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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?
A. Most overworked students are happy students.
B. Some happy students are overworked
C. All overworked students are serious students
D. Some unhappy students go to graduate school
E. All serious students are overworked
Which one of the following can be properly inferred from the statements above?
A. Most overworked students are happy students.
B. Some happy students are overworked
C. All overworked students are serious students
D. Some unhappy students go to graduate school
E. All serious students are overworked
19 Jun 2014, 22:18
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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?
A. Most overworked students are happy students.
B. Some happy students are overworked
C. All overworked students are serious students
D. Some unhappy students go to graduate school
E. All serious students are overworked
You can make Venn diagrams to understand the given data.
Ques3.jpg [ 31.82 KiB | Viewed 21171 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.
Which one of the following can be properly inferred from the statements above?
A. Most overworked students are happy students.
B. Some happy students are overworked
C. All overworked students are serious students
D. Some unhappy students go to graduate school
E. All serious students are overworked
You can make Venn diagrams to understand the given data.
Attachment:
Ques3.jpg [ 31.82 KiB | Viewed 21171 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.
General Discussion
26 Dec 2015, 00:17
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MontrealLady
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
