Page 16 | Maths test - to think Civil Service have it wrong?

Sharingaroomtinightthen · 2025-08-01T20:58:49+00:00

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?

BrickBiscuit · 02/08/2025 00:37

Sharingaroomtinightthen · 02/08/2025 00:30

What? 😂

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What indeed. 50% more people have voted ‘unreasonable’ than ‘reasonable’. Leaving aside that they may just think reporting is unreasonable while your solution is correct (it is), we have stumbled upon Kruger & Dunning (1999) being played out in the wild.

Merryoldgoat · 02/08/2025 00:38

I sadly don’t have a maths degree, but fully intend to get one when I retire, so more than happy to go back to school when I have the resources to do so. But what they won’t be teaching me is that the correct answer to that question is anything other than 225%.

Safe to say you should start witH a GCSE resit if that is manageable for you.

slashlover · 02/08/2025 00:38

HornungTheHelpful · 01/08/2025 23:56

No, the way you are approaching it is wrong. Tell me at which step you think I am wrong:

(a) If circulation after year 1 is X - and as we don’t know what it is we can’t put a figure in (this is what algebra is for),
(b) then after y2 it is 3X.
In y3 circulation drops by a quarter.
(c) So at end y3 the circulation is 3X - (1/4 * 3X), which is properly expressed as 3X -3/4X
(d) which is 2 and 1/4X or 2.25X

We need to express our answer as a %.
(e)100% is the figure at end y1 - that is what we treble in y2,
(f) so X = 100%
(g) we can now use our equation to get an answer - which is 2.25 * 100% which
(h) = 225%

I can tell you now, no step is wrong. But which one do you think is? You might also like to consider how likely it is the test is wrong. Not saying it can’t happen but would be very rare. You may want to take that with various analyses on here that actually think there is a correct answer given and try to understand why 225% is right. If you can’t, maybe night school?

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If X=100% and the final is 225%, how much has that increased? 125%

Original poster

Sharingaroomtinightthen · 02/08/2025 00:40

Horsie · 02/08/2025 00:37

@Samscaff

One hundred percent of 200 is 200.
Twice 200 is 400. That's not the same as 100 percent of 200.

It's an increase by virtue of the fact that we are adding over 100 percent of a quantity.

If you had 100 grapes, a portion of those grapes could only ever be less than 100 grapes, right?

The 25% is the increase.

200 x 1 = 200
25% of 200 is 50.
200 + 50 = 250. So a 25% increase of 200 is 250.

But we are not looking for an answer of 250.
We need an answer of 450.
We are looking for a percentage increase of 200 that fits 450. (200 + 225% is 450.)
The reason we're looking for 450 is because we needed to assign a numerical value (not a percentage) to the starting circulation. OP chose the starting number of papers sold to be 100 papers. It doesn't matter what starting number we use, because what matters is the percentage increases of whatever number we decide to start with.

Start of Year 1, the circulation is 100 papers
End of Year 1, the circulation is 200 papers, because it doubled from 100.
End of Year 2, the circulation is 600 papers, because it trebled from 200.
End of Year 3, the circulation fell by a quarter. That is, a quarter of 600.
600 minus one quarter is 450. (A quarter of 600 is 150. So 600 - 150 = 450.

The question asks by what percentage did the circulation increase from the end of Year One to the end of Year Three.

By assigning a numerical value to the starting circulation, 100 papers, we know that by the end of Year One the circulation is 200 papers and by the end of Year Three it's 450 papers.

When 200 papers increases to 450 papers, that's a 225% increase.

Edited

When 200 papers increases to 450 papers, that's a 225% increase.

No, it’s not.

450 is 225% of 200.

But it’s a 125% increase.

If you had 200 papers and someone increased them by 100%, you wouldnt still have 200, would you? You’d have 400.

OP posts:

HornungTheHelpful · 02/08/2025 00:41

Tandora · 02/08/2025 00:33

The question doesn’t ask you to calculate the percentage increase it asks you what was the percentage increase. **

now I’m completely lost 😂😂😂

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sorry - that may not be well expressed. It asks what is the % increase - I.e what is end y3 expressed as a % of end y1.

It doesn’t ask you to find the difference between end y3 and end y1 and then express that difference as a % of either the y1 or y3 figure - which is what op does.

I think that is the correct way to interpret the q, first, because that way you can pick an answer that is correct (dead give away that’s what’s required if you ask me 😉) but also because if you interpret the q the way op has it is ambiguous. Approaching it that way, the % increase needs to be expressed as a % of something. That could be of the y1 figure or y3 figure. Which should it be? You can’t answer without making an assumption that you do not have the information to make.

RawBloomers · 02/08/2025 00:44

HornungTheHelpful · 02/08/2025 00:31

This is where you are wrong. You say

“This is wrong. You need to calculate the percentage increase between X and 2.25X.
If you increase X by 100% you get 2X. By 125% you get 2.25X.”

The question doesn’t ask you to calculate the percentage increase it asks you what was the percentage increase. End Y3 is 2.25 times end Y1 so the percentage increase is, I’m afraid, 225% - as per @Horsie’s explanation.

What you have done is look at the difference between end y1 and end y3 and expressed that as a percentage of end y3 (I think, from memory). That is not what the question asks. There was no sanctimony in my post; you are obviously interested in this but are also wrong, and don’t seem to have the skill set to understand why. In those circumstances further education on this matter might be something you would enjoy?

I sadly don’t have a maths degree, but fully intend to get one when I retire, so more than happy to go back to school when I have the resources to do so. But what they won’t be teaching me is that the correct answer to that question is anything other than 225%.

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So hornung,

If y1 had a distribution of X and so did y2 and so did y3, what would the percentage increase between the end of y1 and the end of y3 be?

Original poster

Sharingaroomtinightthen · 02/08/2025 00:44

HornungTheHelpful · 02/08/2025 00:41

sorry - that may not be well expressed. It asks what is the % increase - I.e what is end y3 expressed as a % of end y1.

It doesn’t ask you to find the difference between end y3 and end y1 and then express that difference as a % of either the y1 or y3 figure - which is what op does.

I think that is the correct way to interpret the q, first, because that way you can pick an answer that is correct (dead give away that’s what’s required if you ask me 😉) but also because if you interpret the q the way op has it is ambiguous. Approaching it that way, the % increase needs to be expressed as a % of something. That could be of the y1 figure or y3 figure. Which should it be? You can’t answer without making an assumption that you do not have the information to make.

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It asks what is the % increase - I.e what is end y3 expressed as a % of end y1.

These are two different questions.

The percentage increase between 200 and 450 is 125%.

450 expressed as a percentage of 200 is 225%.

They are not interchangeable. It specifically asks for the increase.

OP posts:

Tandora · 02/08/2025 00:44

Horsie · 02/08/2025 00:37

@Samscaff

One hundred percent of 200 is 200.
Twice 200 is 400. That's not the same as 100 percent of 200.

It's an increase by virtue of the fact that we are adding over 100 percent of a quantity.

If you had 100 grapes, a portion of those grapes could only ever be less than 100 grapes, right?

The 25% is the increase.

200 x 1 = 200
25% of 200 is 50.
200 + 50 = 250. So a 25% increase of 200 is 250.

But we are not looking for an answer of 250.
We need an answer of 450.
We are looking for a percentage increase of 200 that fits 450. (200 + 225% is 450.)
The reason we're looking for 450 is because we needed to assign a numerical value (not a percentage) to the starting circulation. OP chose the starting number of papers sold to be 100 papers. It doesn't matter what starting number we use, because what matters is the percentage increases of whatever number we decide to start with.

Start of Year 1, the circulation is 100 papers
End of Year 1, the circulation is 200 papers, because it doubled from 100.
End of Year 2, the circulation is 600 papers, because it trebled from 200.
End of Year 3, the circulation fell by a quarter. That is, a quarter of 600.
600 minus one quarter is 450. (A quarter of 600 is 150. So 600 - 150 = 450.

The question asks by what percentage did the circulation increase from the end of Year One to the end of Year Three.

By assigning a numerical value to the starting circulation, 100 papers, we know that by the end of Year One the circulation is 200 papers and by the end of Year Three it's 450 papers.

When 200 papers increases to 450 papers, that's a 225% increase.

Edited

When 200 papers increases to 450 papers, that's a 225% increase.

except it’s not.

200 x 225% =450.

But this is not the correct calculation.

The calculation is :

(450-200)/200 x 100 =125%

WhatColourTiles · 02/08/2025 00:44

Horsie · 02/08/2025 00:37

@Samscaff

One hundred percent of 200 is 200.
Twice 200 is 400. That's not the same as 100 percent of 200.

It's an increase by virtue of the fact that we are adding over 100 percent of a quantity.

If you had 100 grapes, a portion of those grapes could only ever be less than 100 grapes, right?

The 25% is the increase.

200 x 1 = 200
25% of 200 is 50.
200 + 50 = 250. So a 25% increase of 200 is 250.

But we are not looking for an answer of 250.
We need an answer of 450.
We are looking for a percentage increase of 200 that fits 450. (200 + 225% is 450.)
The reason we're looking for 450 is because we needed to assign a numerical value (not a percentage) to the starting circulation. OP chose the starting number of papers sold to be 100 papers. It doesn't matter what starting number we use, because what matters is the percentage increases of whatever number we decide to start with.

Start of Year 1, the circulation is 100 papers
End of Year 1, the circulation is 200 papers, because it doubled from 100.
End of Year 2, the circulation is 600 papers, because it trebled from 200.
End of Year 3, the circulation fell by a quarter. That is, a quarter of 600.
600 minus one quarter is 450. (A quarter of 600 is 150. So 600 - 150 = 450.

The question asks by what percentage did the circulation increase from the end of Year One to the end of Year Three.

By assigning a numerical value to the starting circulation, 100 papers, we know that by the end of Year One the circulation is 200 papers and by the end of Year Three it's 450 papers.

When 200 papers increases to 450 papers, that's a 225% increase.

Edited

It really is not.

TimeForABreak4 · 02/08/2025 00:45

Jesus fucking christ I can't believe the people trying to work this out using algebra and getting the wrong answer then saying see you're wrong. It doesn't even need algebra!

Op, you are correct. I had an intray test for my previous job in a finance role. It was to spot 10 errors in a reconciliation. I spotted 12. When I went to the actual interview, the interview panel said "well done no one else spotted that and we hadn't even realised they were mistakes". So they aren't infallible.

slashlover · 02/08/2025 00:45

Horsie · 02/08/2025 00:11

No, she really isn't right. 125% of 200 is 250, not 450.

The correct answer is 225%.

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But it wants the INCREASE, so you're looking at the increase to 450 from 200. The increase is 250, which you calculated here to be 125%.

InWalksBarberalla · 02/08/2025 00:46

HornungTheHelpful · 02/08/2025 00:41

sorry - that may not be well expressed. It asks what is the % increase - I.e what is end y3 expressed as a % of end y1.

It doesn’t ask you to find the difference between end y3 and end y1 and then express that difference as a % of either the y1 or y3 figure - which is what op does.

I think that is the correct way to interpret the q, first, because that way you can pick an answer that is correct (dead give away that’s what’s required if you ask me 😉) but also because if you interpret the q the way op has it is ambiguous. Approaching it that way, the % increase needs to be expressed as a % of something. That could be of the y1 figure or y3 figure. Which should it be? You can’t answer without making an assumption that you do not have the information to make.

Show quote history

The question clearly asks what was the percentage increase in circulation - not what percentage is the final circulation to that at the end of year 1.

So the correct answer is 125%.

TimeForABreak4 · 02/08/2025 00:46

Horsie · 02/08/2025 00:37

@Samscaff

One hundred percent of 200 is 200.
Twice 200 is 400. That's not the same as 100 percent of 200.

It's an increase by virtue of the fact that we are adding over 100 percent of a quantity.

If you had 100 grapes, a portion of those grapes could only ever be less than 100 grapes, right?

The 25% is the increase.

200 x 1 = 200
25% of 200 is 50.
200 + 50 = 250. So a 25% increase of 200 is 250.

But we are not looking for an answer of 250.
We need an answer of 450.
We are looking for a percentage increase of 200 that fits 450. (200 + 225% is 450.)
The reason we're looking for 450 is because we needed to assign a numerical value (not a percentage) to the starting circulation. OP chose the starting number of papers sold to be 100 papers. It doesn't matter what starting number we use, because what matters is the percentage increases of whatever number we decide to start with.

Start of Year 1, the circulation is 100 papers
End of Year 1, the circulation is 200 papers, because it doubled from 100.
End of Year 2, the circulation is 600 papers, because it trebled from 200.
End of Year 3, the circulation fell by a quarter. That is, a quarter of 600.
600 minus one quarter is 450. (A quarter of 600 is 150. So 600 - 150 = 450.

The question asks by what percentage did the circulation increase from the end of Year One to the end of Year Three.

By assigning a numerical value to the starting circulation, 100 papers, we know that by the end of Year One the circulation is 200 papers and by the end of Year Three it's 450 papers.

When 200 papers increases to 450 papers, that's a 225% increase.

Edited

When 200 papers increases to 450 papers, that's a 225% increase.

Are you serious, no it is not 😂

Merryoldgoat · 02/08/2025 00:48

This is actually the intersection of poor literacy skills and poor numeracy, isn’t it?

I feel exhausted by the delusion on here. It’s not the not knowing either, it’s the absolute certainty they are correct in the face of very clear evidence to the contrary.

niadainud · 02/08/2025 00:48

Horsie · 02/08/2025 00:37

@Samscaff

One hundred percent of 200 is 200.
Twice 200 is 400. That's not the same as 100 percent of 200.

It's an increase by virtue of the fact that we are adding over 100 percent of a quantity.

If you had 100 grapes, a portion of those grapes could only ever be less than 100 grapes, right?

The 25% is the increase.

200 x 1 = 200
25% of 200 is 50.
200 + 50 = 250. So a 25% increase of 200 is 250.

But we are not looking for an answer of 250.
We need an answer of 450.
We are looking for a percentage increase of 200 that fits 450. (200 + 225% is 450.)
The reason we're looking for 450 is because we needed to assign a numerical value (not a percentage) to the starting circulation. OP chose the starting number of papers sold to be 100 papers. It doesn't matter what starting number we use, because what matters is the percentage increases of whatever number we decide to start with.

Start of Year 1, the circulation is 100 papers
End of Year 1, the circulation is 200 papers, because it doubled from 100.
End of Year 2, the circulation is 600 papers, because it trebled from 200.
End of Year 3, the circulation fell by a quarter. That is, a quarter of 600.
600 minus one quarter is 450. (A quarter of 600 is 150. So 600 - 150 = 450.

The question asks by what percentage did the circulation increase from the end of Year One to the end of Year Three.

By assigning a numerical value to the starting circulation, 100 papers, we know that by the end of Year One the circulation is 200 papers and by the end of Year Three it's 450 papers.

When 200 papers increases to 450 papers, that's a 225% increase.

Edited

That was a very long-winded way to arrive at the wrong answer...

carryingawatermelon · 02/08/2025 00:49

OP is correct.

The ‘year 3 end’ value is 225% of the ‘year 1 end’ value (and presumably what the examiner meant to ask).

But the percentage increase between those two figures is 125%.

Just as an increase of 100% means we double the original value, which is the same as a new value which is 200% of the original.

Myalternate · 02/08/2025 00:50

450 (final figure) less 200 (initial figure) = 250 difference
250(diff)/200 (initial figure) = 1.25 x 100 = 125%

niadainud · 02/08/2025 00:50

HornungTheHelpful · 02/08/2025 00:33

I love how you’ve confidently said this without tacking your mathematical colours to your mast 🤣

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Haha! Yes, fair point. The answer is 125%, as the OP says.

InWalksBarberalla · 02/08/2025 00:53

I wonder if the people who think it's 225% would be happy if their boss gave them a 5% pay rise to suddenly find their £1000 income has decreased to £50. Because apparently using multiplication is how you calculate a percentage increase.

slashlover · 02/08/2025 00:54

Start of Year 1, the circulation is 100 papers
End of Year 1, the circulation is 200 papers, because it doubled from 100.
End of Year 2, the circulation is 600 papers, because it trebled from 200.
End of Year 3, the circulation fell by a quarter. That is, a quarter of 600.
600 minus one quarter is 450. (A quarter of 600 is 150. So 600 - 150 = 450.

The circulation was 200.
If there was a 10% increase it would be 220.
If there was a 25% increase it would be 250.
If there was a 50% increase it would be 300
If there was a 100% increase it would be 400
If there was a 125% increase it would be 450.

It's 125%.

Samscaff · 02/08/2025 00:55

Horsie · 02/08/2025 00:37

@Samscaff

One hundred percent of 200 is 200.
Twice 200 is 400. That's not the same as 100 percent of 200.

It's an increase by virtue of the fact that we are adding over 100 percent of a quantity.

If you had 100 grapes, a portion of those grapes could only ever be less than 100 grapes, right?

The 25% is the increase.

200 x 1 = 200
25% of 200 is 50.
200 + 50 = 250. So a 25% increase of 200 is 250.

But we are not looking for an answer of 250.
We need an answer of 450.
We are looking for a percentage increase of 200 that fits 450. (200 + 225% is 450.)
The reason we're looking for 450 is because we needed to assign a numerical value (not a percentage) to the starting circulation. OP chose the starting number of papers sold to be 100 papers. It doesn't matter what starting number we use, because what matters is the percentage increases of whatever number we decide to start with.

Start of Year 1, the circulation is 100 papers
End of Year 1, the circulation is 200 papers, because it doubled from 100.
End of Year 2, the circulation is 600 papers, because it trebled from 200.
End of Year 3, the circulation fell by a quarter. That is, a quarter of 600.
600 minus one quarter is 450. (A quarter of 600 is 150. So 600 - 150 = 450.

The question asks by what percentage did the circulation increase from the end of Year One to the end of Year Three.

By assigning a numerical value to the starting circulation, 100 papers, we know that by the end of Year One the circulation is 200 papers and by the end of Year Three it's 450 papers.

When 200 papers increases to 450 papers, that's a 225% increase.

Edited

"When 200 papers increases to 450 papers, that's a 225% increase".
No, it isn’t. That is not how to work out % increases. You have to take the increase as a % of the starting figure, e.g. if sales rose from 200 to 300 that would be a 50% increase. If sales rose to 400 (doubled) that is a 100% increase.

If you were told unemployment had increased by 100% from last year's figures, would you not agree that would mean unemployment had doubled?

Out of curiosity, what would you say a 100% increase, from a starting figure of 200 papers, would be, then?

Firenzo · 02/08/2025 00:55

How does one go about nominating a thread for Classics?

Anyone taken the name Team125 yet?

niadainud · 02/08/2025 00:58

summertimeinLondon · 01/08/2025 23:24

@Sharingaroomtinightthen Re whether to tell them….I personally would have to. It would niggle away at me otherwise!

HOWEVER — I have many times been told that the civil service, even for (especially for) the nicher fast stream roles, doesn’t like people to be too clever. 2:1s are preferred to Firsts; team workers to geniuses, leaders, mavericks or those whose thinking style is a little too intellectual or individualist. (Even when I have several times been a referee for civil service developed vetting, the vetters are very keen to check that the candidate is not too intellectual/too much of an individualist, and the successful ones are generally even now still the good eggs who are bright but not too bright, follow the rules and take instruction from management, rather than people who go out of their way to make a stand on being right or point out where their managers are wrong….)

On this basis, maybe you shouldn’t stick your neck out to point out that the test is wrong 😆 That is, if you want the job…?

The poster above complaining about the public sector was being egregious, but in all seriousness there might be something in that. If the test being wrong annoys you (and it would annoy me — and I’m not a good fit for the CS because I always have to point out where I’m right and someone in authority is wrong 😆) — might you genuinely be better off doing something in private sector consultancy or third sector or similar, where you can follow your more individual instincts, rather than the civil service, where you’re very much trained to suppress them?

Edited

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This is interesting. I know two people who joined the Civil Service fast stream. One has a starred first from Cambridge and the other has a PhD in astrophysics.

HappyNewTaxYear · 02/08/2025 01:01

HornungTheHelpful · 02/08/2025 00:41

sorry - that may not be well expressed. It asks what is the % increase - I.e what is end y3 expressed as a % of end y1.

It doesn’t ask you to find the difference between end y3 and end y1 and then express that difference as a % of either the y1 or y3 figure - which is what op does.

I think that is the correct way to interpret the q, first, because that way you can pick an answer that is correct (dead give away that’s what’s required if you ask me 😉) but also because if you interpret the q the way op has it is ambiguous. Approaching it that way, the % increase needs to be expressed as a % of something. That could be of the y1 figure or y3 figure. Which should it be? You can’t answer without making an assumption that you do not have the information to make.

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THIS

niadainud · 02/08/2025 01:03

Merryoldgoat · 02/08/2025 00:48

This is actually the intersection of poor literacy skills and poor numeracy, isn’t it?

I feel exhausted by the delusion on here. It’s not the not knowing either, it’s the absolute certainty they are correct in the face of very clear evidence to the contrary.

I suppose if you suffer from the afore-mentioned intersection of poor literacy and poor numeracy you're not going to appreciate said evidence to the contrary, regardless of its undeniable clarity.

I'm also finding it exhausting.