SAT Blue Book Test 4 Section 3 Question 18 -- flawed question??

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1

My daughter worked on this question which asks for the formula that “represents the customer’s cost, in dollars, for n shirts bought during [a] sale” where the first shirt costs x dollars and each additional shirt costs x-z dollars.

She struggled for a while on the question because, she says, none of the answers is fully correct. While the supposedly “correct” answer, choice (A), is indeed correct for n at all numbers > or = 1, it provides the incorrect answer of $2 in the case where n = 0. She ultimately chose (A) because it was better than any of the other options, but she spent longer than she should have on the problem, futily searching for a choice that was fully correct.

I could reason that if a customer in the real world were to purchase 0 shirts, the formula would not be needed. However, my daughter reasons that the question does not state that there is a minimum purchase of 1 shirt; it asks for a formula where “n” shirts are purchased and in such cases it’s reasonable that the formula should work for a purchase of 0 shirts.

I’m surprised, because the College Board is usually very thorough in vetting all of its questions to eliminate ambiguities. Is this question poorly written, or did my daughter simply over-think it?

2

It’s probably best to assume n >= 1. Otherwise, a “correct” answer would involve a piecewise function or more complicated notation not normally found on the SAT, for example:

cost(n) = { 0 if n = 0
{ x + (x-z)(n-1) if n >= 1

3

Agreed, MITer94. Just wondering if the College Board should have been (and usually is) more precise in saying “(for n >= 1)” or if she should be prepared to make such assumptions that n will not be = 0 on other SAT questions as well.

For anyone else reading this, the “correct” answer A (effectively what MIT’er94 wrote) was:

x + (n - 1)(x - z)

My daughter felt compelled to test all of the other solutions offered to first see if they worked for 0 and, if so, did they also work for n > = 1 (which was a big waste of time).

Big picture this is no big deal. I just thought it was an interesting little question.