A, B, and C are consecutive odd integers such that A

Question

A, B, and C are consecutive odd integers such that A < B < C.

If A + B + C = 81, then A + C =

A) 52

B) 54

C) 56

D) 58

E) 60

Bunuel · Accepted Answer

Say A = x - 2, B = x and C = x + 2 for some integer x. Then A + C = (x - 2) + (x + 2) = 2x.

A + B + C = 81;

(x - 2) + x + (x + 2) = 81;

3x = 81.

Then 2x = 81/1.5 = 81*2/3 = 54.

Answer: B.

spc11 · Answer

B.
I took another route. 
Since the sum is 81, the numbers will end in 5,7,9 respectively. 
Hence the last digit is 4. Thus, B.

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niks18 · Answer

as the numbers are consecutive so  B = Average of the three numbers
Hence  B = \frac{81}{3} = 27 
So  A+C = 81-27 = 54

Option  B

kaulshanx · Answer

2n+1+2n+3+2n+5=81, using general form of odd numbers (2n+1,2n+3...and so on. 
So n=12 after calculating. Hence numbers are 25,27,29 (after equating value of n in general form).
So A+C = 25+29=54 and answer is B

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sashiim20 · Answer

Odd numbers are represented by  2n+1

A   ,   B  and  C  are consecutive odd integers and  A < B < C  .

Therefore  A   ,   B  and  C  can be represented as  = (2n+1), (2n+3)  and  (2n+5)  respectively.

A + B + C = 81

(2n+1) + (2n+3) + (2n+5) = 81

2n + 1 + 2n+3+2n+5 = 81

6n + 9 = 81

6n = 81-9

6n = 72

n = \frac{72}{6} = 12

A = 2n+1 = 2(12) + 1 = 24 + 1 = 25

B = 2n+3 = 2(12) + 3 = 24 + 3 = 27

C = 2n+5 = 2(12) + 5 = 24 + 5 = 29

Therefore  A + C = 25 + 29 = 54

Answer (B)...

thanhtam269 · Answer

If A, B, C is consecutive odd integers, then A + B + C = 3A + 6 = 81 => 3A = 75 => A = 25, B = 27, C = 29
=> A + C = 54
The answer is B

daboo343 · Answer

Consecutive odd means
b= a+2
c=a+4
substitute the value of b and c in the given equation
a+a+2+a+4 =81
=> 3a+6=81
=> 3a= 81-6
=>a=75/3
=>a= 25
now the question is a+c
=>a+a+4
= 2a+4
=2*25+4
=50+4
=54
Hence B

thang62590 · Answer

A, B, and C are consecutive, let alone that they're odd consecutive, B must be the mean; therefore B = 81/3 = 27.

A + C = 81 - B
A + C = 81 - 27 = 54

Answer is B.

adkikani · Answer

Bunuel   chetan2u   niks18

I did understand that you took this approach since it is much faster simplification and 2s get 
cancelled out.

However the Q stem mentions to play with ODD nos , hence should we not take 2x+ 1, 2x+ 3... 
Do we take later approach only when we have odd and even no in same Q?

In your approach if I take x = 2, or x=0 then I do not get consecutive odd numbers.

Bunuel · Answer

x itself there denotes an odd integer. You could represent three consecutive integers as 2k - 3, 2k - 1, and 2k + 1 but it's not necessary here.

niks18 · Answer

Hi  adkikani

In algebra once you have defined a variable as ODD then it will never be even. So once x is defined as ODD you cannot assume x=2 or 0.

Just like in your example 2x+1, 2x+3.... etc. the implicit assumption is that x is even, so you cannot assume x=1 or any odd number because in that case 2x+1 will be even which is not possible.

So you can solve the problem using any kind of variable but once the variable is defined it stays as is.

BrushMyQuant · Answer

Given that A, B and C are consecutive odd integers such that A< B <C and If A+B+C =81 and we need to find the value of A+C

Since, A, B and C are consecutive odd integers
=> B = A + 2 and C = B + 2 = A + 4

=> A + B + C = 81
=> A + A + 2 + A + 4 = 81
=> 3A = 81 - 6 = 75
=> A = \(\frac{75}{3}\) = 25
=> C = A + 4 = 25 + 4 = 29

=> A + C = 25 + 29 = 54

So, Answer will be B
Hope it helps!

Watch the following video to learn How to Sequence problems

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A, B, and C are consecutive odd integers such that A < B < C.

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A, B, and C are consecutive odd integers such that A < B < C.

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