ID: be9cb6a2
(SAT Suite Question Bank > Find Questions > Assessment: SAT + Test: Math + Domain: Algebra)
Comment: Watch out for assumptions. Many of the more challenging questions, particularly word problems, are probably considered Hard by official categorization not because they are inherently difficult, but because they prey on assumptions that students might make. This question is a case in point.
Method 1: If we know the cost is $270 for the first day and $135 for each additional day, then we can look at the equations given in the answer choices and test for logical soundness—i.e. only one answer can stand up to scrutiny. Clearly, the slope should be 135, since that figure represents a rate. Plug in 1 for x (to represent day 1), and the answer needs to be 270.
C. y = 135x + 270 --> y = 135(1) + 270 ≠ 270
The answer must be (D), since it cannot be (C). We can eyeball the equation to check, no calculator necessary.
D. y = 135x + 135 --> y = 135(1) + 135 = 270
Not only is this true, but it is clear that changing the value of x will add another 135 for each increase by 1, exactly what we would expect. Altogether, this solution should take about 15-30 seconds.
Method 2: Graph the four equations and look for the one that corroborates known information—one day costs $270, two would cost $270 + $135, or $405, and so on.
The only line that shows a y-value of 270 at x = 1 is the purple one. The red line is too low, while the others are too high. If you had chosen x = 2, both of these lines would show y = 405, but adding or subtracting another "day" would reveal the correct answer between them. Once again, the answer must be (D).
Method 3: One of the least effective ways to work through this one, namely by modeling the line and then checking the answer choices, could still reinforce conceptual knowledge. Start by modeling the line in slope-intercept form (an SAT favorite), and then fill in the missing pieces.
y = mx + b
y = 135x + b
Now, this is where it pays to see the trap ahead of time. It cannot be true that b = 270, since there is no day 0 built into the cost. So, you could work through the algebra to solve for b instead:
(270) = 135(1) + b
270 = 135 + b
135 = b
y = 135x + 135
Of course, the answer must be (D).
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