Official Guide Explanation:
Data Sufficiency #26




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Solution and Metadata

Question: 26
Page: 274
Difficulty: 6 (Moderately Difficult)
Category 1: Algebra > Equations >
Category 2: Algebra > Functions > other

Explanation: While the given formula looks complicated, there are only three variables. Even better, c is a constant, so when we solve for it once, we'll never need to solve for it again.

Statement (1) is sufficient. The information we're given, combined with the explanation in the question, tells us that t = 1 (the month) and n = 180 (the number of units). Start with the given formula and then plug in the values:

n = (900/(1 + c2-t))

180 = (900/(1 + c(2-1)))

I don't recommend spending the time to solve for c, but recognize that you could solve for c in that equation. Once you have c, a constant, the formula only has two variables. The question is asking how many units (n) are product in month 6--in other words, what is the value of n when t = 6? Since we know t and we know c, n is the only variable, meaning we can solve for it.

Statment (2) is also sufficient. The same reasoning applies as in (1). In this case, we just plug different values of n and t into the equation to find the constant c:

300 = (900/(1 + c(2-2)))

Again, no reason to solve, but you can find c. That's enough to find the value of n when t = 6. Choice (D) is correct.

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