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Home » Case 1: Neither A nor B is selected - 500apps

Case 1: Neither A nor B is selected - 500apps

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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However, if we interpret the question as seeking the **smallest** such...
x = 504 - 3 = 501
But since the question asks for a two-digit number, and none exists, t...
But let's double-check by checking smaller common differences.
Alternatively, suppose the condition is that $ x \equiv -3 \pmod{7,8,9...
Then $ x \equiv -3 \pmod{504} $, so $ x = 504k - 3 $.
For $ x $ to be two-digit:
\leq 504k - 3 \leq 99 \Rightarrow 13 \leq 504k \leq 102 \Rightarrow k...
Only $ k = 0 $ gives $ x = -3 $, $ k = 1 $ gives $ x = 501 $.
No two-digit solution.

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