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Percentage

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by [email protected] » Thu Jun 26, 2014 6:48 pm
Hi Experts,

In this problem why cant we simply assume a number for example the given ration 3:2 therefore we can take 30 and 20 as the registered republican and Democrat voters respectively?

and then if we calculate we get 24 for republicans (80% of 30) and 3 democrats (30% of 20), i.e. a total of 27 for candidate X and everyone else i.e. 6 republicans and 17 Democrats for candidate Y.

The question is by what percentage candidate x is expected to win the election that is ((27-23)/23)*100- but im not getting the answer correct, please explain where I m going wrong. Thanks
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by Brent@GMATPrepNow » Thu Jun 26, 2014 7:50 pm
Your calculations look good to me. The problem is that you are answering a different question. The question asks "By what percent is candidate X expected to win?" I'm not crazy about the wording of this question, but let's look at an example.
If A gets 40% of the votes, and B gets 60% of the votes, we COULD says that B got 50% more votes than A got. ORRRRR we COULD say that B won by 20%. Based on the official answer, the question's author is using the latter.

Here's one approach:

Let's go with 30 registered republicans and 20 registered Democrats (for a total of 50 voters), and do our calculations.

For Candidate X
80% of 30 + 15% of 20 = 24 + 3 = 27

For Candidate Y
There are 50 voters altogether. If 27 vote for Candidate X, then the remaining 23 must vote for Candidate Y (50 - 27 = 23)

Now let's examine the election results.
Candidate X: 27/50 = 54%
Candidate Y: 23/50 = 46%

Candidate X wins by [spoiler]8% [/spoiler]
Answer: C

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by [email protected] » Thu Jun 26, 2014 9:03 pm
Hi shibsriz,

Your approach to this question was great (it's the same way that I would have dealt with it).

If a question expects you to use the Percentage Change Formula, it will use a phrase such as "percentage change", "percent increase" or "percent decrease."

This question didn't use any of those phrases, so I have to assume that we're NOT supposed to use that formula. Elections, much like sporting events, are won by a "difference of the scores." When a soccer team wins a game 3 to 1, then that team "won BY 2 goals."

In this question, Candidate X received 54% of the vote while Candidate Y received 46% of the vote. Thus, Candidate X won the election by 8% of the voters.

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by j_shreyans » Sat Feb 14, 2015 7:36 am
Hi All ,

Whats wrong with the below method? Please advise.

Let Republicans be R and Democrats be D

R/D = 3/2

so R = 3D/2

Now it is given that 80% of R and 15% of D are expected to vote X

so 80R/100 + 15D/100=X

80R+15D=100X .......(|)

and rest 5% will vote Y

so 5(R+D)/100......(||)

now put R in both equation will get

D=20X/27 .....(from |)

and D= 8Y .....(from ||)

so 20X/27=8Y

but i am not getting the right answer.

Please advise and correct me if i am wrong..


Thanks

Shreyans
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by Matt@VeritasPrep » Sun Feb 15, 2015 6:33 pm
j_shreyans wrote:Hi All ,

Whats wrong with the below method? Please advise.

and rest 5% will vote Y

so 5(R+D)/100......(||)
I think this is the issue. We're really given

R/D = 3/2
and
.8R + .15D votes for X
and
.2R + .85D votes for Y

From this, we have

.8(3/2)D + .15D vote X
.2(3/2)D + .85D vote y

or

1.35D vote X, 1.15D vote Y

So X's vote percentage = 1.35D / (1.35D + 1.15D) = 135/250 = 54% of the total.

Since X gets 54% of the total, Y gets the other 46%, and X wins by 8%.
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