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?

Honestly, it really isn’t.

you are talking about the number that you multiply the original number by to get the new number, and that is indeed 225%. It is correct to say that 450 is 225% is 200. But that is not what percentage increase is.

percentage increase has a specific mathematical definition. It maybe wasn’t what the examiner had in mind, but it’s what they asked for.

this is a question in gcse and the difference is confusing to a lot of students. But the way it’s asked here, it is asking for the percentage increase, which is 125%, as defined in standard maths.

Let’s hope there aren’t questions on percentage point increases to add into the mix…!

I think you are right OP. I thought for a minute there was a typo in the question but I think the maths is just wrong.

You are wrong.

Ignoring anything prior to the end of year 1, year 1 finishes at £10.

Year two increases it 300% to £30.

Year three takes a quarter off, so it ends at £22.50.

The question is what is the percentage increase between ends of year 1 and 3.

So what is the percentage increase between £10 and £22.50?

125%.

Part of the point of the question - in the fast stream test - will be your ability to correctly interpret the question. Doing this in your third language (and having that many languages is hugely impressive) will likely pose more of a chalkenge

So you are saying that if you increase 200 by 225%, you get 450

What do you get if you increase 200 by 100%?

@sandyhappypeople

"If you increase 100 by 100%, what do you get?
You don't get an increase because because 100% equals 1, it has to be OVER 100% to get an increase or UNDER 100% to get a decrease.
100% is a baseline.
Do it on the calculator if you're not sure, it will give you an answer of 100.
Honestly, the answer to your question is 225%"

Sorry, but that's absolute twaddle.

You must get very confused with interest on your bank accounts and credit card bills.

oranges and lemons

How can you be so condescending and so wrong at the same time? It’s impressive!

The question is about the percentage increase. They didn’t ask “what percentage of the old number is the new number?”

That second number would be 200% of the original one. But that isn’t the same as it having increased by 200%.

In this example, 200 is equivalent to 100%.
So 450 would be equal to 225% of that original 200.

But the increase is 125%: 225% - 100%.

Still not true. 225 is the percentage of 200 that 450 is, yes, but that is not the definition of percentage increase. It has a specific meaning. You are finding the multiplier, or expressing one number as a percentage of the other. But percentage increase means the difference between the numbers expressed as a percentage of the original.

@sandyhappypeople you are very confused, bless you.

Yes 100% of 100 is 100 you are right.

BUT if I bought a TV for £100 last week and this week it costs £110 then the price has increased by 10%.
Think about the difference 🤔

I think I've changed my mind OP. I interpreted the question as asking you to calculate the end of Year 3 figure as a percentage of the end of Year 1 figure, which would be 225%.

However if you interpret the question as asking you to calculate the increase between the end of Year 1 and the end of Year 3, and then express that figure as a percentage of the end of Year 1 figure, it's 125%.

So if your boss said 'I'm going to increase your salary by 10%' you'd get a 90% pay cut?

No, you add that % increase to the original figure.

Astonishing how many people are totally misinterpreting/misunderstanding this while being confident they are correct. It's only GCSE-level maths, after all.

It is 125%.

If you have one pizza and someone asked if you wanted 100% more pizzas, you’d end up with two, wouldn't you?

I thought that initially, but actually percentage increase from start of y1 would be (450-100)/100 so 350.

I think they are just dim.

It started as 200 and ended up as 450. So it has been multiplied by 2.25. And 2.25, expressed as a percentage, is 225% (any percentage is literally a number multiplied by 100).

However, the disagreement is about what is meant by a "percentage increase". Does it include the original amount, or is it just the extra? If it includes the original, then 225% would be right: 450 is 225% of 200. If it is only the extra, then 125% is right: The extra 250 is 125% of 200.

In this case, I agree with OP that this is a 125% increase.

We can make it simpler by thinking of a smaller increase. For example, imagine the circulation had gone from 200 to 220. I think we would all say it had "increased by 10%". Of course, you can also say that the new value is 110% of the original (i.e., it has been multiplied by 1.1), but clearly if most people were asked "What was the percentage increase in circulation" in that case, they would say 10.

Percentages can get a bit complicated once they get over 100 because many people are used to them being fractions less than 100% (i.e., numbers less than 1.0). In this case it seems that the question setter has also become confused by this. If they want 225% to be the right answer, they would have to say "What is the circulation at the end of the third year, expressed as a percentage of the circulation at the start of the first year?".

Fortunately for the test taker, 125% isn't an option, so if I was given this test I would hold my nose and select 225%. But I would be as annoyed as OP about it.

The question asks for the percentage INCREASE

If my pay increases by 4%, how could you calculate your new pay?

I would multiply it by 1.04.

It works out 4% and then adds it on to my original salary to give me my new salary.

Merry fucking Jesus @Sharingaroomtinightthen

How are you keeping your head?

Personally I’d have to email them and point out the error.

Y0 = x
Y1 = 2x
Y2 = 2x X 3 = 6x
Y3 = 6x x 0.75 = 4.5x

Increase from 2 to 4.5 = 2.5

2.5 as a percentage of 2 - the starting figure =

2.5 / 2 X 100 =125%

There is no other CORRECT answer based on the wording of the problem.

I’ve just realised that 350 isn’t one of the answers. You’re right… this is just bad maths.

Ha! - I was going to use exactly the same example! Pizzas are excellent for teaching maths. And for eating.

If you thought the answer to your question was one pizza it would be the same as a buy-one-get-one-free offer ending up with only the pizza you started with, and that would be no good at all. (Unless it was a Domino's pizza, as they're revolting.)

There's no disagreement on what is meant by percentage increase, it's got a clear mathematical definition, no matter how much posters tie themselves in knots to interpret it differently.

Agree with OP it’s increased by 125%

If the price of an item doubles, e.g. goes up from £2 to £4, or £100 to £200, or £1million to £2 million, it has increased by 100%. You work out a % increase by calculating the amount the price (or whatever) has risen as a % of what it started as.

The question isn’t asking about the start of year one.

I don't understand how people can be so ignorant of basic maths. How do you guys work out how your savings are performing???

The increase is 450-200=250.
In percentage terms that is (450-200)/200 = 125%