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Given below are three quantities named A, B and C. Based on the given information, determine the relation among the three quantities. P is the average of 10 consecutive even numbers starting from 402, Q is the average of 7 consecutive odd numbers starting from 451 and R is the average of the sum of first 39 natural numbers and the sum of first 19 natural numbers. Quantity A: What is the average of P and Q? Quantity B: What is the average of P and R? Quantity C: What is the average of Q and R?

Given below are three quantities named A, B and C. Based on the given information, determine the relation among the three quantities. P is the average of 10 consecutive even numbers starting from 402, Q is the average of 7 consecutive odd numbers starting from 451 and R is the average of the sum of first 39 natural numbers and the sum of first 19 natural numbers. Quantity A: What is the average of P and Q? Quantity B: What is the average of P and R? Quantity C: What is the average of Q and R? Correct Answer Quantity A < Quantity B < Quantity C

P = (402 + 404 + … + 418 + 420)/10 = 400 +

⇒ P = 400 + (110/10) = 411

Q = (451 + 453 + … + 461 + 463)/7 = 450 +

⇒ Q = 450 + (49/7) = 457

∵ Sum of first n natural numbers = n(n + 1)/2

⇒ Sum of first 39 natural numbers = (39 × 40)/2 = 780

⇒ Sum of first 19 natural numbers = (19 × 20)/2 = 190

⇒ R = (780 + 190)/2 = 485

Solving for Quantity A:

⇒ Quantity A = (P + Q)/2 = (411 + 457)/2 = 434

Solving for Quantity B:

⇒ Quantity B = (P + R)/2 = (411 + 485)/2 = 448

Solving for Quantity C:

⇒ Quantity C = (Q + R)/2 = (457 + 485)/2 = 471

∴ Quantity A < Quantity B < Quantity C

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