In 2004, the number of sheep on the farm was equal to the number of pigs. In 2005, the population of pigs and sheep each increased 20%. Which of the following could represent the total number of pigs and sheep on the farm in 2005? (A) 4832 (B) 5034 (C) 5058 (D) 5076 (E) 5128

Answer choices seems to be incorrect. At least one option should be completely divisible by 11.

I'm pretty sure the correct answer is there. Having said that, these are questions that I've created I could be wrong. I'm wondering why the number must be divisible by 11.

I am getting "D" is this correct ?

So the overall number actually increase by 20% , which makes it 120 %, in other words the number needs be divided by 12 It is divisible by 3 and by 4. 324: it is divisible by 3 and by 4. Subtract the last digit from twice the rest. 324: (32 × 2) − 4 = 60. 5076 fits in. Enjoy the link below: https://en.wikipedia.org/wiki/Divisibility_rule

Sheep = Pig 2004 2005 1.2 Sheep = 1.2Pigs The only value that works is D) 5076 5076 divisible by 12 Good problem Brent!

Brent Hanneson wrote:I'm pretty sure the correct answer is there. Having said that, these are questions that I've created I could be wrong. I'm wondering why the number must be divisible by 11. Ok I got my mistake. The number should be divisible by 12. Only (D) is the option that is divisible by both 3 and 4. Will choose (D).

The answer is D - nice work. It's important to note, though, that if the question involved only one animal type, then the resulting population (after the 20% increase) would need to be divisible by 6, not 12. This is because increasing a number by 20% is the same as multiplying the number by 6/5. The 5 in the denominator would have to cancel out with the original population (or else we would have partial animals). The reason the resulting number must divisible by 12 is due to the fact that we have 2 equivalent populations.

What's the least it can be? Well, it's 12 (5 pigs, 5 sheep, 20% of the total is 2, which equals 12). Therefore the choice has to be divisible by 12. Since I know that 12 is divisible by 6, the number has to also be divisible by 6, so now I have to check if the answer choices are divisible by 2 and 3 (as a rule). There is only one choice that is--D.

Composite divisors A number is divisible by a given divisor if it is divisible by the highest power of each of its prime factors. For example, to determine divisibility by 24, check divisibility by 8 and by 3. Note that checking 4 and 6, or 2 and 12, would not be sufficient. A table of prime factors may be useful.