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Each week, between 30 and 50 students show up for an archery class run by Betty and Wilma. Usually the students break up into groups of equal size for target practice. However, this week, Betty noticed that she could not break the students up into multiple groups of equal size. Wilma noticed that if Betty and Wilma joined the students in practicing, they still could not break the archers up into groups of equal size. How many students showed up to the archery class this week?

 Apr 1, 2018
 #1
avatar+175 
+2

The answer is \(\boxed{41}\)

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 Apr 1, 2018
 #2
avatar+98061 
+3

Let's look at AZSun's answer a litlle more in detail.....

 

If Betty  and Wilma  join the group it is still not divisible into equal size groups

 

Note that all the even integers  from 30 - 50  can always be divided into equal groups because, at least, they are all divisible by 2

 

But look at the odd integers between  30 - 50

 

31   33    35    37   39    41   43   45   47  49

 

We are looking for two adjacent prime numbers

 

These  are   41  and 43

 

Note....41 students cannot be divided into equal groups and even if  Betty and Wilma join in....the group size  = 43    which isn't capable of being divided equally, either  !!!!

 

So...AZSun's answer of 41 is good  !!! 

 

cool cool cool

 Apr 1, 2018
edited by CPhill  Apr 1, 2018
 #3
avatar+3994 
+2

Thanks so much, CPhill! Wonderful!

tertre  Apr 1, 2018

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