You have 1 pair of new-born rabbits (one male and one female) that can breed when they reach maturity. You also have 3 pairs of mature rabbits (3 males and 3 females) that can start breeding immediately. They follow these rules:
• Each mature pair of rabbits produces one new pair of offspring (one male and one female) at the end of each month
• Each offspring pair takes one month to mature
How many rabbits do you have at the end of the 3rd month?
A) 42
B) 28
C) 36
D) 18
E) 14
IMAT 2023 · Question 5
Q5 - Problem solving
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The correct answer is C) 36.
Count pairs, not rabbits, and go month by month. At the end of each month every mature pair produces one new pair, and the pairs born the month before become mature.
Start: 3 mature, 1 newborn
End of month 1: 3 born, the newborn matures → 4 mature + 3 newborn = 7 pairs
End of month 2: 4 born, 3 mature → 7 mature + 4 newborn = 11 pairs
End of month 3: 7 born, 4 mature → 11 mature + 7 newborn = 18 pairs
18 pairs = 36 rabbits.
The usual mistake is letting newborns breed in the same month they are born.
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