Compare the two quantities and choose the best answer from four choices given.

1. x and y are both positive and x/y > 5 Quantity A = 0.2x Quantity B = y • Quantity A is greater • Quantity B is greater • The two quantities are equal • The relationship cannot be determined from the information given Answer:Quantity A is greater

Now x > 5y. Dividing both sides of this inequality by 5, we get 0.2x > y.

2. John travels at 60 mph and James travels at 80 mph. Quantity A = Time for John to cover 20 miles Quantity B = Time for James to cover 40 miles • Quantity A is greater • Quantity B is greater • The two quantities are equal • The relationship cannot be determined from the information given Answer:Quantity B is greater

Time = Distance / Speed Time taken by John = 20/60 = 1/3 hour. Time taken by James = 40/80 = 1/2 hour. So Quantity B (time taken by James) is greater.

3.

Diagram is illustrative and is not drawn to scale. Quantity A = Measure of angle 1 + Measure of angle 2 + Measure of angle 4 Quantity B = 180^{o} • Quantity A is greater • Quantity B is greater • The two quantities are equal • The relationship cannot be determined from the information given Answer:The two quantities are equal

In the figure, angles 3 and 4 are vertically opposite angles and are equal. Also the sum of the three angles of a triangle is 180^{o}. Hence angle 1 + angle 2 + angle 4 = 180^{o}.

4.

Diagram is illustrative and is not drawn to scale. Quantity A = Measure of angle 1 + Measure of angle 3 Quantity B = Measure of angle 2 + Measure of angle 4 • Quantity A is greater • Quantity B is greater • The two quantities are equal • The relationship cannot be determined from the information given Answer:The relationship cannot be determined from the information given

Quantity A = 180^{o} - angle 5 and Quantity B = 180^{o} - angle 6. Now the values of A and B depend on angles 5 and 6 about which nothing is given. Hence the relationship is indeterminate.

5.

Diagram is illustrative and is not drawn to scale. Quantity A = Measure of angle 2 + Measure of angle 3 Quantity B = 180^{o} • Quantity A is greater • Quantity B is greater • The two quantities are equal • The relationship cannot be determined from the information given Answer:The two quantities are equal

Angles 2 and 3 lie on a straight line and are supplementary angles. Hence their sum = 180^{o}.

6.

Diagram is illustrative and is not drawn to scale. AB is the diameter of the circle. Quantity A = Measure of angle 1 Quantity B = Measure of angle 2 • Quantity A is greater • Quantity B is greater • The two quantities are equal • The relationship cannot be determined from the information given Answer:The two quantities are equal

Angle subtended by the diameter on the circumference = 90^{o}. So angle 1 = angle 2 = 90^{o}.

7.

Diagram is illustrative and is not drawn to scale. Given AB = AC and angle BAC = 60^{o} Quantity A = Length of side AB Quantity B = Length of side BC • Quantity A is greater • Quantity B is greater • The two quantities are equal • The relationship cannot be determined from the information given Answer:The two quantities are equal

As sides AB and AC are of the same length, angles 1 and 2 must be equal. The angles of a triangle add up to 180^{o}. Since angle A = 60^{o}, the other 2 angles must also be 60^{o}. This is therefore an equilateral triangle. So AB = BC.

8. 0 < -x < 10 11 < -y < 20 Quantity A = x Quantity B = y • Quantity A is greater • Quantity B is greater • The two quantities are equal • The relationship cannot be determined from the information given Answer:Quantity A is greater

x lies between -10 and 0, while y lies between -20 and -11. Hence x is always greater that y.

9. Quantity A = 2^{9} Quantity B = 9^{2} • Quantity A is greater • Quantity B is greater • The two quantities are equal • The relationship cannot be determined from the information given Answer:Quantity A is greater

2^{9} can be written as 2 x 2^{8} = 2 x 16^{2}, which is greater than 9^{2}.

10.

Diagram is illustrative and is not drawn to scale. Given angles 1 and 2 are equal, length of side AB = x, length of side BC = y, length of side AC = z. Quantity A = x + y Quantity B = y + z • Quantity A is greater • Quantity B is greater • The two quantities are equal • The relationship cannot be determined from the information given Answer:The two quantities are equal

Given angles 1 and 2 are equal, the triangle is isosceles and x = z. Adding y to both sides of the equation, we get x + y = z + y

11. y^{2} = 36 Quantity A = y Quantity B = 6 • Quantity A is greater • Quantity B is greater • The two quantities are equal • The relationship cannot be determined from the information given Answer:The relationship cannot be determined from the information given

If y^{2} = 36, then y can be either 6 or -6. So Quantity A and Quantity B may not always be equal. The relationship is indeterminate.

12.

Diagram is illustrative and is not drawn to scale. In triangle ABC, angle A = 60^{o} and AB = AC. Quantity A = Measure of angle 1 + Measure of angle 2 Quantity B = 120^{o} • Quantity A is greater • Quantity B is greater • The two quantities are equal • The relationship cannot be determined from the information given Answer:The two quantities are equal

If angle A = 60^{o}, then angle 1 + angle 2 = 180^{o} - 60^{o} = 120^{o}.

13.

Diagram is illustrative and is not drawn to scale. Quantity A = Measure of angle 3 - Measure of angle 2 Quantity B = Measure of angle 5 - Measure of angle 6 • Quantity A is greater • Quantity B is greater • The two quantities are equal • The relationship cannot be determined from the information given Answer:The two quantities are equal

For the given figure, we have the following relations: angle 3 = 180^{o} - angle 6 = angle 4 + angle 5 angle 2 = 180^{o} - angle 5 = angle 4 + angle 6 Subtracting the two equations, we have angle 3 - angle 2 = angle 5 - angle 6.

14.

Diagram is illustrative and is not drawn to scale. In triangle ABC, AB = AC and measure of angle 1 = 100^{o}. Quantity A = Measure of angle 2 + Measure of angle 3 Quantity B = 90^{o} • Quantity A is greater • Quantity B is greater • The two quantities are equal • The relationship cannot be determined from the information given Answer:Quantity B is greater

Given angle 1 = 100^{o}. angle 2 + angle 3 = 180^{o}o = 80^{o}. Hence Quantity B is greater.

15.

Diagram is illustrative and is not drawn to scale. Consider an isosceles triangle ABC right-angled at A, with a perpendicular dropped from A on to BC at point D. Quantity A = Length of side BD Quantity B = Length of side DC • Quantity A is greater • Quantity B is greater • The two quantities are equal • The relationship cannot be determined from the information given Answer:The two quantities are equal

The perpendicular between the two equal sides of an isosceles triangle bisects the opposite side. So BD = DC.

16. The calorific value of 5 tumblers of orange juice with 4 spoons of sugar equals the calorific value of 3 tumblers of orange juice with 6 spoons of sugar. Quantity A = calorific value of 1 tumbler of orange juice Quantity B = calorific value of 1 spoon of sugar • Quantity A is greater • Quantity B is greater • The two quantities are equal • The relationship cannot be determined from the information given Answer:The two quantities are equal

The equation 5A + 4B = 3A + 6B represents the given condition. On simplifying, we get A = B.

17. x < 0 Quantity A = x^{2} Quantity B = x^{3} • Quantity A is greater • Quantity B is greater • The two quantities are equal • The relationship cannot be determined from the information given Answer:Quantity A is greater

If x is negative, its square will always be positive and cube will be negative. So Quantity A is greater.

18. The chance of an arrow striking the Bull's Eye is 0.07%. An archer fires 10,000 arrows. Quantity A = Number of arrows striking the Bull's Eye Quantity B = 70 • Quantity A is greater • Quantity B is greater • The two quantities are equal • The relationship cannot be determined from the information given Answer:Quantity B is greater

0.07% of 10000 = (0.07/100) x 10000 = 7. So Quantity B is greater.

19. The sum of three consecutive numbers is 150. Quantity A = largest number of the three Quantity B = 50 • Quantity A is greater • Quantity B is greater • The two quantities are equal • The relationship cannot be determined from the information given Answer:Quantity A is greater

Let the three consecutive numbers be n-1, n and n+1. Their sum = 3n = 150. So n = 50. The numbers therefore are 49, 50 and 51. The largest number is 51. Hence Quantity A is greater.

20. Quantity A = (x + y)^{2} Quantity B = x^{2} + y^{2} • Quantity A is greater • Quantity B is greater • The two quantities are equal • The relationship cannot be determined from the information given Answer:The relationship cannot be determined from the information given

Now (x + y)^{2} = x^{2} + y^{2}+ 2xy. Various cases arise depending on whether xy is positive, negative or zero. As this information is not given, the relationship is indeterminate.