The 1982 SAT question with no right answer
Three students found a mistake in a problem about two circles, and the test makers had to admit it. Let’s work out what it was. You’ll see it for yourself.
SAT, May 1, 1982
Solve it yourself first
In the figure above, the radius of circle A is 1/3 the radius of circle B. Starting from the position shown in the figure, circle A rolls around circle B. At the end of how many revolutions of circle A will the center of the circle first reach its starting point?
Pick an answer.
Where the 4 comes from
Press Play or drag the slider. The yellow dot marks the spot on circle A that touches circle B at the start.
R is the radius of circle B, r is the radius of circle A.
Check yourself
The radius of circle B is 5 times the radius of circle A. A rolls once around the outside of B until it is back where it started. How many turns does it make?
Two identical coins. One rolls around the edge of the other until it is back where it started. How many turns does it make?
What happened in 1982
The question was on the SAT of May 1, 1982. The test makers (the College Board and ETS) took 3 to be the answer: B’s circumference is three times A’s, so A should turn 3 times. That would be true if the circle rolled along a straight line. Three students, Doug Jungreis, Shivan Kartha and Bruce Taub, showed that none of the choices was right. The test makers admitted the mistake, and the test was regraded.
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