Gmat_mission wrote:Is |a| + |b| > |a + b| ?
(1) a^2 > b^2
(2) |a|*b < 0
>
Is |a| + |b| > |a + b|?
Because an absolute value cannot be negative, both sides of the inequality above are NONNEGATIVE, allowing us to SQUARE the inequality
(|a| + |b|)² > (|a + b|)²
a² + 2|a||b| + b² > a² + 2ab + b²
2|a||b| > 2ab
|a||b| > ab.
The resulting inequality is valid only if a and b have DIFFERENT SIGNS.
Question stem, rephrased:
Do a and b have different signs?
Statement 1: a² > b²
Statement 2: |a|b < 0
Both statements are satisfied by the following cases:
Case 1: a=2 and b=-1
Case 2: a=-2 and b=-1
In Case 1, a and b have different signs, so the answer to the rephrased question stem is YES.
In Case 2, a and b have the same sign, so the answer to the rephrased question stem is NO.
Since the answer is YES in Case 1 but NO in Case 2, the two statements combined are INSUFFICIENT.
The correct answer is
E.
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