Student Finds Third PSAT Answer

A Harvard graduate student this week proved there is a third correct answer to the controversial "pyramid" question on last fall's Preliminary Scholastic Aptitude Test (PSAT).

However, officials from the Educational Testing Service (ETS), which administers the PSAT, said this week that students who chose the third correct answer will not receive credit for the question.

Lawrence A. Denenberg '76, a Ph.D. candidate in applied mathematics, found the new answer after he heard that Daniel Lowen, a 17-year-old Florida high school student had found an alternative correct answer to the one designated by the ETS.

The ETS, which administered the PSAT to 830,000 high school students in October, changed almost 250,000 scores last month after accepting Lowen's answer.

James Braswell, ETS spokesman, said this week that Denenberg's answer is also correct, but added that ETS would not revise the scores again.

Braswell said, "The math portion of the test is not intended for math professors or graduate students, but rather for the general student. Its function is to measure aptitude--the ability to deal with quantitative concepts."

The disputed question concerns two pyramids for which each corner has been given a corresponding letter. The question states: "If face ABC were placed on face EFG so that the vertices of the triangle coincide, how many exposed faces would the resulting solid have?"

The original ETS answer was seven--each triangle has four faces, and placing two of the faces together leaves a total of seven. Lowen said the answer was five. because in two different places two of the faces form a single plane, for a total of five distinct planes.

Denenberg proposed what he called an "abstract" solution to the problem, involving placing one triangle inside the other. This method results in a total of eight faces--one of the choices listed by the ETS.

"I imagine in the mathematical abstract you could answer it his way, but it would result in such a strange looking object," Braswell said.

An ETS official who refused to be identified said yesterday. "The test-takers were supposed to assume the two triangles were solid, although nothing in the question was there to indicate that."

"I still think the test is a good measure of aptitude, but in the future, we will scrutinize the wording more carefully. Right now, it is virtually impossible to clarify things--the language as is can be interpreted a few ways."

The revision for the Lowen answer cost ETS $110,000 in postage and other expenses and raised the scores of 250,000 students by one to ten points, an ETS spokeman announced this week