ID: 90095507
(SAT Suite Question Bank > Find Questions > Assessment: SAT + Test: Math + Domain: Algebra)
Comment: Either stagger multiple percentage changes or multiply them all at once.
Method 1: Note, first, that the table provides a completely unnecessary column for answering the question at hand. Watch out for distractions. To find the original price of a property, we do not need to know anything about the monthly rental price. We can see that the Glenview Street property was purchased for 140,000 dollars, but that is the price after discounts. Whenever you encounter a question that deals with multiple percentage discounts or increases, the fastest way to solve is typically by multiplying the percentage actually paid at each step. So, a 40% discount would equate to a 60 percent price to pay. Write down what you know, in simple terms, and fill in as you go.
Original price (O) * percentage paid after discount(s) = purchase price
O * 0.60 * 0.80 = 140,000
O * 0.48 = 140,000
O ~ 291,666.67
The correct answer is (B).
Note that because multiplication can be performed in any order and result in the same product, it does not even matter whether you apply the second discount first.
Method 2: To use Desmos, you will probably want to stick to a non-graph solution, since it might not be apparent how to create a meaningful equation. If you want to work through the problem step by step, the calculator can help you get the answer pretty quickly.
Method 3: Because the question asks about a single unknown and the numerical answers are provided, you could work the problem backwards to see which answer choice would lead to the right purchase price for the property. Notice, too, that the numbers are pretty far apart, so it should be clear which way you would need to lean if you were close. If you use this strategy, you should almost always start with one of the middle values, since the answer choices are typically arranged in ascending or descending order. With luck, you will guess, say, (C), and it will either be correct or it will tell you that (B) or (D) must be the answer. You save yourself time by picking from the middle. In this case, because we know the answer is (B), why not start with (C) to illustrate how the process works? Trace the same process outlined above, in method 2.
($233,300) - 0.40($233,300) = $139,980
Actually, you do not need to take this one any further, since the discounted price, before the second discount is even applied, is already less than the purchase price. Furthermore, you can rule out (D), knowing it would also be too low. This means that (A) or (B) must be the correct answer, but you will only need to test one or the other. If you test (A) and it does not work, the only option left is (B), and vice-versa. For fun, try (A).
($350,000) - 0.40($350,000) = $210,000
$210,000 - 0.20($210,000) = $168,000
Because the actual purchase price is less than $168,000, it must be true that the original price was less than $350,000, and that means the correct answer must be (B).
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