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Updated on: 24 Jan 2024, 23:06
Originally posted by guddo on 24 Jan 2024, 04:13.
Last edited by gmatophobia on 24 Jan 2024, 23:06, edited 1 time in total.
Last edited by gmatophobia on 24 Jan 2024, 23:06, edited 1 time in total.
Corrected typos in the question
Kudos
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
85% (01:19) correct
15%
(01:40)
wrong
based on 265
sessions
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In a certain election, \(\frac{3}{5}\) of the voters in District X and \(\frac{1}{2}\) of the voters in District Y voted for Candidate Smith. What percent of the voters in both districts combined voted for Candidate Smith?
(1) In the election, the number of voters in District X was 4 times the number of voters in District Y.
(2) In the election, the number of voters in District X was 800.
2024-01-24_15-12-47.png [ 50.87 KiB | Viewed 4225 times ]
(1) In the election, the number of voters in District X was 4 times the number of voters in District Y.
(2) In the election, the number of voters in District X was 800.
Attachment:
2024-01-24_15-12-47.png [ 50.87 KiB | Viewed 4225 times ]
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24 Jan 2024, 23:15
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guddo
Statement 1
(1) In the election, the number of voters in District X was 4 times the number of voters in District Y.
Assume
- The number of voters in District Y = \(y\)
- The number of voters in District X = \(4*y\)
- The combined number of voters in both districts = \(y + 4y = 5y\)
- The number of voters in District Y who voted for Candidate Smith = \(\frac{1}{2} * y\)
- The number of voters in District X who voted for Candidate Smith = \(\frac{3}{5} * 4y\)
- The combined number of voters in both districts who voted for Candidate Smith = \(\frac{y}{2} + \frac{12y}{5} = \frac{29y}{10}\)
Percent of the voters in both districts combined voted for Candidate Smith = \(\frac{\frac{29y}{10}}{5y} * 100 = 58\)%
The statement alone is sufficient and we can eliminate B, C, and E.
Statement 1
(2) In the election, the number of voters in District X was 800.
We can find the number of voters in District X who voted for Candidate Smith, however, we do not have any information on the number of voters in District Y. Hence, we cannot infer any information on District Y.
The statement alone is not sufficient.
Option A
22 Mar 2025, 00:44
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guddo
Let, Voters in X = 10x and Voters in Y = 10y
Smith = (3/5)*(10x) + (1/2)*(10y) = 6x + 5y
Question: \(\frac{(6x + 5y)}{10(x+y)}*100 = ?\)
STatement 1: 10x = 4*10y
i.e. x = 45
i.e. \(\frac{(6x + 5y)}{10(x+y)}*100 = \frac{(24y + 5y)}{10(4y+y)}*100 = 58\)
SUFFICIENT
Statement 2: 10x = 800
NOT SUFFICIENT
Answer: Option A
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