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18 Dec 2010, 11:55
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
75% (01:47) correct
25%
(02:11)
wrong
based on 2003
sessions
History
Date
Time
Result
Not Attempted Yet
In a group of 68 students, each student is registered for at least one of three classes – History, Math and English. Twenty-five students are registered for History, twenty-five students are registered for Math, and thirty-four students are registered for English. If only three students are registered for all three classes, how many students are registered for exactly two classes?
A. 13
B. 10
C. 9
D. 8
E. 7
A. 13
B. 10
C. 9
D. 8
E. 7
18 Dec 2010, 12:20
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tonebeeze
"Each student is registered for at least one of three classes" means that there are no students who are registered for none of the classes.
Total = {people in group A} + {people in group B} + {people in group C} - {people in exactly 2 groups} - 2*{people in exactly 3 groups} + {people in none of the groups}:
68 = 25 + 25 + 34 - {people in exactly 2 groups} - 2*3 + 0 --> {people in exactly 2 groups}=10
Answer: B.
Look at the diagram:
Attachment:
untitled.PNG [ 5.66 KiB | Viewed 93314 times ]
Similarly when we sum {people in group A} + {people in group B} + {people in group C} we count students who are in exactly 3 groups (blue section) thrice (as it is the portion of all three groups), so to count this group only once we are subtracting 2*{people in exactly 3 groups}.
For more on this check: formulae-for-3-overlapping-sets-69014.html#p729340
As for your question: yes, questions on 3 overlapping sets are quite common for the GMAT.
Hope it helps.
General Discussion
18 Dec 2010, 12:27
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Hi!
There are two approaches you can take for 3 overlapping set questions. Which one works best for you is really a matter of preference.
Many people find Venn diagrams to be the best approach - draw 3 circles that have both double and triple overlapping sections. Venn diagrams are an excellent tool, especially for visual learners.
On the other hand, if you're an equation kind of guy (or gal), there are two different equations that come in handy:
True # of objects = (total # in group 1) + (total # in group 2) + (total # in group 3) - (# in exactly 2 groups) - 2(# in all 3 groups);
and:
True # of objects = (total in exactly 1 group) + (total in exactly 2 groups) + (total in exactly 3 groups).
There are a few other variations of those equations as well. In theory, you should add "+ total in none of the groups" to each equation, but I don't think I've ever seen a 3-set question on the GMAT in which everyone wasn't a member of at least one group.
Even at high levels of the exam, 3 set questions aren't particularly common - most test takers see 0 or 1 of them, rarely 2.
There are two approaches you can take for 3 overlapping set questions. Which one works best for you is really a matter of preference.
Many people find Venn diagrams to be the best approach - draw 3 circles that have both double and triple overlapping sections. Venn diagrams are an excellent tool, especially for visual learners.
On the other hand, if you're an equation kind of guy (or gal), there are two different equations that come in handy:
True # of objects = (total # in group 1) + (total # in group 2) + (total # in group 3) - (# in exactly 2 groups) - 2(# in all 3 groups);
and:
True # of objects = (total in exactly 1 group) + (total in exactly 2 groups) + (total in exactly 3 groups).
There are a few other variations of those equations as well. In theory, you should add "+ total in none of the groups" to each equation, but I don't think I've ever seen a 3-set question on the GMAT in which everyone wasn't a member of at least one group.
Even at high levels of the exam, 3 set questions aren't particularly common - most test takers see 0 or 1 of them, rarely 2.
) for making life simpler
