GRE Test Quantitative Comparision

www.OneStopGRE.com – Your One Stop Destination for GRE Preparation! Visit www.OneStopGRE.com for more Free GRE Study Material. www.OneStopGRE.com Your One Stop Destination for GRE Preparation! GRE Test Preparation : Quantitative Comparison For more resources and latest information on GRE Exam, please visit www.OneStopGRE.com. www.OneStopGRE.com – Your One Stop Destination for GRE Preparation! Visit www.OneStopGRE.com for more Free GRE Study Material. GRE Test Prep : Quantitative Comparison Description: Compare the two quantities and choose the best answer from four choices given. Question 1: 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 = 180o Options: Quantity A equals Quantity B Quantity A is greater Quantity B is greater Relationship Indeterminate Answer: Quantity A equals Quantity B Explanation: 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 180o. Hence angle 1 + angle 2 + angle 4 = 180o. Hint: Angles 3 and 4 are vertically opposite angles and are therefore ... Question 2: Diagram is illustrative and is not drawn to scale. Quantity A = Measure of angle 2 + Measure of angle 3 Quantity B = 180o Options: Quantity A equals Quantity B Quantity A is greater Quantity B is greater Relationship Indeterminate Answer: Quantity A equals Quantity B www.OneStopGRE.com – Your One Stop Destination for GRE Preparation! Visit www.OneStopGRE.com for more Free GRE Study Material. Explanation: Angles 2 and 3 lie on a straight line and are supplementary angles. Hence their sum = 180o. Hint: Are angles 2 and 3 supplementary angles? Question 3: 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 Options: Relationship Indeterminate Quantity A is greater Quantity B is greater Quantity A equals Quantity B Answer: Relationship Indeterminate Explanation: Quantity A = 180o - angle 5 and Quantity B = 180o - 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. Hint: Can Quantity A and Quantity B be expressed in terms of angles 5 and 6? Question 4: a, b, c and d are four consecutive integers. Quantity A = The arithmetic mean of a and d Quantity B = The arithmetic mean of b and c Options: Quantity A equals Quantity B Quantity A is greater Quantity B is greater Relationship Indeterminate Answer: Quantity A equals Quantity B Explanation: If a, b, c and d are four consecutive integers, then b = a + 1 ; c = a + 2 ; and d = a + 3. Quantity A = (a + d)/2 = (a + a + 3)/2 = (2a + 3)/2. Quantity B = (b + c)/2 = (a + 1 + a + 2)/2 = (2a + 3)/2. Hint: If a, b, c and d are four consecutive integers, then b = a + 1 ; c = a + 2 ; and d = a + 3. Question 5: 2 < z < 4 Quantity A = 2z3 Quantity B = 3z2 Options: Relationship Indeterminate www.OneStopGRE.com – Your One Stop Destination for GRE Preparation! Visit www.OneStopGRE.com for more Free GRE Study Material. Quantity A is greater Quantity B is greater Quantity A equals Quantity B Answer: Relationship Indeterminate Explanation: You could substitute values for z between 2 and 4 to compare. An alternative simple strategy is to divide both Quantity A and B by 2z2. Then Quantity A = z and Quantity B = . We note that Quantity A lies between 2 and 4, whereas Quantity B equals about 3.14 Hint: Divide both Quantity A and B by 2z2. Question 6: yz < 0 Quantity A = (y − z)2 Quantity B = y2 + z2 Options: Quantity A is greater Quantity B is greater Quantity A equals Quantity B Relationship Indeterminate Answer: Quantity A is greater Explanation: (y − z)2 = (y − z)(y − z) = y2 + z2 − 2yz. Since yz is negative, −2yz is positive. So, Quantity A > Quantity B. Hint: (y − z)2 = (y − z)(y − z) = y2 + z2 − 2yz. Question 7: A circle of radius r has its center at C. Quantity A = The area of the colored square Quantity B = 0.5r2 Options: Quantity A equals Quantity B Quantity A is greater Quantity B is greater Relationship Indeterminate Answer: Quantity A equals Quantity B Explanation: Let a be the length of the side of the square. Area of colored square = a2. The diagonal of the square is the radius of the circle. By Pythagoras' Theorem, a2 + a2 = r2 or 2 a2 = r2. Area of colored square = a2 = 0.5r2. Hint: The diagonal of the colored square is the radius of the circle. So, by Pythagoras' Theorem, ... www.OneStopGRE.com – Your One Stop Destination for GRE Preparation! Visit www.OneStopGRE.com for more Free GRE Study Material. Question 8: Diagram is illustrative and is not drawn to scale. The total area of the four identical small circles equals the area of the colored region. Quantity A = Radius of the large circle Quantity B = Diameter of the small circle Options : Quantity A is greater Quantity B is greater Quantity A equals Quantity B Relationship Indeterminate Answer: Quantity A is greater Explanation: Let the radius of the large circle be R and the radius of each of the four small circles be r. Total area of four identical small circles = 4 (r2). Area of colored region = R2 − 4 (r2). Since these areas are equal, R2 − 4 r2 = 4 r2 or R2 = 8 r2. Thus, R = 8 r = 2 (2r) = 1.414 (diameter of the small circle). Hint: Let the radius of the large circle be R and the radius of each of the four small circles be r. Total area of four identical small circles = 4 (r2). Area of colored region = R2 - 4 (r2). Question 9: Quantity A = The circumference of a circle whose diameter is 37 Quantity B = The circumference of a circle whose radius is 19 Options: Quantity B is greater Quantity A is greater Quantity A equals Quantity B Relationship Indeterminate Answer: Quantity B is greater Explanation: A circle whose radius is 19 has a diameter equal to 38. A circle with a larger diameter will have a larger circumference, because circumference C is proportional to diameter D (note C = D). Hint: Does the circle with the larger diameter have the larger circumference? Question 10: Quantity A = (1/25)1/2 + (1/144)1/2 Quantity B = [(1/25) + (1/144)]1/2 Options: Quantity A is greater Quantity B is greater Quantity A equals Quantity B Relationship Indeterminate Answer: Quantity A is greater www.OneStopGRE.com – Your One Stop Destination for GRE Preparation! Visit www.OneStopGRE.com for more Free GRE Study Material. Explanation: (1/25)1/2 + (1/144)1/2 = (1/5) + (1/12) = 17/60. [(1/25) + (1/144)]1/2 = [(144+25)/(25 x 144)]1/2 = [169/(25 x 144)]1/2 = 13/60. Hint: Is (1/25)1/2 = 1/5 and (1/144)1/2 = 1/12 ? Question 11: Quantity A = Time to travel 95 miles at 50 miles per hour Quantity B = Time to travel 125 miles at 60 miles per hour Options: Quantity B is greater Quantity A is greater Quantity A equals Quantity B Relationship Indeterminate Answer: Quantity B is greater Explanation: Time = Distance / Speed Time to travel 95 miles at 50 miles per hour = 95/50 < 2 hours. Time to travel 125 miles at 60 miles per hour = 125/60 > 2 hours. Note that you save time by not calculating the exact values of Quantity A and Quantity B. Hint: Speed = Distance / Time Question 12: Quantity A = 4 / 100 Quantity B = 0.012 / 3 Options: Quantity A is greater Quantity B is greater Quantity A equals Quantity B Relationship Indeterminate Answer: Quantity A is greater Explanation: 4/100 = 0.04 and 0.012/3 = 0.004. Note that 0.04 > 0.004 Hint: Is 4/100 = 0.04 and 0.012/3 = 0.004 ? Question 13: Let ABC be any triangle. Quantity A = Measure of angle 1 + Measure of angle 2 Quantity B = 90o Options: Relationship Indeterminate Quantity A is greater Quantity B is greater Quantity A equals Quantity B Answer: Relationship Indeterminate Explanation: Angles 1 and 2 can take any two values. Hence the relationship is www.OneStopGRE.com – Your One Stop Destination for GRE Preparation! Visit www.OneStopGRE.com for more Free GRE Study Material. indeterminate. Hint: ABC can be any triangle, i.e., acute-angled, right-angled, or obtuse- angled. Question 14: 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 Options: Quantity A equals Quantity B Quantity A is greater Quantity B is greater Relationship Indeterminate Answer: Quantity A equals Quantity B Explanation: In triangle ABC, angle 1 + angle 2 + angle 4 = 180o. Angle subtended by the diameter on the circumference = angle 4 = 90o. Therefore angle 1 + angle 2 = 90o. Also the angle between the radius and a tangent at the point of contact = angle 3 = 90o. So angle 1 + angle 2 = angle 3. Hint: What is the angle subtended by the diameter on the circumference of a circle? What is the angle between the radius and a tangent at the point of contact? Question 15: Quantity A = Measure of angle 2 Quantity B = Measure of angle 1 Options: Quantity A is greater Quantity B is greater Quantity A equals Quantity B Relationship Indeterminate Answer: Quantity A is greater Explanation: 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 www.OneStopGRE.com – Your One Stop Destination for GRE Preparation! Visit www.OneStopGRE.com for more Free GRE Study Material. 1. Hint: How does the angle subtended by an arc at the center of a circle compare with the angle subtended by the same arc on the circumference? Question 16: Quantity A = Measure of angle 3 Quantity B = Measure of angle 4 Options: Quantity A equals Quantity B Quantity A is greater Quantity B is greater Relationship Indeterminate Answer: Quantity A equals Quantity B Explanation: Angles 3 and 4 are vertically opposite angles and hence always equal. Hint: Angles 3 and 4 are vertically opposite angles and are ... Question 17: 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 3 Quantity B = Measure of angle 4 Options: Quantity A equals Quantity B Quantity A is greater Quantity B is greater Relationship Indeterminate Answer: Quantity A equals Quantity B Explanation: Angle 3 = angle between the radius and a tangent at the point of contact = 90o. Angle 4 = angle subtended by the diameter on the circumference = 90o. Hint: What is the angle between the radius of a circle and a tangent at the point of contact? What is the angle subtended by the diameter of a circle on the circumference? www.OneStopGRE.com – Your One Stop Destination for GRE Preparation! Visit www.OneStopGRE.com for more Free GRE Study Material. Question 18: Given angle 2 = 120o Quantity A = Measure of angle 1 + Measure of angle 2 Quantity B = 180o Options: Quantity A equals Quantity B Quantity A is greater Quantity B is greater Relationship Indeterminate Answer: Quantity A equals Quantity B Explanation: The angle subtended by an arc at the center is double the angle subtended by the same arc on the circumference. If angle 2 = 120o, then angle 1 = 60o and angle 1 + angle 2 = 180o. Hint: How does the angle subtended by an arc at the center of a circle compare with the angle subtended by the same arc on the circumference? Question 19: Quantity A = Measure of angle 2 Quantity B = Measure of angle 3 Options: Relationship Indeterminate Quantity A is greater Quantity B is greater Quantity A equals Quantity B Answer: Relationship Indeterminate Explanation: Angle 2 + Angle 3 = 180o (supplementary angles). However, the angles 2 and 3 can individually take any value. So the relationship is indeterminate. Hint: All we can say is that angles 2 and 3 are supplementary angles (add up to 180o). www.OneStopGRE.com – Your One Stop Destination for GRE Preparation! Visit www.OneStopGRE.com for more Free GRE Study Material. Question 20: Quantity A = Measure of angle 3 Quantity B = Measure of angle 2 Options: Quantity A is greater Quantity B is greater Quantity A equals Quantity B Relationship Indeterminate Answer: Quantity A is greater Explanation: For the triangles ABC and ABD we have: angle 5 + angle 1 + angle 3 = 180o angle 5 + angle 1 + angle 2 + angle 6 = 180o From the above equations, angle 3 = angle 2 + angle 6. So angle 3 is greater than angle 2. Hint: The angles of a triangle add up to 180o. Based on this fact, write equations for triangles ABC and ABD. Question 21: Quantity A = Measure of angle 1 + Measure of angle 2 Quantity B = 180o Options: Relationship Indeterminate Quantity A is greater Quantity B is greater Quantity A equals Quantity B Answer: Relationship Indeterminate Explanation: 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 60o, (angle 1 + angle 2) will be less than, greater than or equal to 180o. Hence the relationship is indeterminate. Hint: The angle subtended by an arc at the center of a circle is double the angle subtended by the same arc on the circumference. www.OneStopGRE.com – Your One Stop Destination for GRE Preparation! Visit www.OneStopGRE.com for more Free GRE Study Material.