2008 School Cert Maths Question (1 Viewer)

[lath]

How do you solve question 80 from the 2008 school cert maths paper:

During an election between two candidates, the count of the votes was
<DIR><DIR>Isaac - 5 000 votes
Sam - 4 700 votes

There were 1000 postal votes still to be counted. It is known that more than half
the postal votes will go to Sam and Isaac will get at least 20% of the postal votes. Indicate whether each of the following is Correct or Incorrect.
</DIR></DIR>

1. Isaac could win by 250 votes.
2. Sam could win by 250 votes.
3. Isaac could win by 300 votes.
4. Sam could win by 300 votes

 

[mirakon]

Well Sam picks up MORE than 50% of the 1000 postal votes.

Therefore, he has to pick up at least 501. If we take this case, then Isacc picks up the 499 remainning votes, meaning Isaac wins(5499-5201) by 298
Similarly if Sam picks up 502, Isaac will win by 296
Similarly if Sam picks up 503, Isaac will win by 294


The pattern is that the margin (for obvious reasons) reduces over time

Note that Isaac can therefore not win by 300 or more votes. However if Sam picks up 525 votes, Isaac wins by 250

So 1. is correct and 3. is incorrect.

Now Isaac gets at least 20% of the votes. Therefore he has to get AT LEAST 200 votes.

If we take this case, where Isaac gets 200 votes, Sam gets the remaining 800, meaning Sam wins by 300, meaning 4. is also correct.

If Isaac gets 201 votes then Sam wins by 298. The same pattern is now evident, the winning margin decreases over time.

Therefore when Isaac gets 225 votes then Same wins by 250, meaning 2. is also correct.


Therefore 3. is incorrect, and 1.,2. and 4. are correct.

 

[lath]

Thanks!