Mr. Ong is arranging his students into groups for the school debate.?

Question

Mr. Ong is arranging his students into groups for the school debate. When he groups them into 5, 4 and 7, there remainder of 2, 1 and 4 respectively. What is the least number of students Mr. Ong has?

Answer 1

最佳解答

Let x be the number of students

x = 5*4n₁ + 4*7n₂ + 5*7n₃ + (5*4*7)R

x = 20n₁ + 28n₂ + 35n₃ + 140R

When x is divided by 5, the remainder is 2.

Consider 28n₂,

28(4) = 112 is divided by 5, the remainder is 2.

n₂ = 4

When x is divided by 4, the remainder is 1.

Consider 35n₃,

35(3) = 105 is divided by 4, the remainder is 1.

n₃ = 3

When x is divided by 7, the remainder is 4.

Consider 20n₁,

20(3) = 60 is divided by 7, the remainder is 4.

n₁ = 3

∴ x = 20(3) + 28(4) + 35(3) + 140R = 277 + 140R

The least number of students = 137

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