jedit
[quote="chetan2u"]In a zoo, the ratio of elephants to lions is same as lions to deer. If there are at least 5 deer, what is the number of elephants?
(1) The ratio of elephant to lion is 1:5
(2) The number of lions is a Prime number.
source- self made
It should be B.
From stem, we know E : L is same as L : D and know there are at least 5 deer but we do not have exact ratios.
Statement 1: We know \(\frac{E}{L} = \frac{L}{D} = \frac{1}{5}\). If there is just 1 Elephant, E : L tells us there must be at least 5 Lions and if there are at least 5 Lions, there must be at least 25 Deer since L : D = 1 : 5. However, this is not sufficient to provide us actual numbers.
Statement 2: If number of lions is a prime number, then for the ratio to work and for Lions to be prime, one of either Elephants or Deer needs to be 1, however we know there are at least 5 deer, then there can only be 1 elephant since for a greater value, Lions would not remain a prime number. Lets look at these cases to understand this better.
Case 1: Suppose E : L is 1:5 then we know E : L : D would be 1:5:25 and this does not violate the condition of L being prime.
Case 2: If there are more than 1 Elephants say 2 and we have the ratio E:L = 2:5 , then since E: L = L : D, combined ratio E : L : D would be 4 : 10 : 25 but we know Lions are a prime number and this violates the condition.
Case 3: Say Elephants are larger in number as in 25 and there are 5 lions. Then by the ratio E : L = L : D, there must be only 1 Deer, but this violates the conditions given in stem about deer being at least 5. If we need to make Deer at least 5, we would have to multiply Elephants and Lions to the common ratio but that would again make Lions non-prime.
This is a great question and it took me a while to grasp this and I am still hoping to learn more from it.
D - 9 etc...