Among the respondents of a survey, one-fourth do not like to watch mov

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Oh this one is tricky . One tends to assume that the entire population of the people who like to read or do not like to read comes from people who do not like to watch movies

But Statement A bursts that bubble and clearly points to the right direction that there can be people who like to watch movies and a certain % of those may like to read or may not like to read ( the argument provides no info about this segment , nor can it be inferred )

I will go with E

Among the respondents of a survey, one-fourth do not like to watch movies; and of those who do not like to watch movies, two-third do not like to read also. Can the number of respondents who do not like to read be 70?

(1) The number of respondents who like to read and also like to watch movies is 110

(2) The number of respondents of the survey is 480

Total - X
Do not Like to watch movie - X/4
SO Like to watch movie - 3X/4

ALso
Of the X/4 people who do not like to watch movie

Do not like to Read = 2/3 *X/4 ( people who do not like to watch movie and do not like to read , i think they are into sports :D)
So like to read = X/4 - (2/3*X/4)

Statement A - No information can be inferred about people who like to watch movie and like to read SO not Sufficient
Statement B -Gives value of X . but there can be people who like to watch movies and do not like to read , of whom no info has been provided

Please correct me if i am wrong:)

Thanku

No of respondents = x
like movies 1/4x............
like to read 1/3*1/4 x= 1/12 x
not like to read 2/3 *1/4 x = 1/6x

Dont like movies 3/4 x
Dont like to read =a
like to read = b

statement 1
a= 110
Those who like to read can never be 70 as a= 110
hence statement 1 sufficient

statement 2
x= 480
those who dont like to watch movie and dont like to read = (1/6) * 480 = 80
those who dont like to read can never be 70
hence statement 2 is sufficient

answer is D option

Dont you think you have reversed like to read and dont like to read , like movies and dont like movies ?.

Also can you pls explain this statment
statement 1
a= 110
Those who like to read can never be 70 as a= 110
hence statement 1 sufficient

yes! you are right I jumbled the whole answer.
But now as I was attempting this question again. Here is the new solution.

Total respondents = x

dont like movie = 1/4 x
dont like to read = 1/6 x
like to read = 1/12 x

like movies = 3/4 x
dont like to read = a
like to read = b

to find = 1/6 x + a

statement 1
b = 110
a = 3/4 x - 110
now what we have to find is 1/6 x + a = 70
1/6 x + 3/4 x - 110 = 70
11/12 x = 180
( x is coming in decimal which cant be the case as x should always be the natural number)

hence statement 1 is sufficient ( please do tell whether my thought process is correct)

statement 2
total respondent = 480
dont like to read and dont like movies = 1/6 x= 80
and the one who dont like to read can never be 70
statement 2 sufficient

hence option D

We can make a 2 by 2 figure as shown.

I. The number of respondents who like to read and also like to watch movies is 110
This is shown in light blue colour.
Can \(\frac{3x}{4}-110+\frac{x}{6}\) be 70.
Let it be 70, then \(\frac{3x}{4}-110+\frac{x}{6}=70.....\frac{11x}{12}=180...x=\frac{180*12}{11}\).
This means x is not an integer. But the number of persons has to be an integer.
So, we can say that answer is NO
sufficient.

II. The number of respondents of the survey is 480.
x is 480. So question is " Is 480/6 + (watch movies+do not read)=70?"...
80+something=70... Not possible
So answer is NO
Sufficient.

D

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given 1/4 do not like movie and 2/3 of those do not read books as well
Can the number of respondents who do not like to read be 70
#1
The number of respondents who like to read and also like to watch movies is 110
3/4*1/3* x=110
x=440
so 440*1/4 ; 110 * 2/3 ; >70 sufficient ; not integer
#2
total people 480
480*1/4*2/3 = 80 again no and >70
sufficient
IMO D

For evaluating statement 2, we must not consider the info provided in statement 1. So kindly check and correct.
For statement 2,
Don't read + No movie = x/6 = 480/6 = 80
So overall people who don't read cannot be 70.
So sufficient

Posted from my mobile device

Thanks a lot. After answering 7000+ questions, I m sure I would know that.
The solution for statement II, of course, does have an error, so thank you for pointing out.
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