OT: ok the maths one was too easy, try this

[John Rumm]

(100%, but I did have to draw a picture for one!)

[Nightjar]

Also 100%, but ICBA to work out Q2 or Q4, so chose what felt right. Q7 I had seen on TV, Q9 is the basis of fitting parts and Q10 is one of those useless bits of information that stick in my head.

Colin Bignell

[Dave Baker]

Yes, the horizon calculation I assume. The 4 digit multiplication seemed utterly pointless other than to test a small child. I did it with pen and paper and assume that was what they meant by no calculators rather than having to do it in ones head which would have taken a bit longer. It helped that as a cylinder head airflow specialist I already knew the density of air by heart but I suppose that most people have no idea and I presume in a real test you wouldn't be allowed to look that up so I guess that one could stump a lot of people.

The rest were trivial other than Q10 but that's such an old hoary general knowledge question I already knew the answer and just ticked 23 without having to think about it. I confess my grasp of probability theory is probably the worst bit of my maths knowledge and I'm not sure I could have worked out the correct answer from scratch. I also started off by ticking

3/4 for the lemonade question as that initially seemed intuitively right but took care to scribble the descending series on an envelope and sum the fractions before pressing enter and was quite surprised to find it was actually 2/3. A little more thought then revealed that the second person to drink must consume more than half of the half pint that he starts with and so the first person could never reach 3/4. Hey ho. So much for initial intuition.

So a pretty simple 100% and I'm surprised that a university application test is so trivial these days. One also presumes that a pass score would only be

70% or 80% and anyone who couldn't reach that ought to seriously reconsider their education options perhaps.

[Mike Barnes]

90%, but my "wrong" answer was right IMO.

Q.8 "An unbiased cubic die has numbers 1 to 6 inscribed on each side. On average, how many rolls will you need in order to get a 6?"

Correct answer: 1.

The question states that each side has the numbers 1 to 6 inscribed. This is somewhat unusual in that there are apparently six numbers per side, whereas most dice have only one number per side. The result is that the first throw will get a 6 (along with 1, 2, 3, 4, and 5).

I had several quibbles with other questions as well.

[Thomas Prufer]

I think it is meant to be calculated as (a+b)(a-b)=a²-b² which is easy given the numbers used.

Thomas Prufer

[Nightjar]

Not with multiple choice. Both numbers had zero for the units, so the answer would end in 00, which did not help a lot. The tens were 2 and 8.

2*8=16 Therefore the answer would have to end in 600, which eliminated three of the four answers.

Colin Bignell

[dennis]

Well you should know there aren't right or wrong answers, they are there to see how you think rather than a multiple choice right or wrong.

Then you can see they got the answers to some of the questions wrong to start with..

The balloon is free to swing, so when its stationary the CG will be above the mounting point of the string and when the truck accelerates the CG will lag behind the mounting point so the balloon will move away from the truck. It won't sway forwards until there is enough airflow to the rear to increase the pressure there which isn't there when the truck starts. It will then go forwards when the density of the air goes up a bit as its compressed at the rear.

Note Q8 "numbers 1 to 6 inscribed on each side" so each side has the numbers 1 to 6 on it. any roll will produce any number.

[Andy Burns]

I also used the "look for a 6" method (along with a sanity check that roughly 4 thousand squared is roughly 16 million) but they might have fooled us both by having e.g. a multiple choice of 15,998,600 when the correct answer would be none of the above.

[Apellation Controlee]

[Scion]

Mike Barnes put finger to keyboard:

Such as the one that states

"The office also contains a two-draw filing cabinet"

[Mike Barnes]

I spent a lot of time wondering about the "back of the truck" thinking they meant the back of the truck, when in fact they meant the goods compartment.

[Scion]

Mike Barnes put finger to keyboard:

It took me a while, too. And I got that one wrong - I still can't visualise how the balloon moves towards the front of the truck as the truck accelerates.

[Robin]

I am ashamed to say I got the balloon wrong.

But as this is a DIY group I hope we can all applaud the guy who produced this

[Martin Brown]

Then you would already have failed. It is a pattern matching test to spot that you can short circuit any mental arithmetic by spotting

(4000-20).(4000+20) = 4000^2 - 20^2

Not for scientists 1 mol = 24.3L at STP ~ 1kg/m^3

The test is as much about how you go about solving them and depending on how you answer the interviewer has ever more tricky questions up his sleeve. A would be mathematician would be expected to almost immediately write down the closed form solution here in the form

y = 1/2/(1-1/4) = 2/3

The pass mark for those is likely 100% for the institution concerned. They have other questions that are not well publicised and will use them on any candidates that can clearly ace these public ones.

Place 8 queens onto a chess board so they don't interact is another old favourite.

An incredibly hard one that is now so old and beyond modern maths teaching as not to give anything away is given the sides length a,b and d the diameter of the inscribed circle construct the triangle using only ruler and compasses (or compute it algebraically if you prefer).

Since classical straight edge and compass geometrical constructions are no longer taught (and haven't been for many decades) this question is almost unanswerable today in an interview situation even for geniuses.

[Dave Baker]

Helium is less dense than air which is why a balloon filled with it floats. As the truck accelerates the heavier air moves backwards so the lighter balloon is displaced and moves forwards.In effect it's still floating on the air albeit horizontally now rather than vertically.

Take a cup of coffee and float some small specs in it. The undissolved bits of milk powder tend to do that anyway. Stir the coffee. What happens? The floating bits move to the centre, not the outside where you might suppose centrifugal (centripetal?) force might take them. The heavier liquid moves out so the lighter floating bits move inwards. Same principle.

[dennis]

However from stationary the heavier air isn't at the back of the truck its still on the bottom and so the balloon doesn't go forwards. Its only after the heavier air has got to the rear that the balloon moves forwards. there for at the start of acceleration the balloon does not go forwards. The answer given is wrong.

When you start to stir the lighter bits get caught in turbulence and don't settle to the centre until sometime after you stop stirring.

[Scion]

Dave Baker put finger to keyboard:

My intuition says that the bottom of the string moves when the truck does, and inertia means that the rest of the string and the balloon don't immediately move.

And that's presumably why stirring coffee to dissolve sugar is less effective than swishing the spoon back and forth.

[dennis]

But unfortunately not what the question asked. You may have noticed it went back when he started the car, ie accelerated forwards.

[John Rumm]

Its one of those situations were its easier to ignore inertia and think of it as a rotated reference frame. Normally at rest there is gravitational pull straight down. Add acceleration forward, and you now have a reactive force pointing straight back. Add those vectors together and you get a vector pointing down and back. Now readjust your reference frame to point that vector back parallel to gravity, and the truck is pointing up at an angle. It should them be obvious where the balloon will float.

[John Rumm]

Yup.

I suppose that if these questions are given verbally, then it does add a bit of extra mental agility testing into the equation by use of mixed units.

I suspect they would be reconsidered for them in the circumstances ;-)