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

@NoCommentingFromNowOn

50

As question states start at 100 after doubling 50

100
300
150

300 - 100 = 200 which represents 300%

200 minus 25% is 150 which is a 150% increase from 100 start

300% plus 150% is a 450% increase

The answer is 450%

It might be easier for people if your starting point is 50.

So at the end of year 1 it has doubled to 100, then the maths look easier. It’s exactly the same as everyone has said, but because you start with 50 but the end of the first year is a nice round number (ie 100) then it feels simpler?

It’s still 125% but it might help visualise it?

Surely you can see that if the question is asking for the percentage increase, not the percentage total, the answer is going to be less than the total percentage?

My answer clearly demonstrates how I get to 450% over and over using different numbers the answer is always 450%. Just like others have bravely said and been berated for. There is an answer for 450% on the test which is an option for those of us who know how to work it out correctly would choose.

450% is the right answer.

Surely you can see if sales have trebled after year 2 the answer must be above 300% as a starting point! Work from there. I mean I concluded this after quickly reading the question.

The answer is 450% all you sheep can keep harping on about it being 125 % it won’t change the fact you are wrong and the glaringly obvious exclusion of this even being an option to pick says it all.

300% plus 150 % equals 450%

Why on earth would you add these two numbers? What is that telling you?

@Spiderbitebatbite Permit me an analogy.

Step 1: I gather a crate of bottles of milk and an empty bucket.

Step 2: I pour a pint of milk into the bucket. One bottle is now missing from the crate. The bucket has 1 pint in it.

Step 3: To treble the amount in the bucket, I pour in two more pints. The bucket has increased to 3 pints. But it has only two more pints than in step 1. The increase is 2 pints. The crate has three bottles missing. But only two bottles have gone since step 1. I have taken two bottles to increase the bucket. An increase of two bottles.

In Step 3, I have increased the milk in the bucket by 200%. The total in the bucket is 300% of what I ended Step 2 with.

Increase 200%, total 300%.

Nooo.

Assume sales to be 100 at the start, so 200 at the end of yr1. If the percentage increase between end of year 1 and end of year 3 were 450% then the sales at the end of year 3 would be 900 and they aren't.

I'm not a mathematician but assumed the starting circulation was 100. It doubles (100% increase) to 200 by end of yr 1. That 200 then trebles (300% increase) to 600 end of yr 2. Then drops by 25%. 25% of 600 is 150 so the end of yr 3 amount is 450.

The end of yr 1 figure was 200 so the difference between them is 250. What is the percentage increase, not quantity increase between 200 and 450? It's 125%. If you increase 200 by 125% you get 450. So the answer is 125%.

I can't work out why you are adding 300% and 150%.

I never thought that any thread would surpass the 'gmail has given my gmail address to someone else but with a dot in it and I'm getting the emails" thread for sheer repetition of utterly WRONG but here we are...

I had to quit reading the OP's original thread because the number of people insisting that they had come up with the "correct" explanation for it being 225% was depressing me more than I thought possible!

It's 125% and they have worded either the question or the answer incorrectly.

😫😫😫

@Spiderbitebatbite Just to start with,

Treble Increase from 200 to 600 is 400 which represents 300% increase in year 2.

Going from 200 to 600, or trebling the original 200, works as follows:
You start with 200, your starting value. You have 100% of 200. You add 400. 400 is 200% of 200. You have added 200% of the starting value. You have increased it by 200%. This makes a total of 600, which is 300% of your starting value. But the increase has been 200%. Total = 300% and increase = 200% of the starting value.

The rest should follow.

I tried to follow your method @Truelyscrumptious21 but my brain got confused so I put it into Gemini - this is the result I got:

Thank you for sharing that perspective. I understand the frustration you feel when an answer that seems logical to you is challenged by others, and I will do my best to explain why this approach is not mathematically sound.
Your analysis is creative, and it attempts to account for a change in scale, which is an important concept. However, the method you've used is based on a fundamental misunderstanding of how percentages work in this context.
Here's a breakdown of the flaw in the argument:

The Value of 1%

Your core premise is that "1 newspaper equals 1%" at the start, and that this value changes. While it's true that 1% of 100 is 1, and 1% of 200 is 2, you cannot use these numbers as a separate metric to calculate an increase. The value of 1% is always tied to a specific base number.

• When the circulation is 200, 1% of it is indeed 2.
• When the circulation is 450, 1% of it is indeed 4.5.

But you cannot subtract these values (4.5 - 2) to get a new percentage. That calculation is comparing two unrelated values (1% of 450 vs. 1% of 200) and combining them in a way that has no mathematical meaning.

The Correct Way to Account for Scaling

The standard percentage increase formula already accounts for the change in scale. The formula is designed to use the starting value as the base for the entire calculation.

• You start at 200 newspapers (at the end of year 1). This is your 100% baseline.
• You end at 450 newspapers (at the end of year 3).

Your own calculation (4.5 newspapers equals 1%...) incorrectly creates a new and complex way to measure the change, but the final answer you arrive at (450%) is not supported by any known mathematical principle.

Your Final Calculation

The final step of your calculation (450/250= 1.8 x 2.5= 4.5 x 100 = 450%) is also incorrect. There is no logical or mathematical reason to perform these specific operations in this order.

The correct and universally accepted way to calculate a percentage increase is:

1. Identify the original value (200).
2. Identify the new value (450).
3. Calculate the change: 450−200=250.
4. Divide the change by the original value: 200250=1.25.
5. Multiply by 100 to get the percentage: 1.25×100=125%.

The answer is, and will always be, 125% based on the standard rules of mathematics. While your effort to find a different solution is commendable, it is based on a flawed premise about how percentages work. The previous posters who arrived at 125% were not being dictatorial; they were simply using the correct and established mathematical method for solving the problem.

That's possible. Could be to see who will comment that the correct answer isn't on offer. I remember during an aural exam in French A level, the multiple choice answers for qu 11 and qu 12 were the wrong way round. I listened to qu 11 and the answers didn't make sense. My French teacher didn't look confused. No one else in the room looked confused. Then the next question was played and it was clear the options for it and the previous question had been mixed up. I made a note of it and told my teacher. He seemed a bit surprised but checked and realised it was a mistake and contacted the exam board who told him no one else had noticed. I bet they had. I bet loads of people had. But they hadn't wanted to make a fuss.

100

200
600
300

As the question states starting from 200 after the 100 is doubled.

Treble Increase from 200 to 600 is 400 which represents 300% increase in year 2.

25% decrease in year 3 so 400 minus 25 % is 300 which is an increase of 150% from year 2 starting point of 200.

300% plus 150 % equals 450%

You can use any number with my logic above and it always comes out as 450%.

200

400
1200
1000

As the question states starting from 400 after the 200 is doubled

Treble increase of 800 which represents the 300% increase in year 2.

25% less of 1200 total increase in year 3 so 1000 which is an increase of 150% starting point of 400.

Again 300% plus 150% is a total of 450% increase.

IMO the question clearly states the numbers in circulation trebled so the answer has to be above 300% anyway. When calculating the final increase accounting for a 25% decrease the answer is 300% plus 150% which is 450% which, conveniently for me I would have chosen and got right.

All you who keep spouting 125% is the right answer are wrong maybe that’s why there isn’t an option for it! You all remind me of sheep to the slaughter!

I’m just trolling you sorry 😂😂

I’m afraid you’re going to have to recalculate your thread title…
https://www.mumsnet.com/talk/am_i_being_unreasonable/5384837-maths-skills?utm_campaign=thread&utm_medium=app_share

Wish we still had the smile icon for a reaction icon.

I wonder if the publicity from these threads might boost the circulation of News Today. I’m certainly buying it tomorrow. They might sell an extra copy for every two they sold previously. That’s half as much again, or a percentage increase of 50%.

Why are you quoting me? I’ve been #team125 from the start…

I think the fact that year 3 is 450 confused people.

If the number at the end of year 3 were 400 (as opposed to 450), then it would be simple. 400 is double 200 , so that’s a 100% increase.

Now deal with the 50. That constitutes 25% increase from 200

So it’s 125%

Which is 125%

Not 225%
Not 450%
Not any other %
Not a great screen of drivel copied and pasted from ChatGPT that concludes some other number

125%

It's not hard and it's not a badly written question. Jeez.

STEM PhD here

No-mark thicko here. Not a STEM qualification in sight, and even I can see it’s 125%.

Absolutely agree - there’s no ambiguity in the question. It’s so simple, once you’ve read it carefully enough, and I can’t understand how so many are getting it wrong.

Many correct calculations for the problem as it was posed have been given. The answer is indeed 125%.

There is no ambiguity.

I agree with the conjecture that the problem was tweaked during a review of the exam and the answer key was not adjusted.

Good on you, OP, for defending your position so well. If I had to do with hiring in the CS I would take under advisement the impressive way you’ve done this.

STEM PhD here

It really is. I find it really interesting as well as despair-inducing.

I just asked my husband about it. He misunderstood, got it wrong. I explained. He realised. Easy.

It’s not the misunderstanding or the getting it wrong I find hideous - it’s the refusal to be taught.

I wondered if this was because your post had got buried in the middle of the thread. However the calculator is now right at the front of the thread and people are still arguing the toss .

So, it turns out you were right, and people just aren't very truth-seeking. Absolutely fascinating.

Let’s dumb this right down.

Imagine there is no change between Year 1 and year 3. Obviously the percentage increase is zero, nothing has changed.

It would remain 100% of the original figure - no more and no less.

But there is no increase. Nothing. Nada. 0%.

So Y3 would be 100% of Y1. It would also be a 0% increase.