Term 2 Week 6 Junior Problems

01 Jun 2022

Problem 1

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Problem 2

I am thinking of a 5-digit number. If you put ‘1’ at the beginning of the number you get a number that is three times smaller than if you put ‘1’ at the end of the number. What number am I thinking of?

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Solve $3 \times (100000 + x) = 10 \times x + 1$ for $x$ This gives $42857$

Problem 3

Small cubes with side length 1 are combined according to the pattern shown below. If there are 28 layers, find the volume.

Problem 4

Given that $\overline{81A02B}$ is a $6$-digit number which is divisible by $36$ and $B > A,$ find the value of $A + B$.

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Credits:

Problem 1: This problem is from the Cambridge Methods 1/2 Textbook, Chapter 6J: Applications of polynomial functions

Problem 2: This problem is from Richard Wiseman’s Friday puzzles