Edexcel FP2 AS 2024 June — Question 2

Exam BoardEdexcel
ModuleFP2 AS (Further Pure 2 AS)
Year2024
SessionJune
TopicNumber Theory

  1. Tiles are sold in boxes with 21 tiles in each box.
The tiles are laid out in \(x\) rows of 5 tiles and \(y\) rows of 6 tiles.
All the tiles from a box are used before the next box is opened.
When all the rows of tiles have been laid, there are \(n\) tiles left in the last opened box.
  1. Write down a congruence expression for \(n\) in the form $$a x + b y ( \bmod c )$$ where \(a\), \(b\) and \(c\) are integers. Given that
    • exactly 43 rows of tiles are laid
    • there are no tiles left in the last opened box
    • use your congruence expression to determine the minimum number of rows of 6 tiles laid.