In order to find the perimeter of the right triangle in Quantity A, we must find the length of the hypotenuse. We know that by the Pythagorean theorem, the hypotenuse is equal to the square root of (10² + 24²) = 100 + 576 = 676. The square root of 676 is 26, so the perimeter of the right triangle is 10 + 24 + 26 = 60.

We could also have noticed that the right triangle is similar to a 5-12-13 right triangle with a dilution ratio of 2, since the 10-24 sides are twice the length of the 5-12 sides.

The area of the right triangle is calculated with b * h / 2, with the base and height equal to the two short sides of the right triangle. 10 * 12 / 2 = 120 / 2 = 60.

Thus, the two quantities are equal.

The first step in quantitative comparison problems is to make sure they can actually be solved. Quantity B is just a number.  Quantity A is a right triangle, where we're given the hypotenuse, the triangle's classification/an angle measure, and asked to find a perimeter.  And we cannot.

How do we know that?

Draw a right triangle with a hypotenuse of 13. Odds are, you drew the 5/12/13, a right triangle pattern seeen in many books as being very helpful on the GRE (which, well, it is).  In such a case, you probably think that the perimeter will be 30 after adding the sides together, and leave it at that. 

But, hold on a second. Draw another triangle, also with a right angle and a hypotenus of 13, but this time, make the triangle isosceles. It's possible, right? You have met all the conditions Quantity A gives you in this triangle, as well, but it will have a different perimeter.  

Therefore, the information in quantity A is not enough information to determine what the answer is, and that's the answer you need to put.  

The first step of a quantitative comparison question is to see if the quantities can even be determined in the first place.  The Quantity B is just a number, so it is already determined.  In Quantity A, you must find the perimeter of a right triangle with a given side-length and two equal angles.  This is determinable, since you have all three angles and a side length.

To solve Quantity A, first consider that two of the angles in the right triangle must be equal. As you cannot have multiple 90 degree angles in a triangle, then the two equal angles must be the other angles. This means they're both 45 degrees, and you have a 45-45-90 triangle.  This is a special triangle, where the ratio of side:side:hypotenuse is .  Since the hypotenuse is equal to , then the side lengths are both .  

Quantity B is greater.

By definition a parallelogram has two sets of opposite sides that are congruent/parallel. However to find the area of a paralleogram, you need to know the base and height lengths. Since this problem provides both the base and height measurements, apply the formula: 



The solution is: 

By definition a parallelogram has two sets of opposite sides that are congruent/parallel. However, to find the area of a paralleogram, you need to know the base and height lengths. Since this problem provides both the base and height measurements, apply the formula: 


Before applying the formula you must find  of . 

The final solution is: 

By definition a parallelogram has two sets of opposite sides that are congruent/parallel. However, to find the area of a paralleogram, you need to know the base and height lengths. Since this problem provides both the base and height measurements, apply the formula: 



The solution is: 

A parallelogram must have two sets of opposite sides that are congruent/parallel. However, to find the area of a paralleogram, you need to know the base and height lengths. Since this problem provides both the base and height measurements, apply the formula: 


Before applying the formula you must find  of . 

The solution is: 

By definition a parallelogram has two sets of opposite sides that are congruent/parallel. However to find the area of a paralleogram, you need to know the base and height lengths. Since this problem provides both the base and height measurements, apply the formula: 



The solution is: 

By definition a parallelogram has two sets of opposite sides that are congruent/parallel. However, to find the area of a paralleogram, you need to know the base and height lengths. Since this problem provides both the base and height measurements, apply the formula: 


Before applying the formula you must find  of . 



The solution is: 

A parallelogram must have two sets of opposite sides that are congruent/parallel. However, to find the area of a paralleogram, you need to know the base and height lengths. Since this problem provides both the base and height measurements, apply the formula: 



The solution is: 



Note: prior to applying the formula, the answer choices require you to be able to convert  to , as well as  to . Or, you could have converted the mixed numbers to improper fractions and then multiplied the two terms: