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09 Feb 2022, 08:00
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
66% (01:14) correct
34%
(01:13)
wrong
based on 71
sessions
History
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What is the value of \((x – 2)^2\) ?
(1) \(x^2 – 4x + 3 = 0\)
(2) \(x^2 – 7x + 12 = 0\)
(1) \(x^2 – 4x + 3 = 0\)
(2) \(x^2 – 7x + 12 = 0\)
09 Feb 2022, 08:11
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Bunuel
Target question: What is the value of \((x – 2)^2\)
Statement 1: \(x^2 – 4x + 3 = 0\)
Factor to get: \((x-1)(x-3) = 0\)
So, either \(x = 1\) or \(x = 3\)
Important: Many students will automatically assume that, since we have two possible values for x, statement 1 must be insufficient. This would be the case if the target question asked "What is the value of x?," but that's not what the target question asks. In order to correctly answer the target question, we must plug \(x = 1\) and \(x = 3\) into the given expression.
If \(x = 1\), then \((x – 2)^2 = (1 – 2)^2 = (–1)^2 = 1\)
If \(x = 3\), then \((x – 2)^2 = (3 – 2)^2 = (1)^2 = 1\)
In BOTH cases, the answer to the target question is \((x – 2)^2 = 1\)
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: \(x^2 – 7x + 12 = 0\)
Factor to get: \((x-4)(x-3) = 0\)
So, either \(x = 4\) or \(x = 3\)
If \(x = 4\), then \((x – 2)^2 = (4 – 2)^2 = (2)^2 = 4\)
If \(x = 3\), then \((x – 2)^2 = (3 – 2)^2 = (1)^2 = 1\)
Since we can’t answer the target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
23 Feb 2022, 05:17
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Bunuel
(1) can be written as: x^2 - 4x + 3 + 1 = + 1
So, x^2 - 4x + 4 = 1
(x-2)^2 = 1
Hence, it’s sufficient
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