Mathcounts National Sprint Round Problems And Solutions May 2026

(\boxed2)

Intersect F: set 5x = (-15/8)x + 15 → multiply 8: 40x = -15x + 120 → 55x = 120 → x = 120/55 = 24/11. Then y = 5*(24/11) = 120/11. Mathcounts National Sprint Round Problems And Solutions

Memorize symmetric polynomial identities. They save precious seconds. Category 3: Geometry – The Diagram is a Trap Problem (Modeled after 2016 National Sprint #28): In rectangle ABCD, AB = 8, BC = 15. Point E lies on side CD such that CE = 5. Lines AE and BD intersect at F. Find the area of triangle BEF. (\boxed2) Intersect F: set 5x = (-15/8)x +

A harder version asks for (x^4 + y^4). You’d use (x^4 + y^4 = (x^2+y^2)^2 - 2(xy)^2 = 34^2 - 2(15)^2 = 1156 - 450 = 706). AB = 8