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How many integers \(n\)  satisfy the condition that it is between 100 and 200, exclusive, and the condition \(n\)  has the same remainder whether it is divided by \(6\) or \(8\) ?

 Feb 9, 2019
edited by LOL314jnl  Feb 9, 2019
edited by LOL314jnl  Feb 9, 2019
edited by LOL314jnl  Feb 9, 2019
 #1
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Sorry, can't read your "condition"!.

 Feb 9, 2019
 #2
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I revised it.

 Feb 9, 2019
 #3
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If I understand the question...

 

LCM [ 6, 8 ]  =  24

 

The multiples of 24 between 100 and 200 are  :

n = 120, 144, 168, 192    

 

So...n will have the same remainder  when divided by 6 or 8

 

cool cool cool

 Feb 9, 2019
 #4
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All of the following numbers will give the same remainder for both, 6 and 8 ranging from 0 to 5:
n =100, 101, 120, 121, 122, 123, 124, 125, 144, 145,146, 147, 148, 149, 168, 169,170, 171, 172, 173, 192, 193, 194, 195, 196, 197. 

 Feb 9, 2019
 #5
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cheekyThank you!

 Feb 12, 2019

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