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?

😆 If only they’d take it into account.

@Sharingaroomtinightthen You are forgetting the special properties of the number 1.

2 x 2 might be 4, but 1 x 1 isn't 2. It's 1.

That's why you are coming up with 125% instead of the correct answer of 225%.

So, 450 is not 225% of 200. That would make no sense and is mathematically impossible. A portion of 200 must always be less than 200. But 450 IS a 225% increase on 200.

Of course you can have 225% of 200. A percentage of a number doesn’t need to be a smaller portion than the original number.

But the percentage increase between 200 and 450 is the difference between 200 and 450 as a percentage of 200 (the original number). So: the difference between 200 and 450 is 450-200 =250. And 250 is 125% of 200.

This is primary school maths — a percentage increase of 100% is double the original value. An increase of 50% is half of the original value added on.

But do you see where you're going wrong?

So, 450 is not 225% of 200. That would make no sense and is mathematically impossible.

450 is indeed 225% of 200. It is absolutely mathematically possible. 100% mathematically possible, in fact.

But 450 IS a 225% increase on 200.

No, it's a 125% increase, as the OP said.

Can I change my vote?

PLEASE go and email them and tell them they are wrong. Go on please. 😂

Ok, there's clearly no option here but to invoke that once much-loved MN question which fell out of favour a while ago...

ARE YOU ON GLUE??!

Yes, 2.25 times the original value is an INCREASE of 225%

No, it’s not. It’s 125%.

You cannot have 225% OF something. But you can INCREASE it by 225%.

If I have four slices of pizza and the delivery driver drops off another five slices of pizza then I have 225% of the original slices of pizza. If those four original slices were increased by 225%, I’d end up with 13 slices.

So what is a 225% portion of 100 grapes? NOT a 225% increase, which would be more than 100 grapes.

225% portion of 100 grapes is 225. 100 grapes increased by 225% is 325.

You need to give me a 225% portion of 100 grapes that's less than 100 grapes.

This is impossible.

Going back to the OP.

You have a single grape. It’s increased by 100%. You don’t still have one grape. You have two.

A percentage OF a number must always be smaller than that number.

Again, you're talking about percentage increases.

You can INCREASE a number by a percentage. But you can't have a percentage of a given value that's more than said value. You can INCREASE IT BY X but you can't have a portion of that value that's more than 100 percent.

Say you have 100 grapes. You can increase those grapes by 125%, which is an extra 25 grapes.

But you can't have a portion of grapes that is 125% of the grapes....without adding more grapes!

You agree that £110 is a 10% increase on £100, which is what the question is asking about.

Please go back and do a refresher course on percentages! Every post it gets worse! ☹️

😭😂 It isn’t 225%.

I am not sure I'm going to be able to sleep while there are still people arguing against 125% being the right answer.

You have a single grape. It’s increased by 100%. You don’t still have one grape. You have two.

This, here, is exactly where everyone is going wrong - by forgetting the special properties of the number 1.

2 x 2 is 4.

However, 1 x 1 isn't 2.

It's 1.

Get out any calculator. 1 x 1 =1.

It IS. 100 x 100 percent is 100. Just like 1 x 1 = 1. Not 2.

Say you have 100 grapes. You can increase those grapes by 125%, which is an extra 25 grapes.

An extra 25 grapes would be a 25% increase. A 125% increase would be an extra 125 grapes.

But you can't have a portion of grapes that is 125% of the grapes....without adding more grapes!**

It’s asking for the percentage increase, not the percentage of the original amount.

So we agree thar 50% of the 100 grapes is 50 grapes.

If you go from 100 grapes to 150 grapes then you have increased it by 50 grapes. Yes?

So if you go from 100 grapes to 150 grapes you have increased it by 50%.

I have been lying in bed reading this for over an hour & half.

At 12:30am, one of my two dogs got onto my bed. At that point 1 dog represented 100% of "dog" on my bed.

At 1:30am, the other dog jumped onto my bed, meaning the amount of "dog" has increased to 200%.

The % difference in the amount of dog is 100%.

Before even began reading any of the comments almost 2 hours ago, I worked out the answer to the OP to be 125%.

I imagine some of the people who have given different answers to this post actually work in the private sector so that comment feels a bit absurd...

@Horsie said
a percentage OF a number must always be smaller than that number.

This is utter bollocks.

I really need to sleep but this thread is just incredible.

-- signed, a somewhat embarrassed civil servant.

My god I sincerely hope you're not a maths teacher - or someone who uses maths, or indeed logic, in any capacity.

Of course you can add more sodding grapes! What do you think happens when a bank pays you interest on your account? They add more money!

Your original balance is obviously 100% of your balance. When interest is added the total becomes 105% (or whatever) of the original balance: i.e. more grapes.

Right. You have two grapes. Someone gives you 100% more. You now have four grapes. You don’t still have two.

I am right. A portion of a given value - note, a portion, not an increase - must be less than 100 percent.

If you have 100 grapes, and you want to give a percentage of just those 100 grapes to your friend, you have to give less than 100 of them, right?

If you want to give 125% of the grapes to your friend, you can do that, but not without adding more grapes.

Just when I thought it couldn't get any funnier... the special properties of number 1 😂

😂😂 I need to go to bed. Feel like I’m becoming delirious reading some of the answers.