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?

OP didn’t ask if she was right or wrong, she asked if she should point it out to the recruiter. A god proportion may well agree she is right but that it’s not worth pointing it out.

Percentage just means if you divide a number by 100 and then multiply it by the numerator e.g. 80 / 100, it's the number you get at the end.

So to work out 100% of a number, you would divide by 100 to get 1 / 100 and then multiply by 100.

If you wanted to decrease a number by 10%, you would be working out 10% of that number and then take that away from the original. So you are left with 90% of that number. You could multiply the original number by 0.9.A 10% decrease

To increase a number by 10%, you take the original and add on 10%. So you'd multiply by 1.1

You are right about the Maths, the problem is in the wording of the question. Decades of teaching English have taught me to put myself in the pupils' shoes and work out what they actually meant to say, so in your position since the right answer was not available I would have looked again at the question and probably come to the conclusion that they meant "from the first year" i.e. the original 100, not the 200 at the end of it, so I would have then given the answer which corresponded to that, rather than a random one.

No the correct civil service answer would be 'it depends on the question the minister has been asked'. Increase in school places? 225%! Increase in hopsital waiting lists? 125% (but ideally no percentages at all, just throw out random numbers of new beds added or nurses hired with nothing to put them into context).

Yes, fair point.

OP is correct but I’m appalled at the maths ability (or lack of) of the majority of posters here.

I don’t know why you’re so hung up on the "portion" idea. Why do you think the increase has to be a "portion of", i.e. smaller than, the original number?

Here's a statement of fact: if a figure doubles, it increases by 100%, i.e. by the same again. So if it more than doubles, it increases by more than 100%. Tell me exactly why you maintain that statement is incorrect. (Clue: it isn’t.)

You say "You can INCREASE a number by a percentage." Yes. That is exactly what we have been asked to calculate.

Please answer the question I’ve asked before, which you haven’t answered: if I start with 200 of something - 200 grapes, if you like, or daily payments of £200 - and increase it by 100%, what do you maintain the new figure will be?

Thank you @cakeorwine I have a maths A level, science degree and science masters involving a lot of maths so I do understand the basics.

I was asking the poster who stated ‘percentage’ is the correct term for ‘percentage increase’ what the correct term for ‘percentage decrease’ therefore is.

Well you can calculate a percentage increase by using multiplication, but you have to multiply by the correct figure!

I.e. an increase of 5% can be calculated by multiplying by 1.05.

Percentage, fraction, ratios, decimals are all relational concepts - parts of a whole. 50% is half of something, 0.5 of it, one part to two parts of a total something. It is NOT a unit. The change in the relation is the increase or decrease.

"The question is wrong" is a silly way of justifying an incorrect answer.

And whether you take 100 as being the end of year 1, or 200 as the end of year 1, it doesn't matter in percentage terms.

No, this is wrong. 100 to 200 is a 100% increase. That is different to being worth 200% of the original value

Welĺl as this is about specifics, it is not different to beng worth 200% of the original value, it is different from being worth 200% of the original value.

Sorry, I couldn't resist. 😁

Yes I do understand that. But the conflating of ‘percentage of’ and ‘percentage increase’ on the thread I think is causing people to erroneously state the answer as 225%
Clearly these things are not the same.

If circulation doubled, it increased by 100%

Then it trebled to 300%.

If it then fell by one quarter, it fell by (300 / 4) =75%

300 - 75 =225 %

300% increase by being trebled 300%
25% decrease which is now worth 75%

3 x 0.75 = 2.25

225% increase.

You're right in not thinking about the doubling from the first year- information to completely ignore.

eg....
1st year 100% increase = 50 newspapers to 100 newspapers
2nd year it trebled 100 = 300 newspapers
3rd year fell by 1/4 of 300 = 225 newspapers
Therefore ...225/100 x100 = 225%

Sorry, I mathsplained you. But where is the conflation? Percentage of and percentage change (increase or decrease) are very clear and distinct concepts.

I passed maths GCSE with a C though!

I’ve just looked at it again and tried really hard and I’ve come up with 450% now! The wording is vague but I don’t think it means to completely discount year 1 now I have read it multiple times.

Year 1 100 so 50% is 50

Year 2 200

Year 3 450

Difference is 250 which is 4.5 50% so 450%.

Bonkers I know and obviously wrong but that’s the answer I get when I try really hard 😂

Please OP flag it and get back to us with the answer as it’s infuriating!!

If it was from beginning of year 1 it would be 350 so 650%. But they ask from end of year 1 so 250 which is 450%.

I am going mad 😠

Re-read your first two lines again.

Yes exactly- we are agreeing. I perhaps didn’t explain my point well. They are distinct.

I have maths A level, science degree and masters but it’s a long time ago- I was attempting to explain that % increase and % of are different. % doesn’t just mean % increase as suggested by a pp.

Yes it's that addition step (to get the 1.05) that the 225% posters are missing.

I can’t believe people are still coming in this thread to give the wrong answer. It is not 225%.
I posted a bbc bitesize link earlier that showed how to calculate percentage increase for anyone still confused.

Also, here’s a real life example of what a 125% increase looks like. 8,000 to 18,000.

https://portfolio-adviser.com/hargreaves-lansdown-sees-125-increase-in-net-new-clients-ahead-of-next-years-acquisition/

Exactly. I have taught this to ten-year-olds many times. To make it more interesting I often tell them I’m selling some of them.

"Normally I would sell Josh for £10, but today there’s a sale at my shop, with 10% off all boys. What am I selling Josh for today?" Answer: "Today Josh costs 10% less than he did yesterday. Yesterday he cost £10 so today he costs £10 less 10% of that. 10% of £10 is £1, so we take that off the original price and today he costs only £9."

"Normally I would sell Olivia for £10 too, but today the price of all girls in my shop has increased by 150%. 150% of £10 is £15, so we have to add that much onto the original price. So today Olivia would cost £25."

Ten-year-olds normally grasp the concept of percentage increases and decreases pretty quickly.

@Horsie , if you think any of this is incorrect, please tell me exactly what.

Well i thought so too before I read this thread - they clearly aren't clear and distinct concepts to everyone!

I agree OP.

The answer would be 225 if it was from the beginning, but it's from the end of the first year so it's 125.