Page 3 | Maths question - Civil Service is wrong (we now have 100% more threads about the subject)

Sharingaroomtinightthen · 2025-08-02T12:36:13+00:00

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

Samscaff · 02/08/2025 16:16

Truelyscrumptious21 · 02/08/2025 14:59

In my opinion the 125% answer you have all deemed as correct does not take into account the scaling up of how many newspapers 1% actually represents as sales grow yearly. My understanding of this equation is far more complicated than others and I think the previous thread of people berating others shows how dictators dampen down others just because they don’t come up with the same answers a bit like sheep. Some posters even made fun and seriously questioned another poster who I believe had the answer correct. Here goes. I expect to be roasted like others on the previous thread but I’ve tried my hardest to explain my working out as simple as I can! This is how I worked it out.

Using OP’s original 100 as a base.

Year 1 start 100 so

1 newspaper equals 1 %

Year 2 doubles to 200 so

2 newspapers equals 1 %

Year 3 triples so

6 newspapers equals 1%

A correction decreases by 25% so now the end calculation is

4.5 newspapers equals 1%

The difference between end of year 2 one % and end of year 3 one % is 4.5-2 which equals 2.5 newspapers per 1%.

The difference in sales end of year 1 end of year 3 450 minus 200 which is 250.

My calculation is as follows

450/250= 1.8 x 2.5= 4.5 x 100 = 450%

The answer according to my calculations is 450%

Edited

It makes absolutely no difference how many newspapers are represented by 1%. That’s why we use percentages. If half of a family of 6 are female and half of a population of 60,000,000 are female, the % of females in each entity is 50%.

As you say, using 100 as the original number, the difference in sales between the end of Y1 (the starting point of our "increase" calculation) and the end of Y3 (the end point of our "increase" calculation) is 250.

But your next calculation does not make sense. To know the % increase we need to calculate the increase as a % of the starting number. (If the cost of an item increases from £2 to £3, it has increased by half of the original £2, i.e. 50%. If it increases from £2 to £4, i.e. doubled, it has increased 100%.)

25 as a % of 200 is 12.5%
50 as a % of 200 is 25%
100 as a % of 200 is 50%
200 as a % of 200 is 100%
250 as a % of 200 is 125%.

The answer is 125%.

milveycrohn · 02/08/2025 16:18

If you start with 100
At the end if year 1 = 200
At the end of year 2 = 600
At the end of year 3 = 450
Percentage increase from end of year 1 to end if year 3 = 450/200 % =225

Sundaymorningcalla · 02/08/2025 16:18

Sundaymorningcalla · 02/08/2025 16:15

The answer is 225%

The question clearly states what is the net percentage increase from the end of year 1.

Disregarding the doubling of sales from year 1

End of Year 2 (relative to end of year 1) = 300%
End of Year 3 = End of year 2 * 0.75

What's your beef with the question?

Percentage increase is expressed as (change/original) * 100

Change is (1 x 3 x 0.75 / 1) x 100 which is 225%

Sundaymorningcalla · 02/08/2025 16:20

Samscaff · 02/08/2025 16:16

It makes absolutely no difference how many newspapers are represented by 1%. That’s why we use percentages. If half of a family of 6 are female and half of a population of 60,000,000 are female, the % of females in each entity is 50%.

As you say, using 100 as the original number, the difference in sales between the end of Y1 (the starting point of our "increase" calculation) and the end of Y3 (the end point of our "increase" calculation) is 250.

But your next calculation does not make sense. To know the % increase we need to calculate the increase as a % of the starting number. (If the cost of an item increases from £2 to £3, it has increased by half of the original £2, i.e. 50%. If it increases from £2 to £4, i.e. doubled, it has increased 100%.)

25 as a % of 200 is 12.5%
50 as a % of 200 is 25%
100 as a % of 200 is 50%
200 as a % of 200 is 100%
250 as a % of 200 is 125%.

The answer is 125%.

Show quote history

Percentage increase is expressed as (change/original) x 100. So your answer is incorrect.

TeenToTwenties · 02/08/2025 16:28

Sundaymorningcalla · 02/08/2025 16:15

The answer is 225%

The question clearly states what is the net percentage increase from the end of year 1.

Disregarding the doubling of sales from year 1

End of Year 2 (relative to end of year 1) = 300%
End of Year 3 = End of year 2 * 0.75

What's your beef with the question?

percentage increase is (new-original)/original x 100%.

you have done percentage of which is a different calculation

Dimondsareforever · 02/08/2025 16:28

Havnt seen the other thread … and not sure if I’m missing something. But the answer 450%?

Very simply - if it sold 10 in first year, then doubled in second year (20), then trebled (60), minus a quarter = 45.

The original 10 sold had increased by 450% by the end of the third year…..

Am I misreading the question? Don’t quite understand why all the fuss is about? And why would it need reporting??

Merryoldgoat · 02/08/2025 16:30

Sundaymorningcalla · 02/08/2025 16:20

Percentage increase is expressed as (change/original) x 100. So your answer is incorrect.

Show quote history

No - it’s the INCREASE as a percentage of the original

(new - original) / original x 100
(450 - 200) / 200 x 100

250/200 x 100

1.25 x 100

= 125

shocker.

Truelyscrumptious21 · 02/08/2025 16:32

Tryingtokeepgoing · 02/08/2025 15:52

But an increase is relative to a starting point, which in the case of the question posed was 200. Using the end point (450) is nonsensical and innumerate.

Thats before we break down your calculation, which broadly says: divide the end by the increase (450 / 250). And then multiply it again by the increase (2.5 x 100). Which, unsurprisingly, gives you the number you started with. Except you’ve put a % sign after it ;)

Show quote history

Okay let’s use a different number as a base

200

400

1200

900

Same calculation

Total sales difference 900-400 is 500

1 % difference from year 3 to year 2 is 9 minus 4 is 5

900/500 = 1.8

1.8 x 5 = 9

9 / 200 base = 4.5

4.5 x 100 =450%

All the other calculations don’t account for the number of sales increasing per 1% so they don’t use it in their final percentage increase.

Look try it with any number

50

100

300

225

225 minus 100 is 125

2.25 minus 1 is 1.25

225/125 = 1.8

1.8 x 1.25 =2.25 now because we started with 50 we times it by 2 and get 4.5 which x 100 is 450%

Look if it makes you all feel any better my DH and DC all think I am wrong too! They are adamant it’s 125% too.

Merryoldgoat · 02/08/2025 16:37

Am I misreading the question? Don’t quite understand why all the fuss is about? And why would it need reporting??

you are misunderstanding it

Y0 = x
Y1 = 2x (doubled)
Y2 = 6x (trebled)
Y3 = 4.5x (reduced by quarter)

Change from 1st year increase to end year 3 so what is the percentage increase where the starting amount is 2x (amount after first year increase) and 4.5x (amount at end of 3rd year)

the increase is 4.5x - 2x = 2.5x

The percentage change is the value of the increase (2.5x) divided by original amount (2x) multiplied by 100

2.5 / 2 x 100 = 125

Merryoldgoat · 02/08/2025 16:40

@Truelyscrumptious21

You can start with any number you like. If you don’t understand the maths you’ll never get the right answer.

TeenToTwenties · 02/08/2025 16:42

Dimondsareforever · 02/08/2025 16:28

Havnt seen the other thread … and not sure if I’m missing something. But the answer 450%?

Very simply - if it sold 10 in first year, then doubled in second year (20), then trebled (60), minus a quarter = 45.

The original 10 sold had increased by 450% by the end of the third year…..

Am I misreading the question? Don’t quite understand why all the fuss is about? And why would it need reporting??

Wrong two ways.

First they want to base on the end of the first year, not the start.

Then they want percentage increase, which is (new-original)/original x 100 and not new/original x 100%.

Truelyscrumptious21 · 02/08/2025 16:43

Merryoldgoat · 02/08/2025 16:40

@Truelyscrumptious21

You can start with any number you like. If you don’t understand the maths you’ll never get the right answer.

Well that could be said of any of the answers! At least I have a shot at being awarded the points from the exam because 450% is in the drop down menu and 125% isn’t 😂

PeachPumpkin · 02/08/2025 16:46

I’m not that great at maths. It was a nice boost to have calculated the answer as 125% and see that so many others agree. Thanks OP and good luck!

SerendipityJane · 02/08/2025 16:46

Bunnycat101 · 02/08/2025 15:22

You’d be wrong there about civil servants being rubbish at maths. There are some amazing analysts in the civil service doing incredibly clever data wizardry stuff in every department. ONS staff are civil servants as are HMRC staff. Staff working on the budget in Treasury likewise. Those departments will be very numerate.

Edited

So good at maths, but bad at humour ?

Merryoldgoat · 02/08/2025 16:46

Truelyscrumptious21 · 02/08/2025 16:43

Well that could be said of any of the answers! At least I have a shot at being awarded the points from the exam because 450% is in the drop down menu and 125% isn’t 😂

Edited

Show quote history

Can you honestly not accept that there could be an error in the question given all of the people who have clearly explained why?

Ooothatsagoodone · 02/08/2025 16:48

To calculate the percentage increase in circulation from the end of the first year to the end of the third year, we need to consider the initial circulation as 100% at the end of the first year.
At the end of the first year, the circulation doubled, so it became 200%.
In the second year, the circulation trebled, equalling 600%.
In the third year, the circulation fell by a quarter, which means it was reduced to 75% of the previous year, resulting in 75% of 600% = 450%.
Therefore, the percentage increase in circulation from the end of the first year to the end of the third year is 450% - 200% = 250%.

Samscaff · 02/08/2025 16:53

Dimondsareforever · 02/08/2025 16:28

Havnt seen the other thread … and not sure if I’m missing something. But the answer 450%?

Very simply - if it sold 10 in first year, then doubled in second year (20), then trebled (60), minus a quarter = 45.

The original 10 sold had increased by 450% by the end of the third year…..

Am I misreading the question? Don’t quite understand why all the fuss is about? And why would it need reporting??

An increase from 10 to 45 is not an increase of 450%. But that’s not what the question says happened with the figures, anyway! Yes, I’m afraid you are misreading the question.

Start with 10 at the end of Y1, if you like. Sales have already doubled, presumably from an absolute start number of 5, but we’re ignoring that because we’re being asked to calculate the increase from the end of Y1 to the end of Y3.

End of Y1 - 10
End of Y2 - trebles, so 30
End of Y3 - Reduces by a quarter, so 22.5

The increase is the difference between the end of Y1 and the end of Y3, which we were asked to express as a %. The difference is 22.5 - 10, which is 12.5.

12.5 as a percentage of our starting point (10) is 125%.

If your salary doubled, it would have gone up 100%. I expect you’d be happy to agree that if the sales in the question had doubled to 20, they would have gone up 100%. In fact they did a bit better than that.

OffOnOurHols · 02/08/2025 16:53

I think OP from some of the answers on this thread that it is evident that the standard of maths out there is appalling. I think I would have added another box to the end with the correct answer.

niadainud · 02/08/2025 16:56

99bottlesofkombucha · 02/08/2025 14:20

Your title is wrong! Because it’s 200% increase from zero threads op. And before the Mumsnet maths mafia come at me to say 0 x 200% is 0, I remind them that zero is a special number.

I assume this is a joke?

SerendipityJane · 02/08/2025 16:56

OffOnOurHols · 02/08/2025 16:53

I think OP from some of the answers on this thread that it is evident that the standard of maths out there is appalling. I think I would have added another box to the end with the correct answer.

It looked like an online test, and the radio buttons suggest that you had to select an answer before being able to move on.

And we haven't seen the guidance.

Reallybadidea · 02/08/2025 17:00

Ooothatsagoodone · 02/08/2025 16:48

To calculate the percentage increase in circulation from the end of the first year to the end of the third year, we need to consider the initial circulation as 100% at the end of the first year.
At the end of the first year, the circulation doubled, so it became 200%.
In the second year, the circulation trebled, equalling 600%.
In the third year, the circulation fell by a quarter, which means it was reduced to 75% of the previous year, resulting in 75% of 600% = 450%.
Therefore, the percentage increase in circulation from the end of the first year to the end of the third year is 450% - 200% = 250%.

You need to work out the percentage increase not just the change with a percentage sign after it!

Samscaff · 02/08/2025 17:01

You say we need to consider the initial circulation as 100% at the end of the first year.
At the end of the first year, the circulation doubled, so it became 200%.

This doesn’t make sense. Actually we don’t need to consider the doubling at all, because we are asked to calculate the % increase from the end of Year 1. The doubling during the first year should be disregarded - it’s a red herring.

The circulation increased from 200 to 450, an increase of 250.
250 as a % of our starting point of 200 is a 125% increase (if it had doubled to 400 that would have been a 100% increase, and it did a bit better than that.)

niadainud · 02/08/2025 17:03

MontyDonsBlueScarf · 02/08/2025 15:36

I'm thinking for next weekend's entertainment I might start a thread that depends on the difference between divided by and divided into.

Yes, anything containing the instruction "divide by a half" is sure to elicit several pages of innumerate nonsense responses similar to this thread.

Samscaff · 02/08/2025 17:10

Truelyscrumptious21 · 02/08/2025 16:32

Okay let’s use a different number as a base

200

400

1200

900

Same calculation

Total sales difference 900-400 is 500

1 % difference from year 3 to year 2 is 9 minus 4 is 5

900/500 = 1.8

1.8 x 5 = 9

9 / 200 base = 4.5

4.5 x 100 =450%

All the other calculations don’t account for the number of sales increasing per 1% so they don’t use it in their final percentage increase.

Look try it with any number

50

100

300

225

225 minus 100 is 125

2.25 minus 1 is 1.25

225/125 = 1.8

1.8 x 1.25 =2.25 now because we started with 50 we times it by 2 and get 4.5 which x 100 is 450%

Look if it makes you all feel any better my DH and DC all think I am wrong too! They are adamant it’s 125% too.

Edited

Show quote history

500 (the increase) as a % of your start point (200) is a 125% increase.

I think where you’re going wrong is in thinking that if you double a number it increases by 200%, when in fact it is 100%. If your salary increased from 40k to £80k that would be a 100% increase.

If sales doubled from 200 to 400 that would be a 100% increase. In fact they did a bit better than that, increasing not just by the same again (which would be 100%) but by one-and-a-quarter times. Which is 125%.

LegoLivingRoom · 02/08/2025 17:12

I am awful at maths (but good at literacy) and even I understand that it’s 125%.

Why are people sticking random % signs onto the end of their numbers when they are not percentages?