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In a certain state, the ratio of registered Republicans to registered

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In a certain state, the ratio of registered Republicans to registered [#permalink]

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In a certain state, the ratio of registered Republicans to registered Democrats is 3 to 2, and every registered voter is either a Republican or a Democrat. If 80 percent of the Republicans and 15 percent of the Democrats are expected to vote for Candidate X, and everyone else is expected to vote for Candidate Y, by what percent is Candidate X expected to win the election?

A. 2%
B. 5%
C. 8%
D. 10%
E. 15%


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[Reveal] Spoiler: OA

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Re: In a certain state, the ratio of registered Republicans to registered [#permalink]

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New post 10 Feb 2015, 09:18
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C - 8%.....Let the total voters be 5x...

Ratio = 3x : 2x

0.8(3x) + 0.15(2x) = 2.7x voted for candidate X

Winning total = 2.5x.....percentage 0.2x/2.5x*100 = 8%

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Re: In a certain state, the ratio of registered Republicans to registered [#permalink]

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Bunuel wrote:
In a certain state, the ratio of registered Republicans to registered Democrats is 3 to 2, and every registered voter is either a Republican or a Democrat. If 80 percent of the Republicans and 15 percent of the Democrats are expected to vote for Candidate X, and everyone else is expected to vote for Candidate Y, by what percent is Candidate X expected to win the election?

A. 2%
B. 5%
C. 8%
D. 10%
E. 15%


Kudos for a correct solution.


Since we were expected to find a percentage figure - It thought that it might be easier to pick a 'smart number' to represent the total number of voters (republicans and democrats). Therefore, I picked 50 (as the total number of voters) and thus 30:20 represents the number ratio of Republicans:Democrats. If 80% of Republicans (which is (30*0.8) = 24) and 15% of Democrats (20*0.15 = 3) voted for candidate X, means that out of total of 50 voters; 27 (24 + 3) voters voted for candidate X and 23 voted for candidate Y. Thus we can infer that candidate X is expected to win the election by 4 (27-23) votes. Therefore candidate X is expected to win the election by (4/50) votes which is equivalent to 8%.

I think the answer is C.

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Re: In a certain state, the ratio of registered Republicans to registered [#permalink]

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Answer = C = 8%

Republican ...................... Democrats ................ Total

300 ..................................... 200 ......................... 500 (Assume; ratio 3:2)

270 ...................................... 230 ...................... 500 (Votes polled)

From 500 votes polled, Republicans got 40 more

Percentage \(= \frac{40}{500} * 100 = 8%\)
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Re: In a certain state, the ratio of registered Republicans to registered [#permalink]

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Here we go:

Let the total number of voters = p

Republicans = 3/5 * p

Democrats = 2/5 * p

Those who voted for X

0.8 * (3/5 * p) + 0.15 * (2/5 * p) = 0.54p


Those who voted for Y

p - 0.54p = 0.48p


by what percent is Candidate X expected to win the election will be given by

(0.54p - 0.48p / p) * 100

= 8 %


Option C

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Re: In a certain state, the ratio of registered Republicans to registered [#permalink]

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New post 12 Feb 2015, 23:38
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Hi All,

This question is perfect for TESTing VALUES.

You'll notice the "percent sign" in the answer choices and the repeated usage of the word "percent" in the prompt. In these situation, using the number 100 will usually make the math pretty easy to do.

We're told that the ratio of Republicans to Democrats is 3:2

Total voters = 100
Republicans = 60
Democrats = 40

We're told that 80% of Republicans and 15% of Democrats are expected to vote for Candidate X:

80%(60) + 15%(40) = 48 + 6 = 54 voters (or 54% of the total voters) are expected to vote for Candidate X.

We're told that the rest are expected to vote for Candidate Y:

100% - 54% = 46% are expected to vote for Candidate Y.

We're asked for "what percent" Candidate X is expected to win by....

54 percent - 46 percent = 8 percent

Final Answer:
[Reveal] Spoiler:
C


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Re: In a certain state, the ratio of registered Republicans to registered [#permalink]

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New post 16 Feb 2015, 05:39
Bunuel wrote:
In a certain state, the ratio of registered Republicans to registered Democrats is 3 to 2, and every registered voter is either a Republican or a Democrat. If 80 percent of the Republicans and 15 percent of the Democrats are expected to vote for Candidate X, and everyone else is expected to vote for Candidate Y, by what percent is Candidate X expected to win the election?

A. 2%
B. 5%
C. 8%
D. 10%
E. 15%


Kudos for a correct solution.


VERITAS PREP OFFICIAL SOLUTION

Correct Answer: C

First, we must calculate what percent of the total votes Candidate X is expected to get. We know that 60% of the voters are Republican and 40% are Democratic. 80% of the Republicans will vote for X, so .8 * 60% = 48%. 15 percent of the Democrats will vote for X, so .15 * 40% = 6%. Thus, Candidate X is expected to gather 54% of the total vote. Candidate Y gets the remainder, or 100% - 54%, or 46%. Thus, Candidate X is expected to defeat Candidate Y by a margin of 8% (54% - 46%). Thus, answer choice C is correct.
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Re: In a certain state, the ratio of registered Republicans to registered [#permalink]

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New post 14 Sep 2017, 10:45
Bunuel wrote:
In a certain state, the ratio of registered Republicans to registered Democrats is 3 to 2, and every registered voter is either a Republican or a Democrat. If 80 percent of the Republicans and 15 percent of the Democrats are expected to vote for Candidate X, and everyone else is expected to vote for Candidate Y, by what percent is Candidate X expected to win the election?

A. 2%
B. 5%
C. 8%
D. 10%
E. 15%


We are given that the ratio of Republicans to Democrats = 3x : 2x, so the total number of voters is 5x.

Since 80 percent of the Republicans and 15 percent of the Democrats are expected to vote for Candidate X:

0.8(3x) = 2.4x Republicans and 0.15(2x) = 0.3x Democrats are expected to vote for Candidate X.

So, Candidate X receives 2.4x + 0.3x = 2.7x votes out of 5x votes, and the other candidate, Candidate Y, receives 5x - 2.7x = 2.3x votes.

Therefore, Candidate X will win by:

(2.7x - 2.3x)/5x = 0.4/5 = 4/50 = 8%.

Answer: C
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Re: In a certain state, the ratio of registered Republicans to registered   [#permalink] 14 Sep 2017, 10:45
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