SAT ‘Problem of the Day’ gives wrong answer

The College Board’s  SAT “Problem of the Day” is supposed to be helpful —  but that’s hard when it cites the wrong answer. Over at the Rational Mathematics Education Web site, math assessment reform activist Michael Paul Goldenberg explains the problem with the problem, provided by the Educational Testing Service, which creates the SAT for the College Board.

Here’s the actual SAT Problem of the Day:

If , what is the value of ?

Goldenberg wrote that he calculated the problem and came up with B — but the Web site told him his answer was incorrect. “This came as quite a shock to me, even at 4:30 a.m.” he wrote.  “…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 and get pencil and paper so I 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.

I looked at the conveniently provided explanation. It said:

Explanation

Multiplying both sides of the equation  by  gives , which simplifies to . Dividing both sides of the equation by  gives , and so .

Well, that’s interesting: the correct answer is said to be A but the explanation shows that my bleary-eyed calculation was right after all.

Valerie Strauss covers education and runs The Answer Sheet blog.

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· November 23, 2012

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