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?

No, it leaves 125%.

If you start with £5 you’d have £10 by the end of year 1. So the number for the first part of the question, the end of year 1, is £10.

It then trebles to £30 in year 2.

Then by the end of year 3 it has fallen by a quarter to £22.50.

The question wants the percentage increase between £10 and £22.50. It doesn’t matter what came before or after. It’s always 125%.

True though. The disparity between the private and public sectors is astounding.

But the question asks what the increase is from the end of year 1.

So the starting point in your example is 40 (not 20) and we’re being asked to express the growth from 40 to 90 as a percentage.

50 is 125% of 40. The OP is correct.

Oh I can see it when you put it this way!

Yes, it increases 200% from 100% to the 300%

But the answer should be calculated from 40 (at the end of year 1). And 90 is 125% increase on 40.

Ok, so let's pretend the circulation at the start was 250,000.
That means at the end of year one it was 500,000.
Then in the next year (year 2) it trebled, so 1,500,000.
But then it fell by a quarter by the end of year 3. So we are at 1,125,000.
So the increase from end of year one (500,000) to end of year 3 (1,125,000) is 625,000. That is 125%

It is poorly worded. I would have gone for 225%. Final is 225% of the original. But agree the increase is therefore 125

It’s the difference between 40 at end of year 1 and 90 at end of year 3 which is relevant.
difference of 50 over original of 40 is 125%

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.

But £200 at YE1 is 100%

450/200

225/100

Proof the maths:

£200 × 225% = £450

While
£200 × 125% = £250

You're right op. It's not the percentage (225%), it's the percentage increase (225-100=125%)

20 doubles to 40 at the end of year 1.

That trebles 120 in year two.

Falls by a quarter to 90 by the end of year three.

The difference between 40 (not 20, it is asking about the end of year one) and 90 is 125%. It will not change whatever numbers are applied.

The person who tried it starting with 20 - the question is asking the difference between the 40 and 90, so 125% increase. It’s from the end of year 1 (40) not the start (20)

This is not correct working out.

I think you are wrong because you are trebling the wrong thing, you are trebling 100. When you need to be trebling 200. At the end of the first year you have 200% not 100%

you cant have two different answers one from assigning numbers and one from not assigning numbers! If the answer 125 is correct when you assign numbers, it also has to be correct when you don't.

It got to 200% by the end of year 1.

This 200% then becomes the starting point (so 100%)

Because you've already started the first equation, you know that it went

Y0 £100

Y1 £200 (200% of £100)

Y2 £600 (300% of £200)

Y3 £450 (£150 being 25% of £600)

You start the next part

Y1 £200
Y3 £450

£400 is 200% of £200
£50 is 25% of £200

200+25 is 225.

ANS: 225%

CHECK: £200 x 2.25 (so 225%) = £450

It is 225%

To check that this is correct multiple £200 (end of year 1) by 225% (or by 2.25 if you don't have a calculator with that function) and the answer you get is £450 (end of year 3)

I think it is a bit confusing as people might try to calculate £250 (the difference between end of year 1 and end of year 2) as a percentage of £200 (end of year 1) and then you get 125%
[(250÷200) x 100 = 125]

With the method that gets 225% as answer you are finding the percentage which £200 increased by to get to £450

With the method that gets 125% as answer you are finding what percentage the difference is of the end of year 1 amount.

So there is a subtle difference between what is being asked for a and what can be interpreted.

What can be useful in these scenarios if answer you are sure of not there, look for the answer that is closest and see if you can work out how that answer could be calculated.

200 is the start value
450 is the end value
450/200 = 2.25

2 and a quarter times 200 = 450

It is 225% @Sharingaroomtinightthen

if you want to break it down then:

100% = 200
200% (or 2 x 200) =400
25% of 200 = 50
225% of 200 = 450

You’re talking about irrational numbers but can’t work this out to be 125%?

But 200 increasing by (not multiplied by) 125% is 450.

There are 2 people with first class degrees in Maths in my household. Initially A said 125% and B said 225%. When A attempted to explain why it was 125% B changed their answer to “er, dunno,” which is probably because they are on their way to bed.

IMO the second sentence would be clearer if there were a comma after ‘trebled’ or if it began with ‘In”.

It’s been a long time since I’ve done any maths but…

It’s 125 %

Either way, I think they must want you to enter 225 so it's up to you if you do or not, assuming there's no text box to explain 125.

https://www.bbc.co.uk/bitesize/guides/zpjmjty/revision/2

This link explains how to calculate a % change and is consistent with the OPs calculation.

You're right OP, percentage increase is 125%.

(450-200)/200 = 1.25
1.25 * 100 = 125 %