SOLUTION: how many students are there in a class if 2 students remain after 4 equal rows of seats are filled and one student remains after 3 equal rows of seats are filled?

Question 1013405: how many students are there in a class if 2 students remain after 4 equal rows of seats are filled and one student remains after 3 equal rows of seats are filled?
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
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how many students are there in a class if 2 students remain after 4 equal rows of seats are filled and one student remains after 3 equal rows of seats are filled?
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Answer. Possible answers are: 22 students, 34 students, . . . AP with the common difference 12.

Solution


Let x be the unknown number of students in the class.

Add 2 to x and consider the number x+2.

According to the condition, it is multiple of 4 and it is multiple of 3.

Hence, it is multiple of 12. Therefore, the number of students in the class is 12n - 2, where n is positive integer.

n=1 gives 10, but it doesn't fit due to other simple reason;

n=2 gives 22 which does suit;
n=3 gives 34 which does suit
. . .

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