Data Sufficiency

ruwan_s wrote:What is x?

a) x = 4y - 4
b) xy = 8

This question highlights the common myth that 2 equations with 2 unknowns will provide sufficient information to find 1 unique solution. In order for 2 equations with 2 unknowns to provide sufficient information, the equations must be linear equations (i.e., variables aren't multiplied together) AND they must be different equations.

We cover this myth and many others in the following free videos:
- Common GMAT Data Sufficiency Myths - Part I: https://www.gmatprepnow.com/module/gmat- ... cy?id=1106
- Common GMAT Data Sufficiency Myths - Part II: https://www.gmatprepnow.com/module/gmat- ... cy?id=1107

Cheers,
Brent

ruwan_s wrote:What is x?

1) x = 4y - 4
2) xy = 8

In Mitch's approach, he replaced x with 4y-4 and solved for y (and then solved for x)
Another approach is to replace the y-value and then solve for x.
Here's what I mean....


Target question: What is the value of x?

Statement 1: x = 4y - 4
This statement doesn't FEEL sufficient, so I'm going to TEST some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: y = 1 and x = 0. In this case x = 0
Case b: y = 2 and x = 4. In this case x = 4
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: https://www.gmatprepnow.com/articles/dat ... lug-values

Statement 2: xy = 8
This statement doesn't feel sufficient either. So, let's test some values.
There are several values of x and y that satisfy statement 2. Here are two:
Case a: y = 1 and x = 8. In this case x = 8
Case b: y = 2 and x = 4. In this case x = 4
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 2: xy = 8
Solve for y, to get: y = 8/x

Statement 1: x = 4y - 4
Replace y with 8/x to get: x = 4(8/x) - 4
Now, we need only solve for x
Simplify to get: x = 32/x - 4
Multiply both sides by x to get: x² = 32 - 4x
Rearrange to get: x² + 4x - 32 = 0
Factor: (x + 8)(x - 4) = 0
So, x = -8 OR x = 4
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent

ruwan_s wrote:Ans: E - relatively easy question, I want to know if the answer is E because of the two solutions X = -8 or X = 4

You're absolutely right. Whenever you have a DS question that asks for a value, a statement will only be sufficient if it gives one unique value for the unknown. Two potential values = insufficient.

Brent rightly point out that the GMAT often tricks us into assuming that 2 equations will allow us to solve for the value of 2 variables. We use the 2 equation, 2 variable rule often when solving for unknowns in PS word problems, but quite often the rule won't work in DS. Here are some exceptions to the rule:

- when the two equations produce a quadratic, as in this problem. Quadratics will give you two potential values, not just one.

- when the two are secretly the same equation. Consider:
What is the value of x?
(1) 3x - 2y = 4
(2) 5y + 7 = 6x + y - 1

- when one of the variables cancels:
what is the value of m?
(1) 2m + n = 6
(2) 3m - n = 9 - (m + n)

ruwan_s wrote:What is X?

a) x = 4y - 4
b) xy = 8

[spoiler] Ans: E - relatively easy question, I want to know if the answer is E because of the two solutions X = -8 or X = 4[/spoiler]

Yes, the answer is E because of the [spoiler]two solutions: X = -8 or 4.[/spoiler]

This is 'What is the value?' kind of question. In DS, we need a unique answer to the question. No two answers.

The moment I saw statement 2, I anticipated that this may be a case of a quadratic equation, rendering two answers. However, it's not always the case. A quadratic equation can render a unique answer. See this: x^2 + 8x + 16=0. Though this is a quadratic equation, it is a perfect square of (x+4).

x^2 + 8x + 16=0 => (x+4)^2 = 0 => x = -4 (A unique value!).

Similarly, two linear equations in two variables do not guarantee unique values for the variables. The seemingly two different equations may, in fact, be the same.

Take Away: Solve completely!

-Hope this helps!

-Jay
_________________
Manhattan Review GMAT Prep

Locations: New York | Barcelona | Manila | Melbourne | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

Zoser wrote:I think the answer is "C" for this reason:

We got either y=2 and as though x=4
or
Y=-1 and as though x=-8

In case Y=-1 and x=-8 we go back the the formula xy=8
so -8*-1=8
which is correct and x has to be -8 and thus Answer is "C"

What is wrong with my approach?

Thanks

The issue with your approach is that you did not consider y=2 and x=4. These values also make xy=8. Thus x has two qualified values of x: -8 or 4. No unique value!

Hope this helps!

-Jay
_________________
Manhattan Review GMAT Prep

Locations: New York | Barcelona | Manila | Melbourne | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.