Question 3

Quantity B is greater.

In this context, Quantity B, represented as \(y + 90\), is greater than Quantity A, which is \(z\). This conclusion is drawn based on the properties of the rectangle PQRS and the relationships defined in the problem.

A) Quantity A is greater.

This option suggests that \(z\) is greater than \(y + 90\). However, without any additional information or context that supports this relationship, we cannot conclude that \(z\) exceeds \(y + 90\). Thus, this option is incorrect.

B) Quantity B is greater.

This option correctly states that \(y + 90\) is greater than \(z\). Given the properties of the rectangle and the implications of the dimensions involved, this assertion aligns with the relationships defined in the problem, making it the correct choice.

C) The two quantities are equal.

This option posits that \(z\) and \(y + 90\) are equal. However, no information in the context indicates that these two quantities are equal. Therefore, this option is not valid.

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

This option implies uncertainty regarding the relationship between \(z\) and \(y + 90\). However, based on the information provided, we can ascertain that \(y + 90\) is indeed greater, so this option is incorrect.

Conclusion

The conclusion that Quantity B is greater than Quantity A is supported by the analysis of the relationships described. All other options fail because they either misinterpret the relationship or lack sufficient evidence to support their claims. Thus, the analysis confirms that \(y + 90\) exceeds \(z\).