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Question

# The sum of twice the sum of 5 consecutive odd numbers and thrice the sum of 4 consecutive even numbers is 178. The sum of thrice the sum of 5 consecutive odd numbers and twice the sum of 4 consecutive even numbers is 177. The middle number when all the numbers are arranged in descending order is

A

9

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B

8

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C

7

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D

6

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Solution

## The correct option is B 8 Let's assume the five consecutive odd number be (2x +1) (2x -1) (2x + 3) (2x -3) (2x +5) Let's assume the four consecutive even number be (2y) (2y +2) (2y -2) (2y + 4) (2y -4) According to question 2(10x + 5) + 3(8y +4) = 178 20 x + 24 y = 156 -------(i) 3(10x + 5) + 2 (8y + 4) = 177 30x + 16 y = 154 --------(ii) Solving equation (i) and (ii), we will get y = 4 and x = 3. The five consecutive odd number be like 3, 5, 7, 9,11 The four consecutive odd number be like 6, 8, 10, 12. When arranging it in descending order 12, 11, 10, 9, 8, 7, 6, 5, 3. We got 8 as the middle term.

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