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# 600 residents were surveyed about whether they liked 3 different candi

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600 residents were surveyed about whether they liked 3 different candi  [#permalink]

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03 May 2017, 02:43
00:00

Difficulty:

45% (medium)

Question Stats:

70% (02:25) correct 30% (02:20) wrong based on 138 sessions

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600 residents were surveyed about whether they liked 3 different candidates running for certain offices in their town. 35% of those surveyed liked candidate A, 40% liked candidate B, and 50% liked candidate C. If all residents liked at least one of three candidates and 18% liked exactly 2 of the three candidates, then how many of the residents liked all three of the candidates?

A. 150
B. 108
C. 42
D. 21
E. 7

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Re: 600 residents were surveyed about whether they liked 3 different candi  [#permalink]

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03 May 2017, 04:14
1
1
P(Total) = P(A) + P(B) +P(C) - P(exactly 2) - 2*P(all 3)

P(Total) = 600
P(A) = 35% of 600 = 210
P(B) = 40% of 600 = 240
P(C) = 50% of 600 = 300
P(exactly 2) = 18% of 600 = 108

Substituting the values
600 = 210+240+300+108 - 2*P(all 3)
2*P(all 3) = 42
p(all 3) = 21(Option D)
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Re: 600 residents were surveyed about whether they liked 3 different candi  [#permalink]

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03 May 2017, 07:20
35%+40%+50%=125%
(125%-18%-100%)÷2=3.5% liked all three candidates
3.5%*600=21

Ans is D

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Re: 600 residents were surveyed about whether they liked 3 different candi  [#permalink]

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06 May 2017, 16:47
Bunuel wrote:
600 residents were surveyed about whether they liked 3 different candidates running for certain offices in their town. 35% of those surveyed liked candidate A, 40% liked candidate B, and 50% liked candidate C. If all residents liked at least one of three candidates and 18% liked exactly 2 of the three candidates, then how many of the residents liked all three of the candidates?

A. 150
B. 108
C. 42
D. 21
E. 7

We can create the following equation:

Total # people = # who like candidate A + # who like candidate B + # who like candidate C - (# who like 2 candidates) - 2(# who like 3 candidates) + # who like neither

We can let n = the percentage (without the percent sign) of the people who like all 3 candidates; thus, we have:

600 = 0.35(600) + 0.4(600) + 0.5(600) - 0.18(600) - 2(n/100)(600) + 0

600 = 642 - 12n

12n = 42

n = 3.5

Thus, the number of people who like all 3 candidates is 0.035 x 600 = 21 people.

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600 residents were surveyed about whether they liked 3 different candi  [#permalink]

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18 Dec 2017, 11:33
1
ScottTargetTestPrep wrote:
Bunuel wrote:
600 residents were surveyed about whether they liked 3 different candidates running for certain offices in their town. 35% of those surveyed liked candidate A, 40% liked candidate B, and 50% liked candidate C. If all residents liked at least one of three candidates and 18% liked exactly 2 of the three candidates, then how many of the residents liked all three of the candidates?

A. 150
B. 108
C. 42
D. 21
E. 7

We can create the following equation:

Total # people = # who like candidate A + # who like candidate B + # who like candidate C - (# who like 2 candidates) - 2(# who like 3 candidates) + # who like neither

We can let n = the percentage (without the percent sign) of the people who like all 3 candidates; thus, we have:

600 = 0.35(600) + 0.4(600) + 0.5(600) - 0.18(600) - 2(n/100)(600) + 0

600 = 642 - 12n

12n = 42

n = 3.5

Thus, the number of people who like all 3 candidates is 0.035 x 600 = 21 people.

In this part of the equation, "2(# who like 3 candidates)" where does the 2 come from? If it's from 2/3 candidates why is that duplicated from "# exactly 2"? Thanks!
600 residents were surveyed about whether they liked 3 different candi   [#permalink] 18 Dec 2017, 11:33
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