💡 Did you know? · CAT, IPMAT, JIPMAT, CUET · Number system

4 Consecutive Numbers + 1 = Perfect Square

This 10-second trick replaces long multiplication in Quant

Multiply any 4 consecutive numbers and add 1. You will always get a perfect square!

1 × 2 × 3 × 4 + 1 = 25 = 5²
2 × 3 × 4 × 5 + 1 = 121 = 11²
5 × 6 × 7 × 8 + 1 = 1681 = 41²

Why: n(n+1)(n+2)(n+3) + 1 = (n² + 3n + 1)²

Exam shortcut: 7 × 8 × 9 × 10 + 1 → 7² + 3×7 + 1 = 71 → answer is 71² = 5041

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