There are 3 consecutive odd numbers and 3 consecutive even numbers. The smallest even number is 9 more than largest odd number. If the square of average of all the 3 given odd number is 507 less than…

Question

There are 3 consecutive odd numbers and 3 consecutive even numbers. The smallest even number is 9 more than largest odd number. If the square of average of all the 3 given odd number is 507 less than the square of the average of all the 3 given even number, what is the smallest odd number.

PYQPulse · Accepted Answer

11

PYQPulse · Answer

Explanation: Let a consecutive odd numbers = 𝑥 – 2, 𝑥 and 𝑥 + 2 and consecutive even numbers = 𝑦 – 2, 𝑦, 𝑦 + 2 So, 𝑦 – 2 = 9 + 𝑥 + 2 𝑦 – 𝑥 = 13 … (i) and (𝑥)2 + 507 = (𝑦)2 𝑦2 − 𝑥2 = 507 (𝑥 + 𝑦)(𝑦 − 𝑥) = 507 (𝑥 + 𝑦) = 507 13 ⇒ 𝑥 + 𝑦 = 39 … (𝑖) Solving (i) and (ii) 𝑦 = 26 and 𝑥 = 13 so smallest odd numbers = 𝑥 – 2 = 13 – 2 = 11

There are 3 consecutive odd numbers and 3 consecutive even numbers. The smallest even number is 9 more than largest odd number. If the square of average of all the 3 given odd number is 507 less than the square of the average of all the 3 given even number, what is the smallest odd number.

Answer: A. 11

Explanation

There are 3 consecutive odd numbers and 3 consecutive even numbers. The smallest even number is 9 more than largest odd number. If the square of average of all the 3 given odd number is 507 less than the square of the average of all the 3 given even number, what is the smallest odd number.

Answer: A. 11

Explanation