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1.
Sum of 4 consecutive even numbers is greater than consecutive odd numbers by 81. If the sum of the least odd and even numbers is 59 then find the sum of largest odd and even numbers.
- A. 69
- B. 69
- C. 69
- D. 69
Answer: Option A
Explanation:
Let 4 consecutive even numbers be x, x + 2, X + 4 and x + 6 respectively.
3 consecutive odd numbers be y, y + 2 and y + 4
According to question,
[x + x + 2 + x + 4 + x + 6]−[y + y + 2 + y + 4] = 81
= > (4x + 12)−(3y + 6) = 81
4x−3y = 81−12 + 6
4x−3y = 75
x + 4 = 59
On solving equations (i) and (ii), we get
X = 36
y = 23
The sum of largest odd and even number = x + 6 + y + 4 = x + y + 10 = 36 + 23 + 10 = 69
3 consecutive odd numbers be y, y + 2 and y + 4
According to question,
[x + x + 2 + x + 4 + x + 6]−[y + y + 2 + y + 4] = 81
= > (4x + 12)−(3y + 6) = 81
4x−3y = 81−12 + 6
4x−3y = 75
x + 4 = 59
On solving equations (i) and (ii), we get
X = 36
y = 23
The sum of largest odd and even number = x + 6 + y + 4 = x + y + 10 = 36 + 23 + 10 = 69
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