Sum of three consecutive odd numbers & three consecutive even numbers together is 231. Difference between the smallest odd number and the smallest even number is 11. What is the sum of the largest even number and largest odd number?a)71b)91c)101d)81e)Can not be determinedCorrect answer is option 'D'. Can you explain this answer?

Question

Answer

Let the three odd numbers be x, (x + 2), (x + 4) and
The three even numbers be (x + 11), (x + 13) and (x + 15)
Then,
⇔ x + (x + 2) + (x + 4) + (x + 11) + (x + 13) + (x + 15) = 231
⇔ 6x + 45 = 231
⇔ 6x = 186
⇔ x = 31
∴ Required sum :
= (x + 4) + (x + 15)
= 2x + 19
= 2 × 31 + 19
= 62 + 19
= 81

Answer

Let the smallest odd number be y and the smallest even number be x.

Then the odd numbers will be y, y+2, y+4 and the even numbers will be x, x+2, x+4.

Given, the sum of three consecutive odd numbers and three consecutive even numbers is 231.

Then the equation will be

x+x+2+x+4+y+y+2+y+4=231
3x+3y+12=231
3(x+y)=219
x+y=73-(1)

Then given the difference between the smallest odd number and the smallest even number is 11.

Then the 2nd equation will be

x-y=11-(2)

Solving these two equations we get
x=42 & y=31

Therefore the biggest even number will be 46 and the biggest odd number will be 35.

Thereby there sum will be 46+35=81.

Hope this helps.

Answer

Let the smallest odd no.be x
1st odd no.=x, 2nd odd no.=x+2, 3rd odd no.=x+4
1st even no.=x+11, 2nd even no.=x+13, 3rd even no.=x+15
sum of all is 231
x+x+2+x+4+x+11+x+13+x+15=231
6x+45=231
6x=231-45
x=186/6
x=31
largest odd no.+largest even no.
=x+4+x+15
=31+4+31+15
=81

Answer

Let the smallest Odd no =x
three consecutive odd no. will be x , x+2 , x+4
three consecutive even no. will be (x+11) , (x+11)+2 , (x+11)+4
so , based on the sum of them:
= x+(x+2)+(x+4) +(x+11)+(x+13)+(x+15)=231
6x+45=231
6x=231-45
6x=186
x=31
so, smallest odd no. is 31.
three consecutive odd no. are 31, 33, 35.
three consecutive even no. are 31+11=42, 42+2=44, 42 +4=46.
largest odd no. is 35.
largest even no. is 46.
sum of the largest Odd no. and even no. is 35+46= 81.

Answer

Answer is D) 81.
sum of consecutive 3 odd and even numbers is 231.
let middle/average of 3 even numbers is x and middle/average of 3 odd numbers is y.
so 3x+3y = 231
i.e x+y= 77 #(1)
and difference between smallest odd and even is 11 ,
so we get (x-2)-(y-2)=11
i.e x-y=11 #(2)
adding above equation (1)&(2)
we get x=44 ...so 3 even no. are 42,44,46

also we get y=33.... so 3 odd no. are 31,33,35
therefore sum of largest even and odd no. is 46+35= 81

Answer

D

Answer

The sum of three consecutive odd numbers can be expressed as:

n + (n+2) + (n+4)

where n is the smallest odd number.

Simplifying the expression, we get:

3n + 6

Therefore, the sum of three consecutive odd numbers is always a multiple of 3, and is 6 more than three times the smallest odd number.

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