbers you guessed were wrong, but the method is sound, you have proved your intelligence.

as many as you want to...tiill the plane is full sire :-)

All of them. I have never seen a golfball that would not fit in an airplane.

Nothing said that they all had to be in at the same time.

This is not a serious question. What size airplane? A model? Then not even 1 golf ball will fit. If this was a serious interview question then the only value would be to see what kind of clarification questions were returned to the interviewer or to see what kind of assumptions made and methods used by the interviewee. But this would be a poor interview question since it is too open-ended. (Does the interviewee show critical thinking by asking clarification questions or show technical prowess by making a volume ball-plane calculation or .... There are better ways to assess critical thinking and technical proficiency.)

Depends on the plane... puddle jumper, lear jet, 757... I'd say at least 1 golf ball!

clearly you want to show your thought process.... my first question would be "Do we have a budget for golf balls"?

You may consider the load of the airplane. If the airplane is in the air, the amount would be limited by the cargo capacity of the plane. I'd hate to carry too many have have the plane fail to take off.

There's no punctuation mark (?) at the end of the sentence, so presumably they hadn't finished the question ...... "how many golfballs fit in an airplane" ........ hanger? ..... hold? ....... cockpit? .......... while it is in the air? .......... on the ground?

Just shows what a pointless question it is!

Was just asked this question in an interview recently. Personally, I find the question obnoxious and elitist. It is NOT an accurate predictor of how an individual will behave in a real-life situation. It shows how an individual will behave in a situation where they are doing their best to secure an income, need to do backflips just to arrive to this point and are now put on the spot with some nonsense question pertaining to 8th grade geometry. I know somebody who runs the Finance department at a top Fortune 500 company and can't split the dinner bill to save her life. It shows a lack of knowledge and research and the interviewer's part if they are using this question to predict future performance of an individual.

Hilarious posts. The point of this question is to understand the interviewees thought process. You would need to ask smart questions, make smart assumptions, and explain everything that you're taking into consideration.
This is a good way to measure one's ability to think critically, on the fly. They understand you're in an interview, they want to know as much as they can about you by seeing you at work. Its one thing to comminicate your skill set and another thing to demonstrate it.

I think most of you are missing the point to the question. The answer is not important, it is how you get there. You simply state your assumptions (they'll tell you if its way off, because lets face it your not being interviewed for a job designing planes!), then break down the problem. The best attempt at this question was Jim....

So this type of question is to see how you think and if you can do it under pressure. The question is structured to allow you to ask questions, like what kind of plane is it? On the other hand, the interviewer might have an answer from an interviewing book for golf balls in a 757 or whatever he might tell you the plane is. You might have the opportunity to take control, so pick a plane you are familiar with from a recent flight, say “I flew in on a 727 yesterday, so can I use that for my estimate?” (You will probably get a yes answer and he probably does not know a 727 from a 737, so he can’t challenge your numbers if they sound reasonable).

 “Ok, when I made reservations on Orbitz and picked a seat, I remember there were 32 seats with 2 on one side of aisle and 3 on the other. I have not done geometry recently, but I think the area of a circle is Pi-R-squared, so a plane is basically a cylinder which means I can multiply the circle area by the length to get volume. (so you can offhandedly ask the interviewer something like “that’s what we learned in junior high right?” – and probably get a confirmation). So it seems like the plane was widest at the floor level and each seat was about 3 feet including arm rests and the space in between, plus the aisle width gets you a diameter of about 18 feet so radius is 9 feet. Let me do a little math over here on the white board: the area of the circle is 3.1415x9x9, so I am estimating and will use 3 instead of PI, so we get 243 square feet.”

“So there were 32 seats and it seemed like about 3 feet for the seat and the tiny leg room x32=96 feet. But there was more space for exit door rows, bulkhead, attendant station, kitchen, bathroom and first class leg space, that adds about 30 feet = 126. The cockpit is probably 12 feet long, but tapers down, so we will use 9, plus 8 effective feet for the tapered tail area = 143 feet. Given the inaccuracy of this estimate, we can ignore the .1415 I dropped off PI to make math easy on the whiteboard earlier. (Back to the whiteboard and) 143 x 243 = 34,749 cubic feet. When I toss the golf balls in, I will assume the seats and equipment is there, but the overhead bins are open for the balls. That other stuff probably reduces usable volume by 20% or 6800 leaving about 28,000 cubic feet. So now I need to figure out the volume of a golf ball.”

“I have only played golf twice, and was really bad – nearly killed somebody with a slice!” (just adding some humor to the interview - so I make a circle with my finger and say) “I think the golf ball was about this big – looks like less than 2 inches, maybe 1 and three quarters? Do you golf a lot? Does that sound reasonable?” (so he might give you a clue or a nod or admit he doesn’t really know either). “Ok, back to the 8th grade. Volume of a sphere – man, that one’s tough, I kind of forget. Area of circle was PI-R-squared, so that has to be multiplied by something like we did for a cylinder. The “height” of a sphere is the diameter, but it is not a full cylinder, so it would be less than multiplying by the length of the “side” or diameter in this case. So, Mrs/Mr interviewer, I know this question is about estimating, not remembering junior high math, so can you give me a hint on this one? (Yes: it’s V = (four/three)*area of the circle) – (or no, just guess. So then you take the volume if it were a cylinder and reduce it by a reasonable amount. He doesn’t know unless he has a book).

“Now we do painstaking math on the whiteboard, ask for a calculator, or take a guess. 3.1414xR2x four thirds = 3.2 cubic inches. Golf balls will leave gaps when packed into a container, but not too inefficient, let’s say instead of 3.2 cubic inches, let’s say 3.4 (just needs to sound reasonable). How many cubic inches in a cubic foot? 1 foot by 1 foot by 1 foot = 12x12x12 inches = 1728. Now divide that by 3.4 and get 508 golf balls in a cubic foot and we estimated 28,000 in the plane, so that is about 14 million golf balls.”

(sidenote, this involves tedious math on paper or whiteboard, but it gets you an answer. It may be that he is happy with you reasoning out your methodology, but he probably has a number in mind, so when you ask, he will let you do it out on the whiteboard)

So I actually did this by scratch just now and it does take a while. I used Excel for the math so it would take longer on a whiteboard. More importantly, not a single one of my numbers is right, but they don’t seem unreasonable. Does the interviewer know how many seats, rows, wasted space, etc on the plane you are using? No. But he sees an analytical thought process and ability to reason and estimate. Don’t panic. Don’t make a random guess right away. I might give a few hints if I asked this question. So if the real answer is 1 million or 50 million then I sounded dumb, but you have to assume he is asking this to everyone else and they might not do much better, so stay confident and calm.

TSA hasn't banned golf balls, but there are endless stories of them confiscating golf balls. I'd say zero.