The ETS Screws the Pooch Again - Gus Grissom Memorial edition

Virgil I. "Gus" Grissom

I don't mean to be so hard on the ETS. Really I don't But they have this aggravating habit of doing some really stupid things that burn me up (okay, not as badly as was Gus Grissom and two fellow astronauts in January 1967 during a test of the Apollo rocket, but then, I was speaking figuratively). Take today's SAT "Problem of the Day." Please. The link leads you to the problem, showing that my selection of choice "B," in which I claim that 4n = 10 given that the original question was
If 24 over 15 = 4 over n, what is the value of 4 times n?
is incorrect. This came as quite a shock to me, even at 4:30 AM (another weird night in which age and Type 2 diabetes had me answering nature's call often enough that I spent a few moments checking e-mail on my Blackberry before falling back into the arms of Morpheus). As someone who prides himself on being able to do reasonably accessible mental arithmetic, I saw this problem as relatively accessible without pencil and paper. "Cross-multiplying" yielded 24n = 60, and as the problem asked for 4n, not n, it was child's play to divide both sides by 6 to get 4n = 10. So, again, imagine my surprise to click on what assuredly was the correct answer and be informed that it was wrong.

I was in no mood to turn on the light, get pencil and paper, and confirm that either I or the ETS had lost its mind. Instead, I just clicked on the "Show me the right answer" link. Once again, very surprising: the "correct" answer according to the infallible folks at the ETS was 6 (choice A). This just didn't feel right to me. If 4n = 6, then n = 3/2. Substituting into the original problem, that means that 24/15 (which reduces to 8/5) equals 4/(3/2) or 8/3. That is going to mess up a lot of folks. Maybe if NASA had realized that 8/5 = 8/3, Gus Grissom, Ed White, and Roger Chafee would be alive today. Or at least not burnt to cinders back in 1967. Or maybe it's just the reverse. Perhaps some advanced engineer at NASA learned math from the ETS and used precisely that sort of reasoning, thereby screwing the pooch for real.

But wait. Let's not be too hasty. Maybe the conveniently-provided ETS explanation for how they arrived at their answer will remove the scales from our eyes. Scrolling down, we find
The correct answer is A

Explanation

Multiplying both sides of the equation 24 over 15 = 4 over n by 15 times n gives (15 times n) times (24 over 15) = (15 times n) times (4 over n), which simplifies to 24 times n = (15) (4) = 60. Dividing both sides of the equation 24 times n = 60by 6 gives (24 times n) over 6 = 60 over 6, and so 4 times n = 10.
 Well, that's interesting: the correct answer is A (very emphatically so), but the explanation shows that my bleary-eyed calculation was right after all.

What conclusion can we draw? Clearly, US mathematics education has been getting things right all along: math doesn't make sense. Kind of comforting to anyone who struggled through math classes thinking, "Gee, this stuff is crazy, yet some people say that it's all perfectly logical. Looks like the joke is on them after all."

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