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Most serious students are happy students, and most serious [#permalink]
06 Aug 2009, 16:50

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Difficulty:

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Question Stats:

100% (01:31) correct
0% (00:00) wrong based on 2 sessions

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

Re: Most serious students are happy students, and most serious [#permalink]
19 Jun 2014, 21:18

Expert's post

MontrealLady wrote:

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 227 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. _________________