PQRS is a rectangle. Quantity A: z, Quantity B: y + 90

Rationale

Quantity B is greater than Quantity A.

In a rectangle, the sum of the interior angles is always 360 degrees, meaning each angle can be expressed in terms of the other angles. Given that angle z and angle y are angles in the same rectangle, angle z must be less than 90 degrees if angle y is a right angle, which is the case in rectangles.

A (Quantity A is greater.) YOUR ANSWER

If Quantity A were greater than Quantity B, it would imply that angle z exceeds 90 degrees. However, in a rectangle, all angles are right angles (90 degrees), meaning this situation is impossible. Therefore, Quantity A cannot be greater.

B (Quantity B is greater.) CORRECT

This choice correctly indicates that Quantity B, which is y + 90, is always greater than Quantity A, z, since z is an angle less than 90 degrees in a rectangle. Thus, y + 90 will always exceed z, confirming that Quantity B is indeed greater.

C (The two quantities are equal.) YOUR ANSWER

For the two quantities to be equal, angle z would have to equal y + 90. However, since z is less than 90 degrees and y represents one of the right angles in the rectangle, it is impossible for them to be equal. Thus, this statement is false.

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

This choice suggests uncertainty in the relationship between the two quantities. However, the properties of rectangles allow us to conclude definitively that Quantity B is greater than Quantity A. Therefore, this statement is incorrect.

Conclusion

In a rectangle, the relationship between the two quantities can be clearly determined. Quantity B, represented by y + 90, is always greater than Quantity A (angle z), as z cannot exceed 90 degrees while y represents a right angle. Thus, the conclusion that Quantity B is greater stands firm based on the geometric properties of rectangles.

PQRS is a rectangle. Quantity A: z, Quantity B: y + 90

Quantity B is greater than Quantity A.

Related Questions

Related Quizzes

How familiar were you with this question?

Report an Issue

Rate this Practice Test