Bunuel wrote:
If −2 < p < 3 and −1 < q < 10, which of the following expresses the possible values of p – q ?
A. −12 < p – q < 4
B. −12 < p – q < 7
C. −3 < p – q < 4
D. −3 < p – q < 7
E. −1 < p – q < 4
To determine the smallest difference of p and q, we want p to be as small as possible and q to be as large as possible. Thus, we have p - q = -2 - 10 = -12.
To determine the largest difference of p and q, we want p to be as large as possible and q to be as small as possible. Thus, we have p - q = 3 - (-1) = 3 + 1 = 4.
Thus, -12 < p - q < 4.
Answer: A
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