5Question: What two-digit positive integer is one more than a multiple of 5, 7, and 11?

Mon, 04 May 2026 01:20:29 +0000

**5Question: What Two-Digit Positive Integer Is One More Than a Multiple of 5, 7, and 11?**
A quiet puzzle that’s surprisingly tied to modern earning and belonging trends in the US Could you solve this simple but subtle riddle: What two-digit positive integer is one more than a multiple of 5, 7, and 11? It’s not obscure—it’s widely discussed in digital circles and math-focused communities as a catchy challenge that reveals deeper patterns in numbers and molecular matching. Though it seems like a brain teaser, its real-world value lies in how such logic applies to financial patterns, identity systems, and credibility-building online. With mobile users increasingly seeking quick, satisfying answers, this question reflects America’s fast-paced, information-driven mindset—especially among curious, income-minded audiences scanning for smart, easy-to-understand insights. The search for the answer—essentially identifying a number congruent to 1 modulo 5, 7, and 11—connects to real-world patterns found in number theory and modular arithmetic. While it may appear abstract, its relevance extends beyond puzzles: platforms used for income streams, identity verification, and automated systems often rely on detecting unique, predictable sequences. Identifying this integer reveals how seemingly simple rules can highlight reliable, repeatable outcomes—something valuable in algorithmic decision-making, verification processes, and data patterns shaping today’s digital economy. To crack it, consider the combined request: a two-digit number that leaves a remainder of 1 when divided by 5, 7, and 11. The least common multiple of these three numbers is 385, but that exceeds two digits. Instead, we search two-digit values manually by testing numbers that satisfy the condition:
Numbers one more than a multiple of 5, 7, and 11 are generated as:
- 385k + 1, where k is a whole number
For k = 0: 1 (too small)
For k = 1: 386 (too big)
So direct multiplication doesn’t yield a two-digit result—proving why direct computation misses the nuance: modular congruence matters, not just multiples. Two-digit candidates must fit:
Numbers ≡ 1 (mod 5), ≡ 1 (mod 7), ≡ 1 (mod 11) at once.
Testing in order:
12 → 12 mod 5 = 2 → no
21 → 21 mod 5 = 1, 21 mod 7 = 0 → no
22 → 22 mod 7 = 1, 22 mod 11 = 0 → no
…
76 → 76 ÷ 5 = 15 R1, 76 ÷ 7 = 10 R6 → no
87 → 87 ÷ 5 = 17 R2 → no
81 → 81 ÷ 7 = 11 R4 → no
74 → check: 74 ÷ 5 = 14 R4 → no
69 → 69 ÷ 5 = 13 R4 → no
64 → 64 ÷ 7 = 9 R1 → no
59 → 59 ÷ 11 = 5 R4 → no
54 → 54 ÷ 11 = 4 R10 → no
49 → 49 ÷ 11 = 4 R5 → no
44 → 44 ÷ 7 = 6 R2 → no
39 → 39 ÷ 7 = 5 R4 → no
34 → 34 ÷ 5 = 6 R4 → no
29 → 29 ÷ 5 = 5 R4 → no
24 → 24 ÷ 5 = 4 R4 → no
19 → 19 ÷ 5 = 3 R4 → no
14 → 14 ÷ 5 = 2 R4 → no
9 → too small
Wait—manual testing reveals no match—so a better approach uses logic:
Find integers x such that:
x ≡ 1 (mod 5)
x ≡ 1 (mod 7)
x ≡