In an election with only two candidates, before absentee

[guerrero]

In an election with only two candidates, before absentee ballots were counted candidate Jones received a votes and candidate Smith received b votes. If 900,000 non-absentee votes were cast, what was the percent change in the number of votes after the counting of absentee ballots?

(1) Candidate Jones received 43% of the votes cast before absentee ballots were counted and received 43% after absentee ballots were counted.
(2) Candidate Smith received 57% of the votes cast both before and after absentee ballots were counted and received 387,000 votes after absentee ballots were counted.

OAB

[vinay1983]

In an election with only two candidates, before absentee ballots were counted candidate Jones received a votes and candidate Smith received b votes. If 900,000 non-absentee votes were cast, what was the percent change in the number of votes after the counting of absentee ballots?

(1) Candidate Jones received 43% of the votes cast before absentee ballots were counted and received 43% after absentee ballots were counted.
(2) Candidate Smith received 57% of the votes cast both before and after absentee ballots were counted and received 387,000 votes after absentee ballots were counted.

OAB

Don't get mad at me, but on the face of it since I could not understand the question my answer is E.

Did not make sense

[Java_85]

IMO E Here is why:

(1) just gives the percentage and we don't have any idea about the number of votes. so can't solve it --> B C E
(2) Smith have 57% of votes before and after receiving 387,000 votes.
If the percentage wants to stay the same after adding new votes then the ratio of a/b should stay the same i.e. (a/b)=43/57=?/387000 ==> We can say how many new votes are for Jones. Let's call new jones votes Jn

assume x is the number of votes before and 57% of it is for Smith,
Total votes after = x+387000+ Jn?
Total votes before+ 900,000 ==> You can calculate the percentage change --> B is sufficient.

Hope this helps.

[ceilidh.erickson]

Since we're given the original number of votes cast, then in order to find the percent change in number of votes cast, we need a way to find the number of absentee ballots.

1) As Java pointed out, this gives us only PROPORTIONAL information. It's saying that this candidate won the same percentage of absentee ballots as he/she did original votes. This could be true if there were 100 absentee ballots or 1,000,000. It tells us nothing about number. Insufficient.

If we want to express this algebraically (using "V" for original votes and "A" for absentee votes), Jones' vote total can be expressed as:
0.43V + 0.43A
0.43(900,000) + 0.43A
The problem is that we don't have anything to set this equal to, so we can't solve.

2) This statement gives us both PROPORTIONAL and NUMERIC information, which makes a big difference! If Smith received 57% of the original votes and 57% of the absentee votes, then we could express Smith's absentee votes as:
0.57A = 387,000
(Don't actually do the math here to solve for A - just know that it can be done!)

This will give us a value for the absentee ballots, which means that we'll be able to find percent change. Sufficient.

It can be helpful on a lot of percent/fraction/ratio problems to think in terms of PROPORTIONAL info vs REAL NUMBER info.