Neco 2017 Mathematics Question 1

Practice essay / theory question 1 from the 2017 Neco Mathematics examination. This question covers Number and Numeration, Divisibility, Congruences, Chinese Remainder Theorem .

Neco 2017 Mathematics Essay / Theory

Topics: Number and Numeration Divisibility Congruences Chinese Remainder Theorem

Question 1 NECO • 2017 • MATHEMATICS • essay

A school has a total number of students that is a three‑digit integer. When the number of students is divided by 7 the remainder is 3; when divided by 9 the remainder is 5; and when divided by 11 the remainder is 7. Determine the smallest possible number of students that satisfies all three conditions.

Question Parts

( a )

State the system of congruences that represents the conditions given.

( b )

Find the smallest three‑digit integer that satisfies the system of congruences.

( c )

Verify that the number you obtained is indeed a three‑digit integer.

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About This Question

This is Neco 2017 Mathematics Question 1. It is one of the essay questions from the 2017 Neco Mathematics examination.

The question covers Number and Numeration, Divisibility, Congruences, Chinese Remainder Theorem .

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