SOLUTION: For a parade a teacher arranged all the pupils of his class in rows of 12 and then in rows of 16. He noticed that each time 3 pupils were left out. Calculate the number of pupils i

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Question 974165: For a parade a teacher arranged all the pupils of his class in rows of 12 and then in rows of 16. He noticed that each time 3 pupils were left out. Calculate the number of pupils in the class
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The number of pupils minus 3
is a multiple of 12=4%2A3=2%5E2%2B3, and is a multiple of 16=2%5E4.
So, it is a multiple of 2%5E4%2A3=16%2A3=48 .
I would bet that the number of pupils minus 3 is
1%2A48=48 and that the number of pupils is 48%2B3=51 .

NOTE:
Of course, it could be that the number of pupils minus 3 is
2%2A48=96 and that the number of pupils is 96%2B3=9 ,
but this is a lot of pupils to have in one class,
It could be that the number of pupils minus 3 is
3%2A48=154 , or 4%2A48=192 , or ....
but that would make the number of pupils be
154%2B3=157 , or 192%2B3=195 , or ...
but those are even more ridiculously large numbers of pupils to have in one class.