In Greensboro County, 75 people own a television and 35

Question

In Greensboro County, 75 people own a television and 35 people own a radio. The number of people who own both a television and a radio plus the number of people who own neither is half the amount of the people who own either. If the ratio of people who own both to the people who own neither is 5:6 how many people live in the county ?

A 55
B 85
C 105
D 110
E 115

The correct ans is E. How ?

A 55
B 85
C 105
D 110
E 115

The correct ans is E. How ?

AbeinOhio · Answer

something is wrong with this question.. can someone else take a look and confirm?

been spinning my wheels on this for like 45 mins..

I keep getting results that make no sense

Bunuel · Answer

That's because the question is flawed.

In Greensboro County, 75 people own a television and 35 people own a radio. The number of people who own both a television and a radio plus the number of people who own neither is half the amount of the people who own either. If the ratio of people who own both to the people who own neither is 5:6 how many people live in the county ? 
A 55
B 85
C 105
D 110
E 115

Given: "75 people own a television and 35 people own a radio", so we have that: total=75+35-{both}+{neither}, say {both}=x and {neither}=y --> total=75+35-x+y;

"The number of people who own both a television and a radio plus the number of people who own neither is half the amount of the people who own either": x+y=(75+35-x)/2;

"The ratio of people who own both to the people who own neither is 5:6": x/y=5/6.

Now, if you solve x+y=(75+35-x)/2 and x/y=5/6 you won't get integer values for x and y, as you should (they represent # of people). So, there is something wrong with the question.

Based on the OA saying that total=115, Kaplan (if it's really their question) writes first equation as x+y=(75+35)/2, which is wrong because the # of people who own either a television or a radio is 75+35-{both}, we are subtracting {both} to avoid doublecounting of that group, since it's included both in 75 and in 35. But if you solve their version of equations: x+y=(75+35)/2 and x/y=5/6 you'll get x=25 and y=30 --> substitute it in initial equation: total=75+35-x+y=75+35-25+30=115, the answer they got as correct.

Hope it's clear.

stevie1111 · Answer

I think the word either here implies 'any' i.e either television or radio.

Bunuel · Answer

"The amount of the people who own either" means people who own either TV or radio or both, which is 75+35-{both}.

prbhtsngr · Answer

bunnel. a different question
Of a group of people, 10 play piano, 11 play guitar, 14 play violin, 3 play all the instruments, 20 play only one instrument. How many play 2 instruments?

A. 3
B. 6
C. 9
D. 12
E. 15
can v solve this with your 2 formulas u mentioned
t=a+b+c -(sum of 2)+all 3+ neither
t=a+b+c -(sum of exactly 2)-2*all 3+ neither
if not then any other shortcut or formula.

Bunuel · Answer

This question is discussed here: of-a-group-of-people-10-play-piano-11-play-guitar-14-play-86070.html

TGC · Answer

Hi Folks ,

One query on this question:

The number of people who own both a television and a radio plus the number of people who own neither is half the amount of the people who own either.

Does this language says :

x+y = (1/2){75+35-2x} (As Either should mean Either of the two => Only Radio + Only Tele)

Or does it says:

x+y = (1/2){75+35-x} (As   where U implies Union/OR)

Please clarify

Rgds,
TGC !

saurabh35 · Answer

Well i agree with TGC.
Since either means means either radio or Either TV..
Equation will be:

1/2{120-2(Both)}

Anyways, there is some problem with question.

Asifpirlo · Answer

Here,
T = 75 and R = 35
x = have neither and (T n R) = have both And the ratio = (T n R)/x = 5/6
from question,

(T n R) + x = 1/2 (T+R) or, x = 30 (using above values in the calculations)

Now, (T n R) = 5/6 × 30 = 25

So only T = 75-25=50
 only R = 35-25 = 10

So total people = 50+10+ 30 + 25 = 115 (Answer)

In Greensboro County, 75 people own a television and 35

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