We need to find, if there is sufficiency to say that a always equal b or a never equals b.
Statement (1) is the equation . Subtracting 4 from both sides of this equation, we have . Multiplying both sides of this equation by b2, we have a^2 = b^2. Now having a^2 = b^2 does not mean that we must have a = b. It is also possible that a = −b.
For examples, if a = 4 and b = 4, then a2 = b2, and in this case, a = b, so the answer to the question is "yes." However, if a = 4 and b = −4, then a^2 = a^2, and in this case a is not equal to b, so the answer to the question is "no." Statement (1) is insufficient. We can eliminate choices (A) and (D).
Statement (2) is the equation . Let's try to rewrite this equation. Multiplying both sides of this equation by 7, we have 17a + 4b = 21a. Subtracting 17a from both sides, we have 4b = 4a. Dividing both sides of this equation by 4, we have b = a. Thus, a = b. We can answer the question with a "yes." We have determined that a does equal b. Statement (2) is sufficient. Choice (B) is correct.
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