In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.

Q: Problem: the sum of two numbers is 16 and the sum of their squares is 113 . find the numbers . 
Options: a ) 1 and 2 , b ) 4 and 5 , c ) 7 and 8 , d ) 2 and 3 , e ) 6 and 7

A: c
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Q: Problem: what is the smallest positive integer nn such that 6,480 ∗ n √ 6,480 ∗ n is a perfect cube ? 
Options: a ) 5 , b ) 5 ^ 2 , c ) 30 , d ) 30 ^ 2 , e ) 30 ^ 4

A: e
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Q: Problem: a crate measures 5 feet by 8 feet by 12 feet on the inside . a stone pillar in the shape of a right circular cylinder must fit into the crate for shipping so that it rests upright when the crate sits on at least one of its six sides . what is the radius , in feet , of the pillar with the largest volume that could still fit in the crate ? 
Options: a ) 2 , b ) 4 , c ) 5 , d ) 8 , e ) 12

A:
c
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