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?

Ditto! Kruger & Dunning (1999).

This is logical to me and a maths graduate agrees.

The "Maths Graduate" logic is gibberish; the answers from REAL mathematicians stand out.

Multiple-choice questions are a cost-effective way of processing large numbers of exam papers without relying on educated markers. The tactic of picking an answer which is possible (i.e. eliminating the stupid answers as our MG does) is a great way of performing well when you don't know anything about the question, but I believe that OP demonstrating to the examiners a complete understanding of the question (or at least better than the examiner) would be a great way of being identified as a good candidate.

The first page already had all these. I only encountered this thread when it was already page 5 (I run 100 posts per page) and was shocked that people were so adamant about the wrong answers.

a simple way to prove its 225%:

if you dont like algebra give any value - lets say 100
so end of year 1 =200
end of year 3 = 450

get your calculator and enter 225% of 200

Yes, but that's not the calculation that the question asked you to do.

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

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

We could say this until we are blue in the face but it apparently makes little impact...

AI gives your answer> but it still doesnt make sense to me

https://en.wikipedia.org/wiki/Dunning%E2%80%93Kruger_effect

percentage increase is not the same as percentage of.
they are two different things.

If you earn £1000 per month and get a generous 10% increase you end up with £1100 per month.

You haven't had a 110% increase but you now earn 110% of what you did before.

@Iwanttoliveonamountain

But the question was about the % increase, and that’s not what you’ve calculated. No-one is denying that 450 is 225% of 200, but that’s not the same as the % increase.

If you double a number you increase it by 100%. Increasing 200 by 250 is adding on not just the same again, which would be 100%, but making it one-and-a-quarter times bigger. Which is 125%.

Exactly.

I would refuse to pick an answer from the selection given because I would realise that none of them are correct, so I would demonstrate some initiative and say so.
I don’t understand why you talk about "the obsession with taking the end of year 1 as the base figure" - how can we "forget it" when that’s clearly what the question says? If you don’t use that as the base figure you’re simply answering a different question, not the one that has been asked.

I give you the Dunning-Kruger effect.

https://en.m.wikipedia.org/wiki/Dunning%E2%80%93Kruger_effect

Edited to say: just saw somebody already did that wipes smug smile off face

Being rude isn’t going to make you any less wrong. If “percentage increase” means - as you assert - the difference between end y2 and end y3 expressed as a percentage this begs the question “as a percentage of what?”. You have two options - as a percentage of end y2 (the more natural meaning, I agree but not the only possibility) or a percentage of end y3.

But what I think this whole thread misses is this: the question was multiple choice. The aim was to get the answer that the question setter thought was correct. I cannot conceive of getting an answer, thinking “they’re just wrong” and guessing rather than trying to fathom what answer they wanted where - even if you thought 125% was correct - you could have deduced that they wanted 225%.

I also think given there is a significant number of people who think 225% is correct you cannot argue it is unambiguous (though on a different basis to the one I mention above).

Whichever side you’re on, I think we can all agree the wording was non-ideal, but dependent on what role it was, could this have been the point? OP potentially did herself out of a point (unless she guessed correctly) by being inflexible and unwilling to use all the data available to her to answer the q - she didn’t take into account that the question setter likely thought one of the answers was correct.

FYI, you are talking to someone else now. I bailed out hours ago.

Ok? Sorry! That quote history is hard to follow. I just clicked quote to respond to the post I wanted to respond to - can’t say I even noticed the posters name. But apologies if it’s upset your day.

oh, btw, not sure you’ve bailed if you came back that quickly 🤣 to tell me you had

oh, btw, not sure you’ve bailed if you came back that quickly 🤣 to tell me you had

I have. I have "unwatched" the thread. I got a notification to say you had quoted me, so I looked & responded.

125% of 200 is 250 though.

200 * 1.25 = 250

200 * 2.25 = 450

so the answer is 225%

But that's the point. 125% of 200 IS 250. And that's the amount that gets added on to the original (i.e., increased by) to get the final value. So it's an increase of 125%.

So close. 125% of 200 is 200 (same as 200 * 1.25 = 250).
200 + 250 = 450.
200 + (200 * 1.25) = 450.
So the answer is 125%.

Another way:
200 * 2.25 = 450.
(200 1) + (200 1.25) = 450. [edit: sorry, I can’t edit the stupid autocorrect out of this line. It says : two hundred times one, plus two hundred times one point two five, equals four hundred and fifty]

You start with 200. You increase it by 125%. You add the 125% onto the first 200. You get 450.

It's the difference between end of yr 1 and year 3; year 2 is not involved.

It doesn't beg the question "as a percentage of what" (or even raise the question). It's just standard maths to make it the percentage of the original amount, as that is what you're increasing, and it's a question about percentage increase. It really isn't ambiguous, not to anyone that actually understands maths.

The wording is very clear, but just likely not the question the examiner wanted, hence no correct answers. That doesn't make it ambiguous, it just means that the examiner either didn't understand maths either, or just made a mistake. It doesn't make it that there are other right answers. There are wrong arguments to get most of the other possible answers, but they really are just wrong. Yes, I too would probably have guessed the 225% in the end, because I teach maths and I know the sorts of errors that are common, but that doesn't stop it being completely wrong, and I don't think it's inflexible to realise that and not want to put the answer down, as the psychology could just as easily have been to see who recognises that there were no correct answers, or who was willing to report it, etc. (For what it's worth, I don't think it was either of those; I think it was just an examiner who didn't understand/proofreading error/question changed on various proofs and nobody caught it).

Oh Atina, come on now. Have a look at the many other explanations as to why the right answer is 125%. I’m amazed that after hundreds of correct posts and detailed explanations people are still getting such a basic question wrong.

Percentage Increase = (new-original)/original x 100%

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