Can you find the mistake in this SAT question?

This question appeared on the October 1980 SAT exam. Like all questions, it was supposed to have exactly one correct answer. However the test-makers made a mistake. Can you figure out what they did wrong?

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[RoflZack]

Honestly, anyone good enough at math to notice that they could use negative integers would have spotted the 9 and 8 in question B especially since it came first. I kind of doubt that any of the people who chose the 4, 8 solution would have been able to defend why they chose it by using a negative 2.

[Takenzo]

Even though the students were correct, they probably didn't know why when they selected the answer

[robinofficial]

The obvious solution is a row that contains 8=2^3 (only one-digit cube except 1) and 9=3^2 (only one-digit square except 1 and 4=2^2).

The less obvious solution is 8=2^3 and 4=(-2)^2.
Wouldn't have noticed that, probably, though.

[MrKorthos]

"awarded the 1/4 students an additional 10 points"...TEN POINTS TO GRYFFINDOR

[chasmosaurus]

The result of the sqrt function is generally defined to be positive. Otherwise, it's not a function. The confusion here is square versus square root.

[kevinknorr]

As i looked at this, I imagined myself taking an exam. I read the question and within 30 seconds located the intended correct answer B. If I was actually taking the exam I would have just moved quickly to the next question. But, since this is MindYourDecicions I knew to look for another hook. I did not locate it after a few minutes thought.

After hearing the other "correct" answer, I do accept it in a strict interpretation of the question. However, anyone understanding the question would simply mark B and move on. Life is to short to quibble about semantics. As a final note, consider this logical reversal of the question. Is the integer 2 both a square root of 4 AND a cube root of 8. Just sayin...

[MumboJ]

To anyone saying the students should still be marked incorrect because they probably didn't select their answer for that reason:
The most likely reason to choose C is if you misread the question.
So, you're arguing against both a strictly correct reading of the question, AND against a misreading of the same question!
You want to penalise someone for reading the question correctly OR incorrectly?

If you disallow strict interpretations of questions, then you should still give them the marks because they correctly identified both square and cube numbers.

[dontreadmyprofilepic]

If the SAT's in 1980 where *THAT* easy, can someone hurry up and build a time machine?

[jacek_poplawski]

Ah I was thinking it will be something like 1 being both square and cube.

[chinareds]

C - (-2)^2 and (2)^3. Knew right away when you put the question up that it was gonna be a negative integer squared that was the mistake.

[Robbedem]

The question is fine.
Negative numbers and the definitions of integer and natural numbers are only teached at later ages. If they would have used the correct term, the kids wouldn't have understood the question becaues they wouldn't know what "natural number" means.

[JohnRandomness]

I only figured out the problem once he said, "This was supposed to be a distraction." Okay, line C contains 2^3 and (-2)^2.

[Drow]

Commenting before seeing the solution. B could obviously be picked, but C can be picked aswell: 2^3=8 and (-2)^2=4. Since -2 is not equal to 2 and both are integers, the rule in the question is satisfied.

[kamoroso]

Wow you really had to think outside of the box for that one. Normally people don't consider negative integers :)

[MCChubbyUnicorn]

I assumed "different intedger" referred to the answer being a different integer, so I saw B and C right away.

[chrisg]

What a pedantic bureaucratic objection. But then it's a pedantic bureaucratic test.

[bowserfromsonic]

but what if the people who put down answer choice c forgot that the 2 integers had to be different???

[Quantiad]

I'm guessing we're diving into negative squares or cubes.

[Freakschwimmer]

I want straight away with B and C and I couldn't figure out which one the test-makers wanted me to pick.... It was quite obvious to me, that negative numbers were allowed I mean, they specifically stated integer, not Natural Number!!

[aqibasif]

That's right but who thinks like that?