Changing the range from \(\frac{1}{2}<x<\frac{3}{4}\) to \(\frac{50}{100}<x<\frac{75}{100}\)
(1) A shipment of 2000 Type X machine screws weighs more than 1,000 grams.
Let the weight of a screw = \(x\)
\(\frac{1000}{2000} = \frac{1}{2}\) or \(\frac{50}{100}\)
\(x > \frac{50}{100}\)
This means that the weight of a screw could be between \(\frac{1}{2}\) and \(\frac{3}{4}\), or it could exceed the range.
INSUFFICIENT(2) A shipment of 400 Type X machine screws weighs less than 260 grams.Let the weight of a screw = \(x\)
\(\frac{260}{400} = \frac{13}{20}\) or \(\frac{65}{100}\)
\(x < \frac{65}{100}\)
Once again, the weight of a screw could be in the range from the question stem or it could be below it.
INSUFFICIENT(1+2)Together one gets the following range for the weight of a screw:
\(\frac{50}{100} < x < \frac{65}{100}\) which means that \(x\) will be in the range of \(\frac{1}{2}<x<\frac{3}{4}\)
SUFFICIENT
ANSWER C