Here is the complete problem:
The numbers a, b, and c are all positive. If b²+c²=17, then what is the value of a²+c²?
Statement #1: a - b = 3
Statement #2: (a + b)/(a - b) = 7
Since the statements are in terms of a and b, rephrase the question stem in terms of a and b.
Substituting c²=17-b² into a²+c², we get:
a² + (17-b²)
a² - b² + 17.
(a+b)(a-b) + 17.
To determine the value of (a+b)(a-b) + 17, we need to know the value of (a+b)(a-b).
Question stem, rephrased:
What is the value of (a+b)(a-b)?
Statement 1: a-b = 3
No information about a+b.
INSUFFICIENT.
Statement 2: (a + b)/(a - b) = 7
Thus, a+b = 7(a-b).
Case 1: a-b = 1 and a+b = 7
In this case, (a+b)(a-b) = 7*1 = 7.
Case 2: a-b = 2 and a+b = 14
In this case, (a+b)(a-b) = 14*2 = 28.
INSUFFICIENT.
Statements combined:
Statement 1: a-b=3
Statement 2: a+b = 7(a-b) = 7*3 = 21.
Thus, (a+b)(a-b) = 21*3 = 63.
SUFFICIENT.
The correct answer is
C.
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