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Most serious students are happy students, and most serious [#permalink]

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06 Aug 2009, 17:50

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Most serious students are happy students, and most serious students go to graduate school. Furthermore, all students who go to graduate school are overworked.

Which one of the following can be properly inferred from the statements above?

1) Most overworked students are happy students. 2) Some happy students are overworked 3) All overworked students are serious students 4) Some unhappy students go to graduate school 5) All serious students are overworked

Most serious students are happy students, and most serious students go to graduate school. Furthermore, all students who go to graduate school are overworked.

Which one of the following can be properly inferred from the statements above?

1) Most overworked students are happy students. 2) Some happy students are overworked 3) All overworked students are serious students 4) Some unhappy students go to graduate school 5) All serious students are overworked

answer is B

thanks for explaining

You can make Venn diagrams to understand the given data.

Attachment:

Ques3.jpg [ 31.82 KiB | Viewed 1757 times ]

Most serious students are happy students, - More than 50% of serious students are happy so the red and yellow circle overlap such that more than 50% of the red circle is covered by the yellow circle.

and most serious students go to graduate school - More than 50% of serious students are go to graduate schools so the red and green circle overlap such that more than 50% of the red circle is covered by the green circle.

This implies that the yellow and the green circle will definitely have some overlap.

Furthermore, all students who go to graduate school are overworked. - The white circle envelopes the green circle completely.

Since yellow (happy students) circle does overlap with green circle (go to graduate school) and green circle is inside the white (overworked) circle,. it means the yellow circle and white circle must overlap atleast a bit.

So some happy students are overworked.

Answer (B)

None of the other options "must be true". They may or may not be true but we cannot properly infer them. _________________

Most serious students are happy students, and most serious [#permalink]

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25 Dec 2015, 22:44

I will disassemble the argument

1. Most serious-------->Happy Most serious--------->go to grad school

2. All students in grad school----> over worked

Few points before going to answer. Two categories of students here. Most serious and other students.

a. We don’t know how much % does 'most serious' students occupy in the entire pool of students. b. Other students can be happy c. Other students go to school d. Other students do over work e. Most=above 50% f. Some= An unknown quantity(less than 50% ?)

1) Most overworked students are happy students.- we can,t say that 2) Some happy students are overworked- yep an unknown quantity of happy students are overworked. It can be 1% to 100%. 3) All overworked students are serious students – no only some over worked students are serious 4) Some unhappy students go to graduate school- All other students also can be happy. 5) All serious students are overworked---Unhappy students can be there in the pool who is working hard

please do mention if i am wrong in my reasoning.

Last edited by pkm9995109794 on 26 Dec 2015, 01:54, edited 1 time in total.

Most serious students are happy students, and most serious students go to graduate school. Furthermore, all students who go to graduate school are overworked.

Which one of the following can be properly inferred from the statements above?

1) Most overworked students are happy students. 2) Some happy students are overworked 3) All overworked students are serious students 4) Some unhappy students go to graduate school 5) All serious students are overworked

There is a group of serious students.. given that:- 1)Most serious students are happy students... Most would mean >50% 2) most serious students go to graduate school...

since both the groups "happy students" and "students go to graduate school" have most of the serious students within its ambit.. there ha sto be atleast a few of both the groups overlapping, that is some serious students have to be common to the two groups.."happy students" and "students go to graduate school" ... whcih in turn means that some happy students go to graduate school But we are also told that all th egraduate school students are overworked.. so some happy students go to graduate school can be written as some happy students are overworked students B _________________

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