ID: d8789a4c
(SAT Suite Question Bank > Find Questions > Assessment: SAT + Test: Math + Domain: Advanced Math)
Comment: Recognize differences of squares.
Method 1: If (x^2 - c)/(x - b) = (x + b), then given the other constraints, x^2 - c must be equal to x^2 - b^2, and, further, c = b^2. Because the problem tells us that the two unknowns are positive integers, it must be true that c is a perfect square integer, such as 1 (from 1^2), 4 (from 2^2), 9, 16, 25, and so on. Of the four options listed, only 4 is such a number, so the correct answer is (A).
Method 2: For the second question running, a graph would probably not prove too useful. The question is rooted more in knowledge of algebra and number properties than it is in numbers and figures.
Method 3: You could plug in the answer choices to test for equivalence and see whether your findings corroborated known information. Start with the base equation:
(x^2 - c)/(x - b) = (x + b)
(x^2 - c) = (x + b)(x - b)
(x^2 - c) = x^2 - bx + bx - b^2
x^2 - c = x^2 - b^2
-c = -b^2
c = b^2
A. (4) = b^2 --> b = 2; both b and c are positive integers, so the correct answer must be (A).
B. (6) = b^2 --> b = √6 X
C. (8) = b^2 --> b = √8, or √4 * √2, or 2√2 X
D. (10) = b^2 --> b = √10 X
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