Multiple choice general knowledge math & puzzles

A number of cats got together and decided to kill between them 999919 mice. Every cat killed an equal number of mice. Each cat killed more mice than there were cats. How many cats do you think there were ?

  1. 991

  2. 999

  3. 981

  4. 989
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

We need to factorize 999919 into two factors where: (1) both factors are equal (since each cat killed equal mice), (2) each factor > number of cats. Factorizing 999919 = 991 × 1009 (both are prime). Since we need cats = factors = equal, and cats > mice/cat (meaning 991 > 999919/991 ≈ 1009), this doesn't quite work. Actually the question says each cat killed more mice than there were cats, meaning mice per cat > cats. If cats = 991, mice per cat = 1009, and 1009 > 991 ✓.

AI explanation

To solve this problem, let's assume there are "x" cats.

Given that each cat killed an equal number of mice, we can represent the number of mice killed by each cat as "m".

According to the problem statement, each cat killed more mice than the total number of cats. So, we can write the equation as follows:

m > x

The total number of mice killed is given as 999919, and we know that each cat killed an equal number of mice. Therefore, the total number of mice killed can also be expressed as:

m * x = 999919

Now, let's try to find the possible values of "x" by considering the options:

Option A) 991 cats: If we assume there are 991 cats, then each cat would have killed approximately 1010 mice (999919/991 ≈ 1010). Here, the condition m > x holds true, as 1010 > 991.

So, Option A) is a possible solution.

Option B) 999 cats: If we assume there are 999 cats, then each cat would have killed approximately 1000 mice (999919/999 ≈ 1000). Here, the condition m > x does not hold true, as 1000 is not greater than 999.

So, Option B) is not a possible solution.

Option C) 981 cats: If we assume there are 981 cats, then each cat would have killed approximately 1019 mice (999919/981 ≈ 1019). Here, the condition m > x holds true, as 1019 > 981.

So, Option C) is a possible solution.

Option D) 989 cats: If we assume there are 989 cats, then each cat would have killed approximately 1011 mice (999919/989 ≈ 1011). Here, the condition m > x holds true, as 1011 > 989.

So, Option D) is a possible solution.

Based on our analysis, the possible number of cats that satisfy the given conditions is 991.

Therefore, the correct answer is Option A) 991.

Keep practicing — related questions