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: what is the max number of rectangular boxes , each measuring 5 inches by 2 inches by 7 inches , that can be packed into a rectangular packing box measuring 15 inches by 20 inches by 35 inches , if all boxes are aligned in the same direction ? 
Options: a ) 200 , b ) 350 , c ) 100 , d ) 150 , e ) 120

Answer: d


Question: Problem: the number 42 can be written as the sum of the squares of 3 different positive integers . what is the sum of these 3 integers ? 
Options: a ) 17 , b ) 10 , c ) 15 , d ) 14 , e ) 13

Answer: b


Question: Problem: an order was placed for a carpet whose length and width were in the ratio of 3 : 2 . subsequently , the dimensions of the carpet were altered such that its length and width were in the ratio 3 : 1 but were was no change in its perimeter . what is the ratio of the areas of the carpets ? 
Options: a ) 12 : 7 , b ) 15 : 11 , c ) 25 : 16 , d ) 30 : 23 , e ) 32 : 25

Answer:
e