Unit 2 · Number Theory

Valerie's Secret Number — How Many Work?

Lesson 8 of 18

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About this lesson

Valerie subtracts a positive multiple of 7 from her secret number and gets 59. So her number = 59 + 7k for some whole number k ≥ 1. List every valid value of k that keeps her number strictly between 0 and 100, and count them.

Chapters

0:00Introduction
0:20The Question
0:58Reversing the logic (setting up the bounds)
1:23Mapping the possibilities systematically
1:53Testing the boundary failure limit
2:19Exam strategy — calculating the multiplier cap
3:00Confirming the final option

Question

Valerie says:

"I think of my favourite number, which is between 0 and 100.

Then I subtract a multiple of 7 that is greater than zero.

I get the answer 59."

How many of Valerie's favourite numbers are possible?

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