Maths test - to think Civil Service have it wrong?

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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?

I think you've missed the point.

I agree, but I'm trying to help people who think it's 225% to understand where they are going wrong, as gently as possible.

You are multiplying though - that's not how you work out a percentage increase. You are wrong - its 125%.

But I think they just worded the question unintentionally wrong.

This thread is like playing chess with pigeons. I think it’s time for bed. FWIW OP, I think it’s worth giving them a polite heads up that there was an error on that question.

Whew glad to see many got 225% too.

I skipped reading your answer/explanation and worked through the question.

I don’t understand how you don’t get 225% if you compare end of the first year and end of the third year. What happened in the first year doesn’t matter.

😂😂 That is exactly what it’s like!

I might wait and see how the application gets on then let them know either way.

So you think that 450 is what you get if you increase 200 by 225%

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

Maybe someone else should email the civil service test department and let them know, and the OP can be vindicated without it being tied to her specific score. (Or submit some anonymous feedback?!). Except I’m sure their explanation will be that they wanted to know what percent of the first number the second number is, and they won’t accept that that isn’t what they asked for!!). Unless they get mathematicians - or journalists - involved.

Yep, so it’s the increase. If you increase 200 by 125% you get 450.

No, the way you are approaching it is wrong. Tell me at which step you think I am wrong:

(a) If circulation after year 1 is X - and as we don’t know what it is we can’t put a figure in (this is what algebra is for),
(b) then after y2 it is 3X.
In y3 circulation drops by a quarter.
(c) So at end y3 the circulation is 3X - (1/4 * 3X), which is properly expressed as 3X -3/4X
(d) which is 2 and 1/4X or 2.25X

We need to express our answer as a %.
(e)100% is the figure at end y1 - that is what we treble in y2,
(f) so X = 100%
(g) we can now use our equation to get an answer - which is 2.25 * 100% which
(h) = 225%

I can tell you now, no step is wrong. But which one do you think is? You might also like to consider how likely it is the test is wrong. Not saying it can’t happen but would be very rare. You may want to take that with various analyses on here that actually think there is a correct answer given and try to understand why 225% is right. If you can’t, maybe night school?

If you multiply a number by 2.25., you increase its value by 125%

Well that was silly. Even though I see your point about the increase being 125%, you can see (as per many of the replies) how some people may misinterpret/misword the question in such a way so that the “correct” answer can be calculated at 225%. You could have at least chosen that answer as it made the most sense.
(I’m no Oxbridge maths graduate but did get an A in A level maths many moons ago if that counts for anything).

Your individual steps aren’t wrong, but they are answering a different question. You are working out what percentage of the starting amount the final amount is. But the question asks for percentage increase, which is something different (and something that has a particular definition in maths). It might not be what the examiner originally intended to ask, but it’s clearly what they DID ask.

To the people still holding out at 225%.. This is cut and paste from a percentage increase calculator online.
Give it a Google and try yourself....

Percentage Increase Calculator
Starting Value:
200
Final Value:
450
Answer:
= 125% increase

I did 450/200 which gave me the circulation at the end of year 3 is 225% of the circulation in year one. That gives an increase of 125%

Poorly worded question if they want 225 as the answer.

You are right OP based on the wording of the question.
Doesn’t matter whether you work it out using papers, percentages, pounds or pizza, anything that happens in Year 1 is irrelevant so we have something that trebles then reduces by 25%.
The overall increase is 3 x 0.75 -1 =1.25
so the percentage increase is 1.25/1 x 100 =125 %

Yes you should tell them because they have an error in their assessment and they should want to correct that. We should all expect a civil service workforce to not make too many mistakes in the first place and certainly to want to correct any errors that have been reported.

The answer is 225%.

End of Year One it's 200.
End of Year 3 it's 450.

200 x 225% is 450

Showing the Work:
We know that 200 is the circulation at the end of year one, and 450 at the end of year three.
200 x 2 is 400
25% of 200 is 50. (200 divided by 2 is 100, so 100 is 50 percent of 200. Therefore, 25 percent of 200 is 50.)
400 + 50 = 225% of 200.

This is quite the wake up call to the shoddy state of the mathematical ability of the population and the civil service recruiters who set this question.

The question is not ambiguous.

The correct answer is not an option.

450-200 = 250/200 x 100 =125%

If I buy something for £200 and sell it at a 100% mark up, am I selling it at

a) £200
b) £400

I can’t read any more of this either - it’s making me pretty mad reading all these people insisting that 225% is the correct answer 🤦🏻‍♀️ good luck to you!!!

THAT ISN’T HOW PERCENTAGE INCREASES WORK

I see why people are getting 225% as an answer but that is just stating y3 end as a percentage of y1 end.
i.e y3end x 100 = 225%
y1end

But that isn't the question. The question asks for the % increase from y1 end to y3 end
i.e (y3 end - y1 end) x100 = 125%
y1 end

OP is correct.

I buy something for £200

I sell it at £450

What percentage profit have I made?