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The number of students in RSM online classes is more than  90 and fewer that 140 and 1 less than a multiple of 3, 3 less than a multiple of 5, and 5 less than a multiple of 7. How many students are in RSM online classes?

 Jan 29, 2023
 #1
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The answer is 92.

 Jan 29, 2023
 #2
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N mod 3 =2, 

N mod 5 =2,   

N mod 7 =2, solve for N

 

N = 105C + 2, where C= 0, 1, 2, 3,.......etc.

When C = 1, then:

 

N=[105 * 1  +  2] = 107 - number of students in RSM online classes.

 

Check: 107 is 1 less than a multiple of 3, or: 107 + 1 =108 - which is a multiple of 3

              107 is 3 less than a multiple of 5, or: 107 + 3 =110 - which is a multiple of 5

              107 is 5 less than a mulriple of 7, or: 107 + 5 =112 - which is a multiple of 7 

 Jan 29, 2023

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