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Home » rank the numbers in each group from smallest to largest - Parker Core Knowledge

rank the numbers in each group from smallest to largest - Parker Core Knowledge

📅 May 4, 2026 👤 scraface

May 04, 2026

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Let $ x = 7k + 1 $. Substitute into the second congruence:
7k + 1 \equiv 3 \pmod{5} \Rightarrow 7k \equiv 2 \pmod{5} \Rightarrow...
So $ k = 5m + 1 $, and $ x = 7(5m + 1) + 1 = 35m + 8 $.
We now find a two-digit value of $ x $:
35m + 8 \geq 10 \Rightarrow m \geq 0, \quad 35m + 8 \leq 99 \Rightarro...
Try $ m = 0 $: $ x = 8 $ (not two-digit)
Try $ m = 1 $: $ x = 43 $
Try $ m = 2 $: $ x = 78 $
Both 43 and 78 are two-digit numbers satisfying the conditions.
Thus, the possible answers are $ \boxed{43} $ and $ \boxed{78} $.

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