For the triangles ABC and ABD we have:
angle 5 + angle 1 + angle 3 = 180^o
angle 5 + angle 1 + angle 2 + angle 6 = 180^o
From the above equations, angle 3 = angle 2 + angle 6.
So angle 3 is greater than angle 2.

The product of two negative numbers is always positive and their sum is always negative. So Quantity B will always be greater.

Average = 18/3 = 6.
It is not necessary to individually determine the three consecutive even numbers (4, 6, 8).

Angle 2 + Angle 3 = 180^o (supplementary angles).
However, the angles 2 and 3 can individually take any value.
So the relationship is indeterminate.

The angle subtended by an arc at the center (angle 2) is double the angle subtended by the same arc on the circumference (angle 1).
angle 1 + angle 2 = angle 1 + 2 (angle 1) = 3 (angle 1).Depending on whether angle 1 is less than, greater than or equal to 60^o, (angle 1 + angle 2) will be less than, greater than or equal to 180^o.
Hence the relationship is indeterminate.

The angles opposite the equal sides in an isosceles triangle are equal. So angle 1 = angle 2.

If x = 13 and y = -4, then |x - y| = 17 which is greater than 11.
But if x = 13 and y = 4, then |x - y| = 9 which is less than 11
Hence the relationship is indeterminate.

If x - y > 10, then y - x < -10 (on multiplying by -1).
Hence Quantity B is greater.

3/5 + 4/7 = 41/35, which is greater than 1.
On the other hand, 7/12 is less than 1.

Zero raised to any positive power is zero, so Quantity A = 0.
Any number raised to 0 is unity, so Quantity B = 1.

For the angles, we have the following set of relations:
angle 1 = 180^o - angle 4 = angle 5 + angle 6
angle 2 = 180^o - angle 5 = angle 4 + angle 6
angle 3 = 180^o - angle 6 = angle 4 + angle 5
Adding these three equations, we get
angle 1 + angle 2 + angle 3 = 360^o.

There isn't sufficient information here to decide about the relationship between angle 1 and angle 2. The diagram may be misleading... it is for
illustration only and is not drawn to scale.

Angles opposite to equal sides are equal. Hence angle 2 = angle 3.

ABC is an isosceles right triangle. Hence angle 1 = 45^o.
For the triangle ABD, angle 5 = 90^o and angle 1 = 45^o and hence angle 2 = 45^o.
So triangle ABD is also isosceles and hence BD = AD.

Mary's age is 1/4 th Jason's age.
Mark's age is 1/5 th Jason's age.
So, Mary's age is greater than Mark's.

The radius of Circle 1 will be double the radius of Circle 2 if the area of Circle 1 is four times the area of Circle 2. So, the radius of Circle 1
equals the diameter of Circle 2. Mathematically,
Area of circle 1 = A₁ = π r₁²and Area of circle 2 = A₂ = π D₂²/4.
Since A₁ = 4 A₂, r₁² = D₂² or r₁ = D₂.

If xyz = 1 and x = 1, then z is the reciprocal of y (i.e., z = 1/y).
For example: y = 10, z = 1/10; y = 1/2, z = 2; y = 1, z = 1.
Hence the relationship is indeterminate.

Quantity A = (y² + 3x + z³) 0 = 0.

1 kilometer = 1/1.6 mile = 10/16 mile = 5/8 mile = 0.625 mile.

If 1/z < 0, then z must be negative. So, Quantity B is greater.