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Modulo Arithmetic & Congruence · Question 87 of 97

How many students are in Green house?

Question 87

EasyOriginal question

A school numbers its 60 students from 1 to 60 and puts each in a house by the remainder of the roll number on division by 5: remainder 1 is Red, 2 Blue, 3 Green, 4 Yellow and 0 White.

How many students are in Green house?

11

Correct answerYour answer

12

Correct answerYour answer

13

Correct answerYour answer

15

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

Green holds 3, 8, 13, …, 58: the numbers $5k + 3$ up to 60.
$k = 0$ to 11: 12 students.

Worth noting

Each of the 5 houses gets exactly $\frac{60}{5} = 12$ , since 60 is a multiple of 5.

Concept: Counting a residue class
Typical timeTypical: 90 s
Your timeYours: —

The rule this testsResidue classes

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