Lesson: Chapter - 11
Group Questions
Occasionally, the Math IC will pose questions about groups with overlapping
members. For example:
In a particular school, the school band has 42 members and the school orchestra
has 35 members. Seven students play in both the band and the orchestra, and 231
students play in neither the band nor the orchestra. How many students are in
this particular school?
To answer this question, carefully count the students. 231 + 42 + 35 = 308 is a
tempting answer, but in this solution, we are counting the students who play in
both the band and orchestra twice. We must subtract 7 from this total to get the
right answer: 308 – 7 = 301.
This question illustrates the formula for answering such questions. If two
subgroups of a population share members, the equation that governs the total
number of people in the population is:
Total Population = Group A Population + Group B
Population + Neither Group A nor B population – Group A and B population
The last term of this formula subtracts the elements that were double-counted
earlier.
Try another example:
A room contains 80 people. Thirty have curly hair, 24 have blond hair, and 40
have hair that is neither curly nor blond. How many people in the room have
curly, blond hair?
Use the formula: 80 = 30 + 24 + 40 – x. Thus, x = 14 (14 people in
the room have curly and blond hair). This formula will work for all group
problems, as long as there are only two groups involved.
Next to display next topic in the chapter.
Mathematics Practice Questions
Video Lessons and 10 Fully Explained Grand Tests
Large number of solved practice MCQ with explanations. Video Lessons and 10 Fully explained Grand/Full Tests.