Bunuel wrote:
If a, b, and c are different integers, is \((a − b)^c > 0\) ?
(1) b < a
(2) c = 2a
Target question: Is \((a − b)^c > 0\) ?Key Property: there are two different ways for \((a − b)^c\) to be greater than zero:
(i) The base, \((a - b)\), is positive (in which case the exponent can have any value)
(ii) The exponent, \(c\), is EVEN (in which case the base can have any value)
Statement 1: b < a Subtract \(b\) from both sides of the inequality to get: \(0 < a - b\).
Since \((a - b)\) is positive, we know that
\((a − b)^c \) is POSITIVE. (by property i)
Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: c = 2aSince \(a\) is an INTEGER, we know that \(c\) is a multiple of 2, which means \(c\) is EVEN
By property ii, we can be certain that
\((a − b)^c \) is POSITIVE.Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: D
Cheers,
Brent
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