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A is a set of +ve integers such that when divided by 2,3,4,5 & 6 leaves remainders 1,2,3,4 & 5 respectively. How many integer(s) b/w 0 and 100 belongs to set A?

A is a set of +ve integers such that when divided by 2,3,4,5 & 6 leaves remainders 1,2,3,4 & 5 respectively. How many integer(s) b/w 0 and 100 belongs to set A?

Grade:11

1 Answers

Srishti Nanduri
38 Points
10 years ago
let a = 2q+1 a= 3q+2 a= 4q+3 a= 5q+4 a= 6q+5 Now in the equation a= 6q+5, Let q=1 than a = 6q +5 = 6*1 +5 = 11 If we replace a with eleven with ALL the above equations .. we can infer that 11 satisfies all the equations... So ELEVEN IS THE ONLY NO BETWEEN 0 AND 100 WHICH BELONGS TO SET A...... I hope it helps

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