akhil911 wrote:
A set contains the following 5 numbers: \(a^2, a^5, a, \frac{a}{2}, \frac{a}{5}\). Is the range of the set equal to \(a^2 - a^5\)?
(1) a is negative
(2) \(a^5 < a\)
Given \(a^2, a^5, a, \frac{a}{2}, \frac{a}{5}\), do the first two values yield the greatest difference between any two values in the set?
Statement 1: \(a\) is negativeCase 1: \(a\) is a negative fraction between -1 and 0
Plugging \(a=-\frac{1}{2}\) into \(a^2, a^5, a, \frac{a}{2}, \frac{a}{5}\), we get:
1/4, -1/32, -1/2, -1/4, -1/10
Here, the greatest difference is NOT yielded by the first two values, so the answer to the question stem is NO.
Case 2: \(a\) is less than -1
Plugging \(a=-2\) into \(a^2, a^5, a, \frac{a}{2}, \frac{a}{5}\), we get:
4, -32, -2, -1, -2/5
Here, the greatest difference IS yielded by the first two values, so the answer to the question stem is YES.
Since the answer is NO in Case 1 but YES in Case 2, INSUFFICIENT.
Statement 2: \(a^5 < a\)Case 2 also satisfies statement 2.
In Case 2, the answer to the question stem is YES.
Case 3: \(a\) is a positive fraction between 0 and 1
Plugging \(a=\frac{1}{2}\) into \(a^2, a^5, a, \frac{a}{2}, \frac{a}{5}\), we get:
1/4, 1/32, 1/2, 1/4, 1/10
Here, the greatest difference is NOT yielded by the first two values, so the answer to the question stem is NO.
Since the answer is YES in Case 2 but NO in Case 3, INSUFFICIENT.
Statements combined:Only Case 2 satisfies both statements.
In Case 2, the answer to the question stem is YES.
SUFFICIENT.