Math: ae2287e2

ID: ae2287e2

(SAT Suite Question Bank > Find Questions > Assessment: SAT + Test: Math + Domain: Algebra)

Comment: It is easy to make assumptions looking at the answer choices. Think through the logic of the given information instead.

Method 1: At its heart, profit is equal to revenue minus any associated costs (of production, commissions, etc.), per the middle of the passage.

profit = revenue - cost(s)

As long as we track the given information relative to this simple real-life model of profit, we will arrive at the correct answer, without getting tangled up in what appear to be pretty involved answer choices. For starters, the product costs $65 to make.

profit per unit = revenue per unit - $65

The second sentence tells us about a 20% commission that a salesperson earns for selling this product. On its own, there is not much we can do with this information, other than refine our general equation:

profit = revenue - commission - $65

Scanning ahead a few lines, we can see that the sales price of the product is $100. Now, we can get back to the equation above.

profit = ($100) - ($100(0.20)) - $65

Believe it or not, this is as far as we need to go. Look at the answer choices. If u represents units sold, we just have to play a matching game. I will put the profit on the left-hand side for convenience. Start with (A).

(6,840) = (100(1 - 0.2) - 65)u

6,840 = (100 - 100(0.2) - 65) * units sold

Yeah, that very closely resembles the earlier equation, only with the actual profit and the introduction of u, so (A) must be the correct answer. Working out the math would reveal that the profit per unit sold is $15. For the sake of review, consider the other answer choices, and work out some of the arithmetic. Start with (B).

(6,840) = (100 - 65)(1 - 0.8)u

6,840 = (35)(0.2)u

6,840 = 7 * units sold

We can stop there. This is saying that the profit per unit is $7, which is untrue, not to mention that 6,840/7 is a non-integer (~ 977.143), and it is impossible to sell partial units as far as we know. Now test (C).

(6,840) = 0.8(100) - 65u

6,840 = 80 - 65u

6,760 = -65 * units sold

This one is now a complete mess, and we are forced to abandon it. It is impossible to sell negative units to earn a profit. Believe it or not, I have seen some pretty strong Math students miss this question in practice by assuming that (C) is correct without actually thinking it through. Finally, test (D).

(6,840) = (0.2(100) + 65)u

6,840 = (20 + 65)u

6,840 = 85 * units sold

This equation tells us that the profit per unit sold is $85, which clearly does not make sense, even without the commission. (How can a product that sells for $100 that costs $65 to make still generate an $85 profit per unit?)

Method 2: You could graph each answer choice and substitute one of x or y for u, then check the appropriate intercept to get the number of units sold that would generate a profit of $6,840. Test (A) first.

This tells you that 456 units sold would generate a profit of $6,840. That could work, since the answer represents a whole number of units, and, importantly, the question does not say anything about approximating or rounding. The correct answer must be a whole number. Hang on to (A) and move on to (B).

This will not work, since it is impossible to sell 977 and 14/100 units. There either is or is not a whole unit to sell. Check (C).

Just as I wrote above under method 1, it makes no sense to sell a negative number of units. This is clearly incorrect. Last up, answer choice (D).

Again, we see a non-integer answer, which rules it out. There is no need to get into the math when a single option passes the basic test of logic. The correct answer must be (A).

Method 3: Toss out the $6,840 total profit and figure out the profit for selling a single unit, then check the answers.

profit = revenue - commission - cost

profit = 100 - 0.2(100) - 65

profit = 100 - 20 - 65

profit = 100 - 85

profit = 15

So, the profit on a single unit is $15. Plug in 1 for u, ignoring the 6,840 in the answer choices, and think of it as 1 instead.

A. (100(1 - 0.2) - 65)(1) = 100(0.8) - 65 = 80 - 65 = 15 √

B. (100 - 65)(1 - 0.8)(1) = (35)(0.2) = 7 X

C. 0.8(100) - 65(1) = 80 - 65 = 15 √

D. (0.2(100) + 65)(1) = (20 + 65) = 85 X

Since you know the profit is $15 per unit, you can change 1 to 2, knowing the answer should be 30.

A. (100(1 - 0.2) - 65)(2) = (100(0.8) - 65)(2) = (80 - 65)(2) = (15)(2) = 30 √

C. 0.8(100) - 65(2) = 80 - 130 = -50 X

To be clear, this is probably not the fastest way to get the answer, but with a calculator and a little insight, you could likely get to (A) just the same within a reasonable amount of time.