SOLUTION: When the teacher divided her students into groups of four, she had three students remaining, when she divided them into groups of five , she had four students remaining. There were

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Question 1158265: When the teacher divided her students into groups of four, she had three students remaining, when she divided them into groups of five , she had four students remaining. There were fewer than 40 students in the class. How many students could be in the class?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
19 students

Done using lists, very crude, not the best method
Better way is possible 
DIV 4, r 3       DIV 5, r 4
  7               9
 11              14
 15              19
 19
 23

First value found common to both is 19.

Answer by ikleyn(52777)   (Show Source): You can put this solution on YOUR website!
.

Let "n" be the unknown number under the question.


Add 1 (one) to the number, and consider N = n+1, instead of "n".


Then the number N  is a multiple of 4 (OBVIOUS).

Also, the number N is a multiple of 5 (OBVIOUS).


The only numbers lesser than or equal to 40 and multiple to 4 and 5 are the numbers 20 and 40.


Returning from "N" to "n", we have, therefore, two answers for the given problem:  19 and 39.

Solved.

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    | It is how this problem is designed, is intended and is expected to be solved. |
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For similar solved problems,  see the lesson
    - The number that leaves a remainder 1 when divided by 2, by 3, by 4, by 5 and so on until 9
in this site.


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