In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
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Question: Problem: a circular rim a having a diameter of 45 inches is rotating at the rate of x inches / min . another circular rim b with a diameter of 30 inches is rotating at the rate of y inches / min . what is the value of y in terms of x , if both the rims reach their starting positions at the same time after every rotation . 
Options: ['a ) 3 x / 2', 'b ) 4 x / 5', 'c ) 7 x / 5', 'd ) 5 x / 7', 'e ) 3 x / 4']

Answer: a


Question: Problem: a lady grows cauliflower in her garden that is in the shape of a square . each cauliflower takes 1 square foot of area in her garden . this year , she has increased her output by 223 cauliflower when compared to last year . the shape of the area used for growing the cauliflower has remained a square in both these years . how many cauliflowers did she produce this year ? 
Options: ['a ) 12541', 'b ) 12542', 'c ) 12544', 'd ) 12545', 'e ) can not be determined']

Answer: c


Question: Problem: a box has 12 shapes ; 3 circles , 5 squares , and 4 triangles . how many groups of 3 shapes can be made with at least 1 triangle ? 
Options: ['a ) 46', 'b ) 64', 'c ) 164', 'd ) 146', 'e ) 56']

Answer:
c