Question 16

Quantity B is greater.

Since the ratio of the length of line segment PQ to the length of line segment OR is defined as k, we know that k is a positive number. However, we do not have specific values for the lengths of PQ and OR, and thus, we cannot definitively compare k to the value of 3/2.

A) Quantity A is greater.

This option suggests that the ratio k is greater than 3/2. Without specific information about the lengths of PQ and OR, we cannot conclude that k exceeds this value. Therefore, this option is incorrect.

B) Quantity B is greater.

This option correctly identifies that since k is undetermined, it could potentially be less than, equal to, or greater than 3/2. Without additional information specifying the lengths of the segments, we can conclude that it is indeed plausible that k is less than 3/2, making Quantity B greater.

C) The two quantities are equal.

This option implies that k is equal to 3/2. Given that k can take on any positive value depending on the lengths of PQ and OR, we cannot assert their equality without specific measurements. Thus, this option is incorrect.

D) The relationship cannot be determined from the information given.

While this option acknowledges the lack of specific lengths, it implies that no comparison can be made at all. However, since we can deduce that k could be less than 3/2, leading to Quantity B being greater, this option does not fully capture the relationship and is therefore not the best choice.

Conclusion

The correct answer is that Quantity B is greater because we do not have sufficient information to determine a specific value for k. Given that k is merely a ratio and could potentially be less than 3/2, Quantity B is a more reliable assertion. All other options either misrepresent the relationship or incorrectly assert a definitive comparison without the necessary information.