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

1. x > 0 ; x + y = 0 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

As x + y = 0 and x is always positive, y will have to be negative. Hence Quantity A is greater.

2. Quantity A = Probability of getting tails in a toss of a coin Quantity B = Probability of getting a number greater than 2 in a throw of a dice • 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

We can get a number greater than 2 when the dice shows 3, 4, 5 or 6. Hence the probability is 4/6 or 2/3. The probability of getting tails in a toss of a coin is 1/2. So Quantity B is greater.

3.

AB is the diameter of the circle, and the line touching the circle at point D is a tangent to the circle. Quantity A = Measure of angle 1 + Measure of angle 2 Quantity B = Measure of angle 3 • 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 triangle ABC, angle 1 + angle 2 + angle 4 = 180^{o}. Angle subtended by the diameter on the circumference = angle 4 = 90^{o}. Therefore angle 1 + angle 2 = 90^{o}. Also the angle between the radius and a tangent at the point of contact = angle 3 = 90^{o}. So angle 1 + angle 2 = angle 3.

4.

Let ABC be any triangle. Quantity A = Measure of angle 1 + Measure of angle 2 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:The relationship cannot be determined from the information given

Angles 1 and 2 can take any two values. Hence the relationship is indeterminate.

5.

Quantity A = Measure of angle 2 Quantity B = Measure of angle 1 • 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

Angle subtended by an arc at the center of a circle is double the angle subtended by the same arc on the circumference, i.e., angle 2 is twice angle 1.

6.

The triangles ABC and CED are right-angled at A and D respectively. Quantity A =AC/CD Quantity B = BC/CE • 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 two triangles ABC and CED, Angle ACB = Angle DCE as they are vertically opposite angles Angle CAB = Angle CDE = 90^{o} So angle CBA is equal to angle CED. The two triangles are hence similar and the ratio of their corresponding sides will be equal.

7.

AB is the diameter of the circle. Quantity A = Measure of angle 2 Quantity B = 45^{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 A is greater

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

8.

In right-angled triangle ABC, AB = 5 and angle 1 = 45^{o}. Quantity A = Measure of angle 2 Quantity B = 45^{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

For the triangle, the sum of all the angles is 180. So angle 2 = 45^{o}

9. x > 1 and y > 1 Quantity A =(x + y)/xy Quantity B = 1/x + 1/y • 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

(x + y)/xy = x/xy + y/xy = 1/x + 1/y.

10. Quantity A = 0.5 Quantity B = (2)^{-1} • 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

(2)^{-1} = 1/2 = 0.5 Hence both are equal.

11. Quantity A = 90% of 200 Quantity B = 200% of 90 • 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

90% of 200 = (90/100) x 200 = 180. 200% of 90 = (200/100) x 90 = 180.

12.

In triangle ABC, angle A = 60^{o} and AB = AC. Quantity A = Length of side BC Quantity B = Length of side AB

• 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 A = 60^{o} and AB = AC, then angle 1 = angle 2 = 60^{o}. Hence the triangle is equilateral. So AB = BC.

13.

Quantity A = Measure of angle 1 Quantity B = 210^{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

angle 1 = 180^{o} - angle 4 = angle 5 + angle 6. So the maximum value that angle 1 can take is 180^{o}.

14.

In triangle ABC, measure of angle 1 = 100^{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:Quantity B is greater

The side opposite to a greater angle is longer. Now if angle 1 = 100^{o}, then no other angle can be larger than it. So side BC is longer than any other side.

15.

Consider an isosceles triangle ABC right-angled at A. A perpendicular is dropped from A on to BC at point D. Quantity A = Length of side BC Quantity B = Length of side AC • 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

BC is the hypotenuse of the triangle ABC and is the longest side. So length of side BC is necessarily greater than the length of side AC.

16. The average of three numbers x, y and z is 150. Quantity A = x + y Quantity B = x + 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 relationship cannot be determined from the information given

average = (x + y + z)/3 = 150. So, x + y + z = 450. No further information is provided, so the relationship between (x + y) and (x + z) is indeterminate.

17. xyz = 1; x = y Quantity A = z Quantity B = 1 • 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 x = y and xyz = 1, then z = 1/x^{2}. Therefore z can take any value and the relationship is indeterminate.

18. Quantity A = (1/5)^{2} Quantity B = 1/5 • 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

If the numerators are equal, then the fraction with the smaller denominator is greater. (1/5)^{2} = 1/25 < 1/5.

19. Quantity A = 30% of 30 Quantity B = 40% of 40 • 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

30% of 30 = (30/100) x 30 = 9. 40% of 40 = (40/100) x 40 = 16.

20. |x/y| = 1 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:The relationship cannot be determined from the information given

If x and y are both positive or both negative, then x = y. But, either x or y can be negative. Then, x = -y. Hence relationship is indeterminate.