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Solve for value X

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Solve for value X

by vinhaha » Wed Feb 17, 2016 8:04 am
Hi, could anybody double check my approach and answer? Many thanks in advance!

14. What is the value of x?
(1) 3x+2y=6
(2) 4y=12-6x

1
2
Together
Either <- my answer
None

-

(1) 3x+2y=6
3x = 6 - 2y
x = 2 + 2y/3y

(2) 4y=12-6x
6x = 12 - 4y
x = 2 - 2y/3y
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by Brent@GMATPrepNow » Wed Feb 17, 2016 9:50 am
vinhaha wrote:Hi, could anybody double check my approach and answer? Many thanks in advance!

14. What is the value of x?
(1) 3x+2y=6
(2) 4y=12-6x

1
2
Together
Either <- my answer
None

-

(1) 3x+2y=6
3x = 6 - 2y
x = 2 + 2y/3y

(2) 4y=12-6x
6x = 12 - 4y
x = 2 - 2y/3y
In both cases above, you are dividing both sides of the equation by 3.
However, you end up dividing by 3y

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by Brent@GMATPrepNow » Wed Feb 17, 2016 9:57 am
vinhaha wrote:
What is the value of x?
(1) 3x + 2y = 6
(2) 4y = 12 - 6x
Target question: What is the value of x?

Statement 1: 3x + 2y = 6
Here we have ONE equation with TWO variables, which means there's more than 1 solution.
For example, one possible solution is x = 0 and y = 3.
Another possible solution is x = 2 and y = 0.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 4y = 12 - 6x
This equation looks similar to the one in statement 1.
Take 4y = 12 - 6x and add 6x to both sides to get: 4y + 6x = 12
Divide both sides by 2 to get: 2y + 3x = 6
Aha, this is the SAME as the equation in statement 1.
Since it's the same, we can be certain that statement 2 is NOT SUFFICIENT.

Statements 1 and 2 combined
Since both statements provide the same information AND both statements are not sufficient, the combined statements are also NOT SUFFICIENT

Answer = E

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Brent
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by [email protected] » Wed Feb 17, 2016 10:07 am
Hi Vinhaha,

Since Brent has already explained the error in your work, I won't rehash any of that here.

This DS question asks us for the value of X without giving us any 'starting' information to work with.

1) 3X + 2Y = 6

In this Fact, we have to deal with another variable. By doing a bit of algebra, we can isolate the value of X...

3X = -2Y + 6

X = -2Y/3 + 2

The value of X will clearly be based on the value of Y. Since Y can be ANY value, X can be more than one value.
Fact 1 is INSUFFICIENT

2) 4Y = 12 - 6X

With this fact, we're dealing with a similar situation to the one that we dealt with in Fact 1 (above). With a bit of algebra we have...

6X = -4Y + 12
3X = -2Y + 6

At this point, you should notice that this is the SAME equation as the one we had in Fact 1, so we don't have to do any more work here (we already know the end result will be insufficient).
Fact 2 is INSUFFICIENT

Combined, we do NOT have two unique equations - we have the same equation twice. That equation was NOT enough to get us the value of X.
Combined, INSUFFICIENT

Final Answer: E

As an aside, ANY time both Facts provide the exact SAME information, the correct answer will be either D or E.

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