40% of the dogs at a certain animal shelter have been microchipped. How many of the dogs have not been microchipped?
(1) 37.5% of the dogs that have been microchipped are also either spayed or neutered.
(2) There are less than 50 dogs at the animal shelter
Given: 40% of the dogs at a certain animal shelter have been microchipped.
Asked: How many of the dogs have not been microchipped?
40% of the dogs at a certain animal shelter have been microchipped
=> 60% of the dogs at the animal shelter have not been microchipped
Let the number of dogs at the shelter be x dogs
40% of x have been microchipped
=> 40% x = 2x/5 is an integer
=> 60% x = 3x/5 is also an integer
=> x = 5k format => x is a multiple of 5 (i)
(1) 37.5% of the dogs that have been microchipped are also either spayed or neutered.
37.5% = 3/8 of the dogs that have been microchipped are also either spayed or neutered.
=> 3/8 of 2x/5 is also an integer
=> 3x/20 is also an integer
=> x = 20k x is a multiple of 20
If x= 20y = total no of dogs
=> 8y = Number of the dogs that have been microchipped &
=> 3y = Number of the dogs that have been microchipped are also either spayed or neutered.
But y can take multiple values
NOT SUFFICIENT
(2) There are less than 50 dogs at the animal shelter
If there are less than 50 dogs at the animal shelter
=> no of dogs may be 5, 10, 15, 20,25,30, 35, 40,45
NOT SUFFICIENT
Combining (1) & (2)
(1) 37.5% of the dogs that have been microchipped are also either spayed or neutered.
=> x = 20y format => number of dogs are multiple of 20
(2) There are less than 50 dogs at the animal shelter
Number of dogs = 20 or 40
Number of dogs which have not been microchipped = 12 or 24
NOT SUFFICIENT
IMO E
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