If 2x + y = 7 and x + 2y = 5, then (x + y)/3 =

Question

(A) 1
(B) 4/3
(C) 17/5
(D) 18/5
(E) 4

BrentGMATPrepNow · Accepted Answer

We have two equations: 
2x + y = 7
x + 2y = 5

Notice that something nice happens when we ADD them. We get: 
3x + 3y = 12
Divide both sides by 3 to get:  x + y = 4

So, ( x + y )/3 =  4 /3

Answer: B

Cheers,
Brent

avigutman · Answer

Video solution from Quant Reasoning:
 https://www.youtube.com/watch?v=704u7izgfNk

asethi · Answer

x=3, y=1, so x+y/3=4/3

Ans:B

Skywalker18 · Answer

2x+y = 7 --1
x +2y= 5 --2
Adding equations 1 and 2 , we get
3x+3y=12
=>x+y=4

(x+y)/3 = 4/3
Answer B

camlan1990 · Answer

3x + 3y = 12
Divide both sides by 9 to get: 4/3

Ans B

BASSLJ · Answer

2*(x+2y = 5) equals 2x+4y=10
 2x+4y=10
- 2x + y= 7
= 3y=3
Therefore Y = 1

Plug and solve...

2x + 1 = 7
2x=6
x=3

(3+1)/3= 4/3

Mun20 · Answer

Adding the 2 equations 
3x + 3y= 12 
Dividing both sides by 3 
X+y=12/3
Again dividing both sides by 3 
(X+y)/3=4/3

AkshdeepS · Answer

My Solution:

2x+y=7 ----- (1) and x+2y=5 ------>(2)

Solving eqn. (1) & (2) we get x = 3 and y = 1,

Therefore, x+y/3 will be (3+1)/ 3

Answer = 4/3 Option B

kanusha · Answer

Multiply 2nd equation with 2, on solving 
-3y = -3
y =1 
Substitute, x = 3
 \frac{4}{3} 
B

AkshdeepS · Answer

Add both equations:

3x + 3y = 12

3 (x + y) = 12

x + y = 4

(x + y)/3

4/3

(B)

Mo2men · Answer

2x + y = 7.............1

x + 2y = 5.............2
-----------------------------Sum the 2 eqautions

3x +3 y = 12 .................Divide by 3

x + y =4........................ divide by 3

(x + y)/3 =4/3

Answer: B

adkor95 · Answer

Thanks  BrentGMATPrepNow  very quick and efficient. But I'm curious how you spotted it so quickly? I tried subst./elimination first before I realised adding was quicker.

Was there a clue you picked up on?

Cheers

MathRevolution · Answer

Since there are two variables and two distinct equations, we can often solve it by elimination or substitution. But before applying those approach, look at the question what does it need and try adding both the equations or subtracting one from the other and it likely happens 90% times that we get the same kind equation which is in question.

2x + y = 7 and x + 2y = 5

Adding both the equations: 2x + y + x + 2y = 7 + 5

=> 3x + 3y = 12

=> x + y = \(\frac{12}{3}\) = 4

=> \(\frac{(x + y)}{3}\) = \(\frac{4}{3}\)

Answer B

2x + y = 7 and x + 2y = 5

Adding both the equations: 2x + y + x + 2y = 7 + 5

=> 3x + 3y = 12

=> x + y =  \frac{12}{3}  = 4

=>  \frac{(x + y)}{3}  =  \frac{4}{3}

Answer B

BrentGMATPrepNow · Answer

If a question involves a system of two equations, and we're asked to find the value of  ONE  specific variable, then we're pretty much forced to solve the system.
HOWEVER, if the question asks us to find the SUM (or DIFFERENCE) of the variables, then I look for some kind of shortcut in which we combine the two equations.

arileib · Answer

I solved using substitution:

2x + y = 7...
y = 7 - 2x (plug this into the other equation now)...
x + 2(7 - 2x) = 5 ...
x + 14 - 4x = 5 ...
14 - 3x = 5 ...
-3x = -9
x = 3 (plug this into either original equation given in question to find y)...

2(3) + y = 7 ...
6 + y = 7 ...
y = 1 (now we have both our x and y, which is 3 and 1 respectively)...

3 + 1/ 3 = 4/3
Ans: B

ScottTargetTestPrep · Answer

Solution: 
 
If we add the two given equations, we have:

3x + 3y = 12

Dividing the above equation by 3, we have:

x + y = 4

Dividing again by 3, we have:

(x + y)/3 = 4/3

Answer: B

GMATinsight · Answer

Video solution by  GMATinsight

https://www.youtube.com/watch?v=2JMi3Vf_6Hk

bumpbot · Answer

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