600 residents were surveyed about whether they liked 3 different candi

Question

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

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

pushpitkc · Answer

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)

jxav · Answer

35%+40%+50%=125%
(125%-18%-100%)÷2=3.5% liked all three candidates
3.5%*600=21

Ans is D

Sent from my SM-G935F using  GMAT Club Forum mobile app

ScottTargetTestPrep · Answer

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.

Answer: D

rnz · Answer

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!

Fdambro294 · Answer

Instead of converting the Percentages% ---> to Numbers:

Find the %Percentage of Voters who Liked ALL 3 Exactly and then apply that to the 600 Total People.

Total Unique Elements = (A + B + C) - (EXACTLY 2 Sets) - (2) * (Exactly 3 Sets)

When we counted (All of A) + (All of B) + and (All of C) we OVER-Counted the people who like ALL 3 by THREE Times too many.

Since we are only Subtracting the number of people who like EXACTLY 2, we need to Subtract the no. of people who like All 3 TWICE to remove the over-counting and have these people only counted ONCE.

Also, since everyone liked "at least one": Neither = 0

100% = (35% + 40% + 50%) - (18%) - (2)*(p)

100% = (125% - 18%) - (2)*(p)

100% = 107% - (2)*p

(2)*p = 7%

p = 3.5% = percentage% of the Unique people who like ALL 3

(600 people) * (3.5%) = 21 people who like ALL 3

-D-

MathRevolution · Answer

Total = (A + B + C) - (Exactly 2 ) - (2) * (Exactly 3)

=> 100% = (35% + 40% + 50%) - (18%) - (2) * (Exactly 3)

=> (2) * (Exactly 3) = 125 - 100 - 18 = 7%

=> (Exactly 3) =  \frac{7 }{ 2}  = 3.5%

=>  \frac{3.5 }{ 100}  * 600 = 21

Answer D

jackfr2 · Answer

Can anyone solve this with venn diagram ? I am not being able to visualize it

Posted from my mobile device

bumpbot · Answer

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