Page 13 | Maths test - to think Civil Service have it wrong?

Sharingaroomtinightthen · 2025-08-01T20:58:49+00:00

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?

Merryoldgoat · 02/08/2025 00:03

cakeorwine · 02/08/2025 00:02

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

a) £200
b) £400

£650 surely?

Tandora · 02/08/2025 00:04

cakeorwine · 02/08/2025 00:02

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

a) £200
b) £400

Exactly this.

Clarabell77 · 02/08/2025 00:04

UsingAMansNameInAWomensWorld · 01/08/2025 22:18

You could stick any number in

So 20 sold pre Y1, doubles to 40 at end of Y1
40 trebles to 120 at the end of Y2
120 falls by 1/4 to 90 at end of Y3
The % difference between 20 and 90 is not 125%, it's just over 400%

Which is why you don't add in numbers but work out with the %

The number you should be comparing with 90 is 40 though, not 20.

Horsie · 02/08/2025 00:05

Sharingaroomtinightthen · 01/08/2025 22:05

The question is from the end of year one until the end of year three.

The end of year one, if you’ve started with £100, would be £200.

The end of year three would be £450.

125% difference.

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Because increasing 200 by 125% isn't 450. Increasing 200 by 125% is 250.

1 x 200 = 200
25% of 200 is 50.
125% of 200 is 250.

summertimeinLondon · 02/08/2025 00:05

HornungTheHelpful · 01/08/2025 23:56

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?

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@HornungTheHelpful You’re forgetting after (d) that a percentage increase is not 2.25x, but 2.25x - 1x = 1.25x, which should be your step (e)

Original poster

Sharingaroomtinightthen · 02/08/2025 00:06

HornungTheHelpful · 01/08/2025 23:56

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?

Show quote history

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

Okay then.

(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),

Okay.

(b) then after y2 it is 3X.

Agreed.

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*

Sure.

(d) which is 2 and 1/4X or 2.25X

Okay.

We need to express our answer as a %.
(e)100% is the figure at end y1 - that is what we treble in y2,

Okay.

(f) so X = 100%

Okay.

(g) we can now use our equation to get an answer - which is 2.25 100% which
(h) = 225%*

This is wrong. You need to calculate the percentage increase between X and 2.25X.

If you increase X by 100% you get 2X. By 125% you get 2.25X.

If you increased X by 225%, you’d get 3.25X.

I can tell you now, no step is wrong.

One step very much 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.

It has happened, because their answers are all wrong.

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?

Maybe you should try and master maths yourself before attempting to be so deeply patronising? Enroll in that night school?

OP posts:

Original poster

Sharingaroomtinightthen · 02/08/2025 00:07

NoSoapJustUseShowerGel · 02/08/2025 00:00

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).

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Right well I wasn’t testing for telepathy.

OP posts:

Underthinker · 02/08/2025 00:07

Merryoldgoat · 02/08/2025 00:01

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.

I think that's harsh. I did A level and some degree level maths, but I don't remember the exact definition of every term from GCSE.
Most people agree on the calculation but have forgotten or never learned the specific meaning of "percentage increase". To someone unfamiliar with the term it is not ridiculous to think it could mean a percentage to multiply the original number by to get the result.

cakeorwine · 02/08/2025 00:07

Horsie · 02/08/2025 00:05

Because increasing 200 by 125% isn't 450. Increasing 200 by 125% is 250.

1 x 200 = 200
25% of 200 is 50.
125% of 200 is 250.

Edited

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

I run a business, I ask you to sell this £200 item for 125% MORE than I paid for it?

What price are you going to sell it at?

Jellybean23 · 02/08/2025 00:08

Profit is £250. £250 as a percentage of £200

250 x 100 = 125%
200

Original poster

Sharingaroomtinightthen · 02/08/2025 00:08

Horsie · 02/08/2025 00:01

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.

They asked for the increase.

OP posts:

Horsie · 02/08/2025 00:10

Sharingaroomtinightthen · 02/08/2025 00:06

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

Okay then.

(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),

Okay.

(b) then after y2 it is 3X.

Agreed.

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*

Sure.

(d) which is 2 and 1/4X or 2.25X

Okay.

We need to express our answer as a %.
(e)100% is the figure at end y1 - that is what we treble in y2,

Okay.

(f) so X = 100%

Okay.

(g) we can now use our equation to get an answer - which is 2.25 100% which
(h) = 225%*

This is wrong. You need to calculate the percentage increase between X and 2.25X.

If you increase X by 100% you get 2X. By 125% you get 2.25X.

If you increased X by 225%, you’d get 3.25X.

I can tell you now, no step is wrong.

One step very much 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.

It has happened, because their answers are all wrong.

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?

Maybe you should try and master maths yourself before attempting to be so deeply patronising? Enroll in that night school?

Show quote history

You don't need algebra to work out this problem. It's just simple percentages! I think the maths above makes this insanely complicated for no reason.

225% of 200 is 450. OP was right to choose a starting value - that the circulation started at 100. The actual numbers themselves aren't the issue, it's the percentages.

Answer is 225%.

Samscaff · 02/08/2025 00:10

HornungTheHelpful · 01/08/2025 23:56

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?

Show quote history

Your step g is wrong. The question is asking you to calculate the increase. The increase, from 100 to 225, is 125.

125 is 125% of 100, the starting point.

Surely you agree that doubling the price of something means a 100% increase. So if I was raising the price of something from £1.00 to £2.25, or from £100 to £225, it would be an increase of 125%.

Original poster

Sharingaroomtinightthen · 02/08/2025 00:10

Horsie · 02/08/2025 00:05

Because increasing 200 by 125% isn't 450. Increasing 200 by 125% is 250.

1 x 200 = 200
25% of 200 is 50.
125% of 200 is 250.

Edited

Show quote history

Erm, yes it is. If you increase 200 by 100% what do you get?

OP posts:

NoSoapJustUseShowerGel · 02/08/2025 00:11

Sharingaroomtinightthen · 02/08/2025 00:07

Right well I wasn’t testing for telepathy.

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No but rather than choosing randomly, choose one which might make sense.

cakeorwine · 02/08/2025 00:11

1 x 1 = 1
1 x 2 = 2

2 is 100% more than 1
1 is 100% of 1
2 is 200% of 1

2 is what I get if I increase 1 by 100%

Azaleahead · 02/08/2025 00:11

Omg, this is doing my head in. OP is definitely correct.

Interesting that none of the 225% brigade have engaged with the point that an INCREASE is different from working out the yr3 figure as a percentage of the yr1 figure.

Nor have any of them been swayed by the helpful example of a gas bill increasing by 50% NOT resulting in a halved bill, as their reasoning would have it…

Horsie · 02/08/2025 00:11

LegleEagle · 01/08/2025 22:14

You are completely right OP. There are some mad answers on here.

No, she really isn't right. 125% of 200 is 250, not 450.

The correct answer is 225%.

Tandora · 02/08/2025 00:12

Azaleahead · 02/08/2025 00:11

Omg, this is doing my head in. OP is definitely correct.

Interesting that none of the 225% brigade have engaged with the point that an INCREASE is different from working out the yr3 figure as a percentage of the yr1 figure.

Nor have any of them been swayed by the helpful example of a gas bill increasing by 50% NOT resulting in a halved bill, as their reasoning would have it…

Nor have any of them been swayed by the helpful example of a gas bill increasing by 50% NOT resulting in a halved bill, as their reasoning would have it…

Right. This!!!

NoSoapJustUseShowerGel · 02/08/2025 00:13

Horsie · 02/08/2025 00:11

No, she really isn't right. 125% of 200 is 250, not 450.

The correct answer is 225%.

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And 250 is the INCREASE (ie the difference, not the final amount), so it’s 125%.

Original poster

Sharingaroomtinightthen · 02/08/2025 00:13

Horsie · 02/08/2025 00:10

You don't need algebra to work out this problem. It's just simple percentages! I think the maths above makes this insanely complicated for no reason.

225% of 200 is 450. OP was right to choose a starting value - that the circulation started at 100. The actual numbers themselves aren't the issue, it's the percentages.

Answer is 225%.

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No it’s not. It’s 125%.

OP posts:

cakeorwine · 02/08/2025 00:13

Horsie · 02/08/2025 00:11

No, she really isn't right. 125% of 200 is 250, not 450.

The correct answer is 225%.

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But it's not "of". It's "Increase"

450 is 225% of 200

But 450 is what you get if you increase 200 by 125%

Merryoldgoat · 02/08/2025 00:14

Underthinker · 02/08/2025 00:07

I think that's harsh. I did A level and some degree level maths, but I don't remember the exact definition of every term from GCSE.
Most people agree on the calculation but have forgotten or never learned the specific meaning of "percentage increase". To someone unfamiliar with the term it is not ridiculous to think it could mean a percentage to multiply the original number by to get the result.

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I don’t. There are basic calculators online (I posted a screenshot of one), people with obvious understanding and knowledge showing workings (including the OP) which can be verified online in myriad places and yet posters are still absolutely certain their incorrect calculations are correct.

Basic percentages/fractions are introduced at age 11. This is not high level maths. We’re not even talking trigonometry which is also introduced pre-GCSE.

Original poster

Sharingaroomtinightthen · 02/08/2025 00:15

Horsie · 02/08/2025 00:11

No, she really isn't right. 125% of 200 is 250, not 450.

The correct answer is 225%.

Show quote history

It’s not asking what 225 is as a percentage of 200.

It”s asking for the percentage increase.

If you increase 200 by 100% what number do you get?

OP posts:

SecretNameAsImShy · 02/08/2025 00:15

200x225%=450. The answer is 225%