A few days ago, this blog's Feedjit widget showed that a visitor from Redmond, WA (home of Microsoft's headquarters) clicked on this post, "Algebra Challenge". Seeing that, I wondered if someone an interviewer at Microsoft was binging math questions for the company's notorious interview questions1. I happen to have middling math skills myself, but I think this could be an decent interview question, as long as the interviewer just asked the interviewee how he would solve the problem, instead of requiring him to actually solve it (since, the arithmetic is messy, andas commenter J.K. noted in that thread, the actual formula is heavily rounded). The key insight here would be to recognize that the problem can be stated and solved as a system of three equations.
This raises a question I've wondered about in the past, which is to what extent these sorts of questions actually measure intelligence. Maybe it doesn't even matter though, if the questions test for a similarly valuable attribute other than intelligence.
Consider, for example, a couple of word problems I remember from tests I had to take as part of the application process for jobs in the past. Without digging up the exact text of the two word problems this was the gist of them: The first asked how many of each type of coin you would have if you had a certain amount of money in change; the second asked how far apart two individuals would be if one walked so far in one direction and then so far to the left, and the other did the exact opposite. I remember these two word problems for two reasons: I know I got them right, and I know that my getting them right wasn't a reflection of my intelligence or math aptitude. I got the problems right because I had seen them before.
I knew that the first problem could be solved with elementary algebra (using 25x for a quarter, 10x for a dime, and so on), and the second one could be solved with elementary geometry (adding the hypotenuses of the two resulting right triangles). Although these questions didn't measure my intelligence or math aptitude, my getting them right did demonstrate something else: that I had paid attention in math class, or perhaps that I had studied this stuff relatively recently while preparing for a standardized test needed for a graduate degree. So getting those problems right demonstrated either intelligence/aptitude, conscientiousness, or ambition, or some combination of those attributes; and whichever of these attributes a test-taker had would reflect well on him, as far as the employer was concerned.
1I was reminded of this by a conference call I had today with an ABD finance Ph.D. who is doing some consulting for me and one of my web developers. My finance consultant created an algorithm for me, and he was going over it with one of my web developers. My finance consultant assumed that my web developer, who has a bachelors degree in computer science, would have had all the math background necessary to understand the algorithm. My web developer noted that he had a minor in math, in addition to his comp sci degree, but he just wasn't familiar with a particular function the finance consultant specified (an infimum function). I hadn't heard of the function before either, and if a comp sci major/math minor hasn't heard of it, I guess a question based on that function wouldn't be a good one for a Microsoft interviewer.
From Prof Arthur Waldron.
Sir, Japan’s allies have left it in the cold before (“A diplomatic feint that looks set to leave Japan in the cold”, Philip Stephens February 27), most notably after the Washington Conference of 1921-22, which saw the security treaty with Britain, fundamental to Japan, discarded, with a fine-sounding set of multilateral guarantees as substitute. The rationale then, as now, was the need to yield before the inevitable rise of China.
What happened? China entered an unexpected period of turbulence that threatened Japanese interests. Tokyo drifted for a while trying to work within the multilateral framework, but when it proved useless found a new compass in dictatorship at home and pre-emptive attack abroad, against China and eventually the US.
History does not repeat itself but it has lessons. One is never to sell short Japan, least of all as a power. Another is that all long positions on China should be carefully hedged.
Arthur Waldron,
Bryn Mawr, PA, US
Lauder Professor of International Relations,
University of Pennsylvania
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