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Question

At a dance party a group of boys and girls exchange dances as follows:
one boy dances with 5 girls, a second boy dances with 6 girls, and so on, the last boy dancing with all girls. If b represents the number of boys and g the number of girls, then:

A
b=g
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B
b=g5
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C
b=g4
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D
b=g5
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E
It is impossible to determine a relation between b and g without knowing the total number of boys and girls
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Solution

The correct option is C b=g4
Set up the following table, a one to tone correspondence between the elements of the boy set and the girl set:
Boy number =1,2,3,...b
Girl danced with =5,6,7,.....b+4;
g=b+4;b=g4
or the formula for the last term of the arithmetic sequence 5,6,7,....g;
g=5+(b1)(1);b=g4

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