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

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Math Expert
Joined: 02 Sep 2009
Posts: 46166
In a certain state, the ratio of registered Republicans to registered [#permalink]

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10 Feb 2015, 08:35
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45% (medium)

Question Stats:

72% (01:47) correct 28% (02:31) wrong based on 104 sessions

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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%

Kudos for a correct solution.

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

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10 Feb 2015, 09:18
1
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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GMAT Date: 05-05-2015
Re: In a certain state, the ratio of registered Republicans to registered [#permalink]

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10 Feb 2015, 10:16
5
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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12 Feb 2015, 02:19
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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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12 Feb 2015, 03:30
1
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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12 Feb 2015, 23:38
3
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

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Math Expert
Joined: 02 Sep 2009
Posts: 46166
Re: In a certain state, the ratio of registered Republicans to registered [#permalink]

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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

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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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.

Therefore, Candidate X will win by:

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

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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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