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Question

If twice the sum of 5 consecutive odd numbers and thrice the sum of 4 consecutive even numbers is 178 and thrice the sum of 5 consecutive odd numbers and twice the sum of 4 consecutive even numbers is 177, then find the biggest odd number.


  1. 9

  2. 11

  3. 13

  4. 15


Solution

The correct option is B

11


Let the odd numbers be x,x+2,x+4,x+6 and x+8.
Their Sum = 5x+20
Let the even numbers be y,y+2,y+4 and y+6.
Their Sum = 4y+12
Given that:
2(5x+20)+3(4y+12)=178 and
3(5x+20)+2(4y+12)=177
Simplifying the above two equations, we get
5x+6y=51 ...(1)
15x+8y=93 ...(2)
Multiplying (1) by 3,
15x+18y=153 ...(3)
Subtracting (2) from (3), we get
10y=60y=6
Substituting y=6 in (1), we get x=3.
Therefore, the odd numbers are 3, 5, 7, 9, 11
and the even numbers are 6, 8, 10, 12.

The biggest of the odd number is 11.

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