Algebra question

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

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

B

Given:
2x + y = 7
x + 2y = 5

ADD the two equations to get: 3x + 3y = 12
Divide both sides by 3 to get: x + y = 4

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

Answer: B

Hi AbeNeedsAnswers,

This is an example of a 'system' question (2 variables and 2 unique equations), but before jumping right in and solving algebraically, it's important to consider the specific question that is ASKED...

Here, we're asked for (X+Y)/3, but that does NOT necessarily mean that we have to solve for X and Y individually. Looking at the two equations, you should notice that we're dealing with (2X+Y) and (X+2Y). Remember that nothing about the questions that you'll see on Test Day is ever 'random' - every number and every word are carefully chosen (to provide you with the necessary information and often to provide you with 'shortcuts' that you can use to get to the correct answer faster).

Thus, someone specifically chose to give us (2X+Y) and (X+2Y)... the 'shortcut' is to recognize that (2X+Y) + (X+2Y) = 3X + 3Y.... and that sum is exactly 3 times what we're looking for (re: X+Y). Thus, adding the two equations into one big equation, we get....

3X + 3Y = 12

Now we can divide both sides by 3...

X + Y = 4

And plug this value into the question....

4/3

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

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

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

B

This is indeed an easy question. The great thing about this question is how quickly you do it. It should be done in 30-45 seconds.

If one finds the values of x and y, and then compute the value of (x+y)/3, he/she is bound to take 60-120 second, which is not the purpose of this question.

In the GMAT questions, you need not jump to start solving questions; the GMAT does not simply tests your math skills, it tests your quantitative aptitude.

Once we look at 2x + y = 7; x + 2y = 5, and (x + y)/3, we see that the expression (x + y)/3 can be written as (3x + 3y)/9.

The value of (3x+3y) can be achieved by adding the two equations, thus there is no need to compute the values of x and y.

Hope this helps.

-Jay
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AbeNeedsAnswers wrote:If 2x + y = 7 and x + 2y = 5, then (x + y)/3 =

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

We can add our two equations together and we have:

3x + 3y = 12

Dividing both sides by 3, we have:

x + y = 4

Dividing by 3 again, we have:

(x + y)/3 = 4/3

Answer: B