Maths Olympiad Prep

Library / CEMC Cayley /111 of 470

CEMC Cayley, 2011

Algebra Difficulty 1.0 Junior Find the answer Canada

The operation "∇\nabla" is defined by (a,b)∇(c,d)=ac+bd(a, b)\nabla(c, d) = ac + bd. For example (1,2)∇(3,4)=(1)(3)+(2)(4)=11(1, 2)\nabla(3, 4) = (1)(3) + (2)(4) = 11. The value of (3,1)∇(4,2)(3, 1)\nabla(4, 2) is

(A) 1010 (B) 1111 (C) 1313 (D) 1414 (E) 2424

We don't reproduce this publisher's solutions. Their own solution is here — work the problem first.
Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.