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Original poster

Maths test - to think Civil Service have it wrong?

1000 replies

Sharingaroomtinightthen · 01/08/2025 21:58

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?

Maths test - to think Civil Service have it wrong?
OP posts:
Thread gallery
12
Original poster
Sharingaroomtinightthen · 01/08/2025 22:31

AnSolas · 01/08/2025 22:25

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

It does not matter what happens before the end of year one. The question wants the increase from the end of year one to end of year three.

OP posts:
Lemniscate8 · 01/08/2025 22:31

Ohnobackagain · 01/08/2025 22:28

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

Edited

225, the n take away the 100 because you are being asked for the difference, so 125, I make it

RafaistheKingofClay · 01/08/2025 22:31

AnSolas · 01/08/2025 22:25

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

It’s asking for the % increase not for what % of the end of year 1 sales the end of year 3 sales were.

One is comparison of the two numbers and the other finding the difference between the them.

ShesTheAlbatross · 01/08/2025 22:32

Ohnobackagain · 01/08/2025 22:28

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

Edited

Increasing by is not the same as multiplied by.

100 multiplied by 100% is 100
100 increasing by 100% is 200.

The question asks what it increases by. Not what percentage of the original the end number is.

SeaShellsSanctuary1 · 01/08/2025 22:33

You are looking at it wrongly. You have to look at growth rate over time.

So with your 200 in at end of year one it trebled to 600 or 300%.

Now drop your 600 by a quarter to take it to 450. That growth is 0.75%.

Therefore the growth from end of year one to end of year 3 is 300% - 0.75% which is 225%

Ohnobackagain · 01/08/2025 22:33

@Lemniscate8 pretty sure they want to know the second value as a percentage of the end year 1 value, so as a % of 200. In which case 450 is 2.25 x (or 225% of) 200

Original poster
Sharingaroomtinightthen · 01/08/2025 22:34

NeverDropYourMooncup · 01/08/2025 22:27

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

£400 is an 100% increase on £200, not 200%.

OP posts:
ShesTheAlbatross · 01/08/2025 22:34

Ohnobackagain · 01/08/2025 22:33

@Lemniscate8 pretty sure they want to know the second value as a percentage of the end year 1 value, so as a % of 200. In which case 450 is 2.25 x (or 225% of) 200

Edited

I think that’s what they think they want to know.

It’s not what they’ve written.

5foot5 · 01/08/2025 22:34

This thread will be so frustrating if we never get any feedback from the people who set the question.

Just for once it would be good if this thread got taken up by a journalist!

LegleEagle · 01/08/2025 22:34

Ohnobackagain · 01/08/2025 22:28

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

Edited

You are using that calculation to confirm the final circulation figure. The question is not about that. It asks you to calculate the growth in circulation as a percentage.

In your example, the growth is from 200 to 450 - ie an increase of 250.

250 is 125% of 200. The increase is 125% of the figure at the end of year one. The final figure is 225% of the circulation at the end of year one, but that is not what the question asks.

Original poster
Sharingaroomtinightthen · 01/08/2025 22:35

lucertola28 · 01/08/2025 22:28

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.

The question asks for the percentage increase between end of year one and end of year three. It is 125%.

OP posts:
irredeemablyperfidious · 01/08/2025 22:35

@StrokeCity , that’s the answer to the instruction “Express the circulation at the end of year 3 as a percentage of the circulation at the end of year 1.”

What level of the Civil Service is this intended for?

cakeorwine · 01/08/2025 22:36

I agree:

If I have £200 and I increase it by 100% I have £400. Because 100% of £200 is £200.

I I increase it by 125%, then I add £250 because 125% of £200 is £250

Original poster
Sharingaroomtinightthen · 01/08/2025 22:36

Ohnobackagain · 01/08/2025 22:28

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

Edited

The percentage increase between £200 and £450 is 125%, not 225%.

OP posts:
Lemniscate8 · 01/08/2025 22:37

Ohnobackagain · 01/08/2025 22:33

@Lemniscate8 pretty sure they want to know the second value as a percentage of the end year 1 value, so as a % of 200. In which case 450 is 2.25 x (or 225% of) 200

Edited

I dont think so because you are being asked the INCREASE, ie the difference

????

Original poster
Sharingaroomtinightthen · 01/08/2025 22:38

StrokeCity · 01/08/2025 22:30

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

The percentage increase between 2x and 4.5x is 125%, not 225%.

OP posts:
LegleEagle · 01/08/2025 22:38

Would be interested to know where any MN mathematicians fall on this. I have an A level and use maths quite a bit in my job and it seems obvious to me that the OP is right, but are there any holders of maths degrees / professional mathematicians out there?

NaicePeachJoker · 01/08/2025 22:38

SeaShellsSanctuary1 · 01/08/2025 22:33

You are looking at it wrongly. You have to look at growth rate over time.

So with your 200 in at end of year one it trebled to 600 or 300%.

Now drop your 600 by a quarter to take it to 450. That growth is 0.75%.

Therefore the growth from end of year one to end of year 3 is 300% - 0.75% which is 225%

Edited

600 is a 200% increase on 200. Each 200 is a 100% increase. If something increases by 100% it’s doubled.

Ohnobackagain · 01/08/2025 22:38

@Lemniscate8 and @Sharingaroomtinightthen yes you’re right! I mis-read it (Friday night drink, hic!)

YanTanTetheraPetheraBumfitt · 01/08/2025 22:38

I agree OP, 125%.

Ohnobackagain · 01/08/2025 22:39

@Sharingaroomtinightthen yes you’re right

NeverDropYourMooncup · 01/08/2025 22:39

Sharingaroomtinightthen · 01/08/2025 22:34

£400 is an 100% increase on £200, not 200%.

Show quote history

200 is 100% of 200.

400 is 200% of 200.

That's where you went wrong.

Original poster
Sharingaroomtinightthen · 01/08/2025 22:40

SeaShellsSanctuary1 · 01/08/2025 22:33

You are looking at it wrongly. You have to look at growth rate over time.

So with your 200 in at end of year one it trebled to 600 or 300%.

Now drop your 600 by a quarter to take it to 450. That growth is 0.75%.

Therefore the growth from end of year one to end of year 3 is 300% - 0.75% which is 225%

Edited

No, the percentage increase between £200 and £450 is 125%.

OP posts:
Gagagardener · 01/08/2025 22:40

The answers you can choose from are: 150, 225, 450, 550, and 650.

cakeorwine · 01/08/2025 22:41

If you increase £100 by 10%, you get £110. So £110 is 10% more than £100. What it isn't is 110% more than £100.

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