1. ## Percentages

Hello all

I have another percentages question that I think that you could help me with as it looks fairly basic but I am having trouble understanding the logic behind it.

Q. What percentage of total eligible adults in the 18–24 age category turned out to vote in Thundersley?

a) 3.8% b) 6% c) 9.5% d) 12.8% e) 15%

All the information is below in the table.

Any help would be great.

Cheers!

2. ## Re: Percentages

What exactly was your difficulty with this? The table says that 6% of the 18-24 voters turned out to vote in Thundersley.

3. ## Re: Percentages

Originally Posted by HallsofIvy
The table says that 6% of the 18-24 voters turned out to vote in Thundersley.
No, I think the table says that 6% of those who turned out to vote in Thundersley were in the 18-24 age category. Since we don't know from the table which share of the total population constitutes this age category, I don't see how we can answer the question.

4. ## Re: Percentages

Hi, I have just found the answer booklet and it suggests that the answer is A 3.8%. Does anybody know how they got this number? All the information is above.

Many thanks

5. ## Re: Percentages

Well what I did was: in Thundersley, subtract the percentage of voters who did not vote from the total eligible, so 22,397 minus 36% of 22,397 is 14,334.08 voters who actually voted.

Then 18-24 year olds were 6% of the total voters who did vote so the total amount of 18-24 year olds who voted is 6% of the 14,334.08 voters who did vote, which is 860.0448 18-24 year old voters.

So what percent of all eligible voters (including ones who didn't vote) in Thundersley (22,397) were 18-24 year olds who did vote (860.0448 as we found earlier)?

(x% of total possible voters 22,397 = 860.0448 18-24 year old voters)

6. ## Re: Percentages

Out of the Adults 36% did not vote at all

100% of all elidgable voter munus that figure = 64% voted

6 percent of 64% = 3.84

7. ## Re: Percentages

To avoid confusion, let's introduce some notation. We are talking about Thundersley only in this question. Let $\displaystyle v_{\text{ac}}$ be the number of people in the age category ac who voted, and let $\displaystyle e_{\text{ac}}$ be the number of eligible voters in the age category ac. For example, $\displaystyle v_{\text{18-24}}$ is the number of people between 18 and 24 who voted, and $\displaystyle e_{\text{18-24}}$ is the number of people between 18 and 24 who could have voted (maybe they did, maybe they didn't). Obviously, $\displaystyle v_{\text{ac}}\le e_{\text{ac}}$ for each age category ac.

Also, let

$\displaystyle e = e_{\text{18-24}} + e_{\text{25-34}} + e_{\text{35-44}}+e_{\text{45-54}}+e_{\text{55-74}}+e_{\text{75+}}$

be the total number of eligible voters and let

$\displaystyle v=v_{\text{18-24}} + e_{\text{25-34}} + v_{\text{35-44}}+v_{\text{45-54}}+v_{\text{55-74}}+v_{\text{75+}}$

be the total number of people who voted. Then the table provides the following facts:

$\displaystyle e=22,397$

$\displaystyle v_{\text{18-24}} / e = 6\%$

$\displaystyle v_{\text{25-34}} / e = 12\%$

...

$\displaystyle v_{\text{75+}} / e = 4\%$

$\displaystyle (e - v) / e = 36\%$

Since we know $\displaystyle e$, we can find $\displaystyle v_{\text{ac}}$ for each category ac. However, we can't find $\displaystyle e_{\text{ac}}$ for each ac because we don't know how people who didn't vote are distributed over the age categories. One possible scenario is that all eligible voters who did not vote are between 18 and 24. Then $\displaystyle e_{\text{18-24}} = v_{\text{18-24}} + (e - v) = (6 + 36)\%$ of $\displaystyle e$, i.e., $\displaystyle e_{\text{18-24}}=0.42\cdot22,397=9,407$ people. Another scenario is that all eligible voters who did not vote are between 25 and 34. Then everybody who is eligible between 18 and 24 voted, i.e., $\displaystyle e_{\text{18-24}} = v_{\text{18-24}} = 6\%$ of $\displaystyle e$, i.e., $\displaystyle e_{\text{18-24}}=0.06\cdot 22,397=1,344$ people.

As far as I understand the question:
Originally Posted by lm320
Q. What percentage of total eligible adults in the 18–24 age category turned out to vote in Thundersley?
it asks to find $\displaystyle v_{\text{18-24}}/e_{\text{18-24}}$. I don't think this question is answerable. Indeed, in the first scenario above, $\displaystyle v_{\text{18-24}}/e_{\text{18-24}}=6/42=14\%$, while in the second scenario $\displaystyle v_{\text{18-24}}/e_{\text{18-24}}=100\%$.

I found the book "How to Pass Numerical Reasoning Tests" by Heidi Smith in Google Books. The answer 3.6% to this question appears on p. 190. It says,
The percentage of all voting adults in Thundersley = 64%. 6% of 64% = 0.06 x 64 = 3.8% of eligible adults who voted were aged 18-24.
However, this number is $\displaystyle v_{\text{18-24}}/v$ and not $\displaystyle v_{\text{18-24}}/e_{\text{18-24}}$, for which the original question is asking.

Originally Posted by daigo
Well what I did was: in Thundersley, subtract the percentage of voters who did not vote from the total eligible, so 22,397 minus 36% of 22,397 is 14,334.08 voters who actually voted.

Then 18-24 year olds were 6% of the total voters who did vote so the total amount of 18-24 year olds who voted is 6% of the 14,334.08 voters who did vote, which is 860.0448 18-24 year old voters.
No, 18-24 year olds were 6% of the total eligible voters.

Originally Posted by daigo
So what percent of all eligible voters (including ones who didn't vote) in Thundersley (22,397) were 18-24 year olds who did vote (860.0448 as we found earlier)?
The answer to this question is given in the table: 6%.

8. ## Re: Percentages

Originally Posted by emakarov
No, 18-24 year olds were 6% of the total eligible voters.
I didn't think the graph clearly stated that, so I guess I read the graph incorrectly. Since all the voters in Thundersley add up to 64% (6% + 12% + 13% + 13% + 16% + 4%), and the people who didn't vote make up the remaining 36%, it would seem like the 6% of the total 100% which include those who didn't vote (6% + 12% + 13% + 13% + 16% + 4% + 36%) were 18-24 year olds.

Originally Posted by emakarov
The answer to this question is given in the table: 6%.
See my reasoning above

9. ## Re: Percentages

Originally Posted by daigo
Since all the voters in Thundersley add up to 64% (6% + 12% + 13% + 13% + 16% + 4%), and the people who didn't vote make up the remaining 36%, it would seem like the 6% of the total 100% which include those who didn't vote (6% + 12% + 13% + 13% + 16% + 4% + 36%) were 18-24 year olds.
Yes, the fact that the percentages in the Thundersley row of the table add up to 100% made me also conclude that the first number is $\displaystyle v_{\text{18-24}}/e$, not $\displaystyle v_{\text{18-24}}/v$.