Maths question - Civil Service is wrong (we now have 100% more threads about the subject)

[Sharingaroomtinightthen]

When I posted late last night I thought I’d get maybe half a dozen replies confirming the question didn’t have the correct answer and advising whether to tell the Civil Service recruiters. But here we are 1000 posts later.

https://www.mumsnet.com/talk/am_i_being_unreasonable/5384347-maths-test-to-think-civil-service-have-it-wrong

200 to 600 trebles circulation. Yes. The amount of increase is 400. Yes.

As a percentage of the base, 200, that amount of increase is only 200%.

As others have also pointed out, it seems the effect uncovered by Kruger & Dunning (1999) applies. Comprehension is the key. The question is unambiguous, though a bit complex. I suppose a misreading of the question is one way to be convinced one has the correct solution. Even where the error is wholly mathematical, comprehension come in. For example, ‘percentage increase’ does not mean ‘percentage’ or ‘total’.

My post just above was for @Spiderbitebatbite and should conclude

’that percentage is only 200%, not 300%’

This was all in reference to her ‘explanation’ for someone else earlier

Unicorns, actually

Ffs - unicorns are MYTHICAL CREATURES. They can’t possibly be the answer.

Get it together @poetryandwine

Students, too

Super example

… though I should have said “last year you got …” and "this year you get …”, as I have a year in the middle where nothing happens. Or maybe said ‘year 1’ and ‘year 2’. Oh forget it, the 225 or 450% brigade aren’t going to get it anyway, are they?

TBF the very first number at the beginning if Y1 is 100. I don’t recall any quantity of 50 however

The question doesn't give any quantities. Just proportions.

You can substitute your own quantities - the proportions will be the same regardless of what they are.

But it's probably one of those MCQ tests where the only option is to tick a box and it's then marked by a computer.

It wouldn't be possible to make a comment

Ah yes, my mistake.

There is no number at the beginning of Y1!

Hang on, I made that joke at 09:46! What is my prize?

Students of what, though? Not maths, surely...

Just out of interest as I was trying to do this in my head last night in bed at 1.30 am!...

I'm in the 125% camp BUT, if one did it another way and started off with a 200% increase (from the end of year one to the end of year two) and then DEDUCTED the decrease from end of year two to the end of year three, how would one do this?

Sales fell by a quarter in year three, so if one deducted this decrease from the 200% increase, would that not make it 175% net increase in the relevant period?

Basically...what is the calculation that one should do?

Maths not particularly my strength but my calculations seemed to agree with OP - 125%. So I asked AI and got this:

The question asks for the percentage increase from the end of Year 1 to the end of Year 3:Year 1 ending: 200 unitsYear 3 ending: 450 units Increase: 450 - 200 = 250 units Percentage increase: (250/200) × 100% = 125%

However, 125% isn't among the options. Let me double-check by looking at the closest answer: 225%.

If we calculate what percentage 450 is of 200: (450/200) × 100% = 225%

This represents the total value as a percentage of the original, not the increase. The actual percentage increase should be 125%, but given the available options, 225% appears to be the intended answer, likely representing the final circulation as a percentage of the Year 1 circulation rather than the pure increase.

Sorry - just checking your question:

Y0 = x
Y1 = 2x
Y2 = 6x
Y3 = 4.5x

Which change are you trying to calculate? I don’t understand your wording.

The only real answer is to cancel the cheque

Are we playing Duke of Croydon rules?

Dollis Hill.

I’m not great at maths so this is a genuine question. I don’t get how we got to 125%. I think it’s 150%. Can someone explain why the below is wrong?

Year 0-1 produces the “amount”. Let’s call it A.

Year 1-2 doubles A, therefore A increases by 100%

Year 2-3 trebles A, therefore A increases by 200%

Year 3-4 reduces A by a quarter of A. A is 200% therefore reducing it by a quarter would reduce it by 50% to 150%. So the answer is 150%.

Y1 to y2 percentage increase :200%
Y2 to y3 real number decrease is 150 (25% of 600), and you've got to represent this as a percentage of y1 end value (200), so 75%
Therefore 200%-75%=125

Try that with numbers.
Start A as 100.
See what numbers you end up with.
You will either find your error or we can help you see it.

The circulation is a "point in time" number not the total over a year. It's also cumulative. So doubles: A becomes 2A. The trebles: 2A becomes 6A. Reduces by a quarter: 6A becomes 4.5A. You've taken one quarter off the previous year's increase and failed to take one quarter off the circulation that was already happening before the increase.

So it could be like this:

On 1 Jan 2001 the circulation was 50,000.

It doubled in the first year so circulation on 31 Dec 2001 was 100,000.

The it trebled in the second year, so circulation on 31 Dec 2002 was 300,000.

Then it reduced by a quarter, so circulation on 31 Dec 2003 was 225,000.

How much did it increase from the end of the first year to the end of the third year? 100,000 to 225,000 is an increase of 125,000, which is fairly obviously a 125% increase.

Think of the starting amount as x - the progression is as follows

Y0 = x
Y1 = 2x (doubled at end of year 1)
Y2 = 6x (trebled the y1) amount
Y3 = 4.5x (reduced the y2 amount by 25%)

The question asked for the percentage from end of year 1 to end year 3.

First you calculate the difference

4.5x - 2x = 2.5x

to get the percentage increase you take the increase, divide by the starting value and multiply by 100

2.5x / 2x X 100
= 1.25 X 100

= 125%