Maths test - to think Civil Service have it wrong?

[Sharingaroomtinightthen]

I’ve just applied for a Civil Service test. Part of it is passing a numerical test.

This is the question.

The answer is 125%. I’m sure of it.

If you start with £100, and in the first year it doubles it’s £200. So at the of year one it’s £200.

In year two it trebles to £600.

It then falls by a quarter in the third year to £450.

So end of year 1 - £200.

End of year 3 - £450.

It’s increased by 125%.

125% isn’t an answer option.

WIBU to email and tell them they’ve got it wrong?

225 % 0f 200 is 450. Or 450 as a % of 200 is 225.
O level maths 1985 😂

Let C be the circulation at end of yr 1
At end of yr 2 the circulation is 3C
At end of yr 3 the circulation is
3C - 3C/4

The question refers to the INCREASE in circulation, between end of yr 1 and end yr 3, which is: (3C - 3C/4 ) - C = 1.25C
So the increase is 125%

I'm with the OP.

% increase is worked out by (new-original)/original x 100%
So in this case (450-200)/200 x 100%
So 250/200 x 100 % = 125%.

So I think either the question is incorrectly worded or the answer is wrong.

(My credentials such as they are are an ancient maths degree and recently helping DD with her maths GCSE.)

The bit you are all getting wrong is the trebling in the 2nd year

Note it doesn’t say it trebled FROM THE END OF YEAR 1 FIGURE. It trebled from the original starting value i.e. 100

So at the end of Year 2 it was 300.
It then dropped by a quarter to 225…

It’s a classic case of reading the question carefully.

The fact that it doubled after one year is completely irrelevant to the question (yet everyone is treating this figure as the one to treble)

Start - 100
End of Year 1 - 200 (Doubled)
Next year - 300 (Trebled)
End of third year - 225 (Fallen by a quarter)

Think this through. I'm following your logic here:

100% of 200 is 200. Or 200 as a % of 200 is 100

So by your logic if something changes from 200 to 200 it has increased by 100%. Which it obviously hasn't.

'What percentage of the original' is not the same as 'percentage increase'.

You may well be correct that is what they mean but in that case the question is badly worded!
If I say Take a number, double it, then treble it I would be at 6x.
If they don't want to use the end of the first year for the statement re the second year they should say 'compared with the start' or similar. imo.

I think you are right, and thanks for a clear explanation. It's a shame the question isn't more clear. Giving the increase in Year 1 is irrelevant and misleading. If the question just said the circulation had trebled by the end of Year 2, then fell by a quarter, the answer would be easy.

😆

Hang on though, That can't be right.

If @Mum57756908742136890 is asserting that 225 is the correct end figure, then for %increase from end of first year we would have

final-original/original x 100% (225-200)/200 x100% = 12.5% which still isn't an option.

Let the initial circulation be xxx.
End of Year 1:Circulation doubled, so:
Circulation=2x\text{Circulation} = 2xCirculation=2x
End of Year 2: Circulation trebled, so:
Circulation=3×2x=6x\text{Circulation} = 3 \times 2x = 6xCirculation=3×2x=6x
End of Year 3: Circulation fell by a quarter, so it became:
Circulation=6x×(1−14)=6x×34=18x4=4.5x\text{Circulation} = 6x \times \left(1 - \frac{1}{4}\right) = 6x \times \frac{3}{4} = \frac{18x}{4} = 4.5xCirculation=6x×(1−41)=6x×43=418x=4.5x
Now, compare the circulation at the end of Year 1 (2x) and end of Year 3 (4.5x):
Percentage increase=4.5x−2x2x×100=2.5x2x×100=1.25×100=125%\text{Percentage increase} = \frac{4.5x - 2x}{2x} \times 100 = \frac{2.5x}{2x} \times 100 = 1.25 \times 100 = \boxed{125%}Percentage increase=2x4.5x−2x×100=2x2.5x×100=1.25×100=125%

Chatgpt says 125%

The thread is too long to see whether anyone’s already offered OP but I’m a CS and very happy to flag it to whoever’s commissioned the test. There are some very concerning replies here!

I've worked it out. Finally.

This is Civil Service.
The answer is whatever the politicians want it to be.
Like Big Brother.

Of course its not correct. I figured that was a troll post.

An increase from 200 to 225 is not a 225% increase.

This is so wrong. You didn't stick to your own erroneous premise that all changes are compared to the base number of 100 because it is impossible to do so.
year 1- 1 x100
year 2 -3x100
year 3- 0.75x100

You flipped and compared year 3 to year 2.
None of these numbers would give 225% as the answer anyway.

The question is what percentage increase from 200 to 450, not 450 of 200 expressed as a percentage.

The OP is correct.

They've clearly worded that question incorrectly. It's not "ambiguous" - it's just completely wrong.

They explicitly asked for the percentage increase between the distribution at those two points in time.

The only way that one of their offered answers could be considered correct is if, instead of asking for percentage increase they'd asked for the answer to be expressed as a percentage of the distribution at the end of year 1. That would give you 225%. However, because they said percentage increase, all their offered answers are fundamentally mathematically incorrect.

This is an old question, and had been in use since about 1950.

You start with the average number of regional newspapers per capita in 1950 (0.25), multiply by the number of counties in England (48), then subtract the number of national broadsheets still in print (5):

$ 0.25 x 48 = 12
12 - 5 = 7

Now, multiply by the number of minutes it takes to read a weekday edition cover-to-cover (approx. 18), and divide by the number of minutes spent reading headlines only (approx. 1.008):

(7 x 18)/1.008 = 125

Therefore, the correct answer is 125%.

I suspect that's the standard/EO entry test rather than the fast stream test, and was probably supplied by an external company (it would have been Capita in the case of my department). And yes I would email the recruiters and let them know. There are several possible outcomes to that, none of which I think reflect badly on you. The first (and most likely) is that the person who gets your email forwards it on to whoever supplied the test for future correction as they see fit, and thinks no more of it. The second is that they say oh there's another comment that the test is wrong, forward it on and think no more of it. The third and least likely is that they tell the recruiting panel (and hopefully don't trigger the same display of dodgy maths that has appeared here). Even if they tell the panel though it's highly unlikely that it would impact on their discussions in a negative way. Disclaimer: I would positively welcome your feedback (possibly coloured by being on the other side of the process and having an argument with Capita about their marking of an exercise they supplied for the last big external recruitment I was involved in ...)

Give the answer they’re looking for them raise it at interview?

You’re absolutely right, and your breakdown is spot on:

• Start: £100
• End of Year 1 (doubled): £200
• End of Year 2 (trebled): £600
• End of Year 3 (falls by 25%): £450
• So, from end of Year 1 (£200) to end of Year 3 (£450):

(450 − 200) ÷ 200 × 100 = 125%

That’s a 125% increase, no more, no less.
I would flag this up!

That’s the bit I couldn’t work out.

Which figure it trebled from - the original or the doubled one.

😵

I think it's the written English that's wrong is the problem, not the math

What this all boils down to is the question;
How much is the increase from 100 to 225?

The increase is from the original 100 to the final 225.

They've just put this in there as a little taster of how frustrating life as a civil servant is..