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27 Dec 2015, 10:20
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Difficulty:
55%
(hard)
Question Stats:
71% (02:41) correct
29%
(02:53)
wrong
based on 526
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A polling company surveyed a certain country, and it found that 35% of that country’s registered voters had an unfavorable impression of both of that state’s major political parties and that 20% had a favorable impression only of Party A. If one registered voter has a favorable impression of both parties for every two registered voters who have a favorable impression only of Party B, then what percentage of the country’s registered voters have a favorable impression of both parties (assuming that respondents to the poll were given a choice between favorable and unfavorable impressions only)?
A. 15
B. 20
C. 30
D. 35
E. 45
A. 15
B. 20
C. 30
D. 35
E. 45
01 Jan 2016, 21:48
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A polling company surveyed a certain country, and it found that 35% of that country’s registered voters had an unfavorable impression of both of that state’s major political parties and that 20% had a favorable impression only of Party A. If one registered voter has a favorable impression of both parties for every two registered voters who have a favorable impression only of Party B, then what percentage of the country’s registered voters have a favorable impression of both parties (assuming that respondents to the poll were given a choice between favorable and unfavorable impressions only)?
assume the total pool of registered voters = 100, so 35 of the country’s registered voters had an unfavorable impression of both of that state’s major political parties and 20 had a favorable impression only of Party A
let x = # of voters with a favorable impression of both parties
let 2x = # of voters with a favorable impression only of Party B
so unfavorable A and favorable B # of voters = 2x-x = x
35+x = number of unfavorable A
20+ 35+x = 100
55+x=100
x=45
E. 45
assume the total pool of registered voters = 100, so 35 of the country’s registered voters had an unfavorable impression of both of that state’s major political parties and 20 had a favorable impression only of Party A
let x = # of voters with a favorable impression of both parties
let 2x = # of voters with a favorable impression only of Party B
so unfavorable A and favorable B # of voters = 2x-x = x
35+x = number of unfavorable A
20+ 35+x = 100
55+x=100
x=45
E. 45
02 Jan 2016, 21:01
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Let Total registered voters = 100
35 voters are out.65 left
20 supports A. leaving them behind , we get 45 voters = supporters of B + supporters of both
Let , x be the supports for B
For every 2 voters for B , 1 is for both parties
.. .... 1 ...............,1/2 ..................
.. .... x................,x/2...................
so total x+x/2 = 3x/2 = 45 => x = 30
so x/2 = 15.supporters for both parties out of 100
so Ans A = 15%
35 voters are out.65 left
20 supports A. leaving them behind , we get 45 voters = supporters of B + supporters of both
Let , x be the supports for B
For every 2 voters for B , 1 is for both parties
.. .... 1 ...............,1/2 ..................
.. .... x................,x/2...................
so total x+x/2 = 3x/2 = 45 => x = 30
so x/2 = 15.supporters for both parties out of 100
so Ans A = 15%
