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13 Jul 2021, 06:00
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
75% (02:29) correct
25%
(02:47)
wrong
based on 215
sessions
History
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Not Attempted Yet
In 2011, each member of a committee voted for one of two possible candidates for president. Candidate A received 40% of the vote and Candidate B received the remainder. In 2012, the same two candidates ran for president. Candidate A received 3 more votes than the previous year, a 5% increase in his total number of votes. How many votes did Candidate B receive in 2011?
(A) 40
(B) 60
(C) 75
(D) 90
(E) 150
(A) 40
(B) 60
(C) 75
(D) 90
(E) 150
13 Jul 2021, 08:23
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Let x be the total no. of votes in 2011,
Candidate A = (40/100)*x
Candidate B = (60/100) * x
In 2012,
Candidate A got 5% more votes than last year, which is 3 more votes,
To find total number of votes in 2011 i.e x,
(5/100)*(40/100)*x = 3
2x = 300, x= 150.
Now we need the no of votes Candidate B got in 2011, i.e (60/100) * x
(60/100) * 150 = 90
The answer IMO: D
Candidate A = (40/100)*x
Candidate B = (60/100) * x
In 2012,
Candidate A got 5% more votes than last year, which is 3 more votes,
To find total number of votes in 2011 i.e x,
(5/100)*(40/100)*x = 3
2x = 300, x= 150.
Now we need the no of votes Candidate B got in 2011, i.e (60/100) * x
(60/100) * 150 = 90
The answer IMO: D
13 Jul 2021, 08:42
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Let's pick an option and solve it.
Suppose B got 150 votes in 2011. This is 60% of the total votes.
=> \(\frac{60}{100}\) * Total votes = 150
=> Total votes = 250
Candidate A in 2011 will 250 - 150 = 100 votes.
In 2012, A will have 3 more votes than 2011 that is 103 which is not 5%.
Pick 90:
2011: B = \(\frac{60}{100}\) * Total votes = 90
Total votes = 150
2011: A gets : 150 - 90 = 60
2012: A gets 3 more than 2011 : 60 + 3 = 63. This is 5% increase : \(\frac{63 - 60 }{ 60} * 100 = 5%.\)
Answer D
Suppose B got 150 votes in 2011. This is 60% of the total votes.
=> \(\frac{60}{100}\) * Total votes = 150
=> Total votes = 250
Candidate A in 2011 will 250 - 150 = 100 votes.
In 2012, A will have 3 more votes than 2011 that is 103 which is not 5%.
Pick 90:
2011: B = \(\frac{60}{100}\) * Total votes = 90
Total votes = 150
2011: A gets : 150 - 90 = 60
2012: A gets 3 more than 2011 : 60 + 3 = 63. This is 5% increase : \(\frac{63 - 60 }{ 60} * 100 = 5%.\)
Answer D
