At the Canterbury Dog Fair, 1/4 of the poodles are also show dogs and 1/7 of the show dogs are poodles. What is the least possible number of dogs at the fair?

10

Step-by-step explanation:

Let the total number of poodles =

Let the total number of show dogs =

of the poodles are show dogs

and

 of the show dogs are poodles

As per the question statement, must be divisible by 4 and

must be divisible by 7.

And we have to find the least number of dogs.

So, least number divisible by 4 = 4 and

Least number divisible by 7 = 7

So, least values of i.e. poodles = 4 in which we have 1 show dog

Hence, 3 are not show dogs.

and least value of show dogs i.e. = 7 (it includes the one poodle which is also show dog).

So, least number of dogs at the fair = 7 + 3 = 10

i think the answer is a.( -3, -1 )