Problem 12 · 2015 Math Kangaroo
Medium
Logic & Word Problems
sum-constraintcareful-counting
All the boys in a class are born on different days of the week and all the girls are born in different months. If one new girl or boy joins this class, this is definitely no longer true. How many teenagers are in this class?
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Answer: B — 19
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Hint 1 of 2
There are only 7 days in a week and 12 months in a year.
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Hint 2 of 2
If adding any one new person must break the all-different rule, the class already uses every day and every month.
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Approach: fill every day and every month exactly
- Boys are on different days of the week, so at most 7 boys.
- Girls are in different months, so at most 12 girls.
- For any new boy OR girl to be forced to repeat, there must already be 7 boys and 12 girls.
- So the class has 7 + 12 = 19 (B) teenagers.
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