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21 Dec 2021, 02:30
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
72% (01:04) correct
28%
(01:15)
wrong
based on 64
sessions
History
Date
Time
Result
Not Attempted Yet
If \(x ≠ 0\) and \(p\) is an integer, then what is the value of \(x^p\) ?
(1) \(p = p^2\)
(2) \(p < 1\)
(1) \(p = p^2\)
(2) \(p < 1\)
21 Dec 2021, 05:11
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Bunuel
(1) \(p = p^2\)
p can be both 0 and 1
So we will be getting two different answers, no unique answer possible.
Not Sufficient.
(2) \(p < 1\)
p can be 0 , -ve odd, -even
No unique ans possible.
Not sufficient.
Combining p can be only 0.
Sufficient.
C is the aswer.
21 Dec 2021, 07:47
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Bunuel
Target question: What is the value of \(x^p\) ?
Aside: Some students will look at the statements and conclude that, since there's no information about x, the two statements combined must be insufficient.
However, if \(p = 0\), and \(x ≠ 0\), then \(x^p = x^0 = 1\).
So, if a statement shows that \(p\) must equal \(0\), then that statement will be sufficient.
Statement 1: \(p = p^2\)
Subtract \(p\) from both sides of the equation to get: \(0 = p^2 - p\)
Factor: \(0 = p(p-1)\)
So, EITHER \(p = 0\) OR \(p = 1\)
Case a: If \(p = 0\), then the answer to the target question is \(x^p=x^0=1\)
Case b: If \(p = 1\), then the answer to the target question is \(x^p=x^1=x\)
Since we can’t answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: \(p < 1\)
Definitely not sufficient.
Statements 1 and 2 combined
Statement 1 tells us that EITHER \(p = 0\) OR \(p = 1\)
Statement 2 tells us that \(p < 1\)
Since both statements must be considered true, it must be the case that \(p = 0\), which means \(x^p=x^0=1\)
Since we can answer the target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent
