Problem 19 · 2019 Math Kangaroo
Stretch
Logic & Word Problems
casework
Robert makes 5 statements, exactly one of which is wrong:
(A) My son Basil has 3 sisters.
(B) My daughter Ann has 2 brothers.
(C) My daughter Ann has 2 sisters.
(D) My son Basil has 2 brothers.
(E) I have 5 children.
Which statement is wrong?
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Answer: D — Statement D
Show hints
Hint 1 of 3
Try to find how many sons and daughters Robert has so that four of the five statements come out true.
Still stuck? Show hint 2 →
Hint 2 of 3
Remember a boy counts his brothers as the other boys, and his sisters as all the girls.
Still stuck? Show hint 3 →
Hint 3 of 3
Once you fix the numbers of boys and girls, check which single statement is then forced to be false.
Show solution
Approach: find the family that fits four statements
- Statement A says Basil has 3 sisters (so 3 girls) and B says Ann has 2 brothers (so 2 boys); that makes 2 boys and 3 girls, which agrees with C (Ann's 2 sisters) and E (5 children).
- Check D: Basil's brothers are the other boys, and with 2 boys he has only 1 brother, not 2, so statement D is false.
- All the others fit the 2-boy, 3-girl family, so the single wrong one is statement D (D).
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