**If a^2 = b^2 = c^2 = 4 and abc ≠ 0, how many different values are possible for a+b+c?**

(A) 1 (B) 2 (C) 3 (D) 4 (E) 5

Ans: 4

For those of you who find this question trivial, remember that difficulty is very subjective.

Whst is(are) the BIG IDEAS here?

Can you predict which of your students will choose an algebraic approach vs "plugging in"?

Extension for students: Suppose we use 5 variables instead of 3.

Ans: 6

Generalize and explain!

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## 3 comments:

Is there something missing in the statement of the problem? I can't see why there wouldn't be infinite possible values for a+b+c...

Of course you're right if a,b,c are allowed to represent any "number." I should have avoided this by writing, say, a^2=b^2=c^2=4. Then there would be no ambiguity hopefully!

In the abstract case, the 4 values are, in terms of a:

3a if a=b=c

a, if a=b= -c

-a, if a= -b = -c,

-3a, etc

The more I look at this the more I agree that the problem in its current form is very confusing. Well, I'm writing these from scratch early in the morning! Thank goodness you called me on it!

On the real SAT the "=4" version would be used. My version would have been rejected!

Thanks to Sara I cleaned up the problem! Shame on me...

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