Linear Systems and Optimisation in Puzzle Rounds

Some firms mix plain mathematics into their puzzle rounds. SIG's written tests are known for systems of equations, and Mako lists integer equations among its aptitude topics. The mathematics is school level. What is tested is how fast you turn a paragraph into equations, and whether you notice when a problem has no single answer.

From words to equations

Name one unknown for each quantity you are asked for, then write one equation for each fact in the question. Count them before you solve: two unknowns need two independent equations.

Worked example: pricing calls and puts

Three calls and two puts cost $26. Two calls and five puts cost $32. What does each cost?

Let $c$ be the call price and $p$ the put price.

3c + 2p = 26, \qquad 2c + 5p = 32

Multiply the first equation by 2 and the second by 3, so the calls match: $6c + 4p = 52$ and $6c + 15p = 96$ . Subtract to get $11p = 44$ , so $p = 4$ , and then $c = 6$ .

Lorem ipsum dolor sit amet, consectetur adipiscing elit. Integer sit amet quam auctor, convallis ligula a, aliquet turpis. Vestibulum fringilla sollicitudin leo sit amet lobortis. Nullam accumsan finibus justo quis sollicitudin. Nam sed volutpat nisl, efficitur convallis purus. Curabitur scelerisque tincidunt turpis, vel ullamcorper magna faucibus a. Etiam non lobortis elit, vel egestas ex. Maecenas quis egestas velit. Pellentesque sit amet dolor laoreet turpis convallis elementum. Cras nec dui non turpis tincidunt maximus vitae commodo elit.

Vivamus maximus leo nec sem ultricies, placerat luctus odio scelerisque. Morbi fringilla est neque. Duis fermentum tempor justo ut laoreet. Lorem ipsum dolor sit amet, consectetur adipiscing elit. Etiam feugiat ipsum in nisl fermentum commodo. Aenean viverra, nisl sed gravida facilisis, felis sem malesuada orci, non tincidunt velit risus id risus. Integer gravida fermentum massa, eu viverra felis iaculis non. Suspendisse sit amet hendrerit erat, eget accumsan libero.

Aenean ut quam efficitur felis pulvinar pulvinar quis in libero. In hac habitasse platea dictumst. Suspendisse potenti. Maecenas vel gravida sem. Aliquam aliquam pellentesque cursus. Sed malesuada lacus dignissim odio varius commodo. Vivamus tristique facilisis lorem.

The rest of this lesson is for subscribers

Unlock every lesson in Advanced Topics in Probability and Statistics, and every other premium course.

Subscribe to continue

Test your knowledge

Questions are only available to subscribers.

Continue

Keep reading Advanced Topics in Probability and Statistics

47 lessons in this course, and every other premium course, on one subscription.

Subscribe now

Every lesson in every course, with the worked examples and interactive simulators
Graded questions on every lesson, with explanations for the wrong answers as well as the right one
The trainers, timed assessments and brainteaser library that go with them