What is the sum of two consecutive even numbers, the difference of whose squares is 84?

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OPSC ASO (Maths & Reasoning) 27 Aug 2022 Official Paper
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  1. 34
  2. 38
  3. 42
  4. 46

Answer (Detailed Solution Below)

Option 3 : 42
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Detailed Solution

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Given:

The sum of two consecutive even numbers is to be calculated where the difference of their squares is 84.

Formula Used:

Difference of squares = (a + b)(a - b)

Sum of two consecutive even numbers = a + b

Calculation:

Let the two consecutive even numbers be a and b.

Since they are consecutive even numbers, a = b - 2.

Difference of squares = 84

(b2 - a2) = 84

⇒ (b + a)(b - a) = 84

Substitute a = b - 2:

⇒ (b + (b - 2))(b - (b - 2)) = 84

⇒ (b + b - 2)(2) = 84

⇒ (2b - 2)(2) = 84

⇒ 4b - 4 = 84

⇒ 4b = 88

⇒ b = 22

Substitute b = 22 to find a:

a = b - 2

a = 22 - 2

a = 20

Sum of a and b:

⇒ a + b = 20 + 22 = 42

The sum of two consecutive even numbers is 42.

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