What is x? (1) x = 4y - 4 (2) xy = 8

Question

What is x?

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

My question is that why the answer is E instead of C. Any help would be appreciated.

What is x?
1) x=4y-4
2) xy=8

The solution given in the MGMAT guide explains that because after substitution, there are two different answers y = -1 and y = 2 which makes x = -8 and x = 4.
Since we can solve x with two statements together, why isnt the answer C? Instead of E (both statements together are not sufficient). Thanks in advance.

WillEconomistGMAT · Answer

The often forgotten qualification to the "n variables, n distinct equations" rule is that the equations must be linear. The second equation in the problem you provided will not plot a line. Rather, it plots a hyperbola.

So, the rule does not apply here. Hope that helps!

So, the rule does not apply here. Hope that helps!

mau5 · Answer

Say you take both together:

x=4y-4. Replace y with  \frac{8}{x}

You get, x=4*\frac{8}{x}-4 
Thus, as you can see,this is a quadratic for x, of the form :  x^2+4x-32=0 
Thus,  (x-4)(x+8) = 0

Thus, x = 4, or x = -8.Insufficient.

Note: The answer would have been C, say if the problem read:

1.x=-4-4y
2. xy = 1.

Try reasoning it out.

Hope this helps.

Bunuel · Answer

There are two kinds of data sufficient questions: YES/NO DS questions and DS questions which ask to find a value. In a Yes/No Data Sufficiency questions, statement is sufficient if the answer is “always yes” or “always no” while a statement is insufficient if the answer is "sometimes yes" and "sometimes no". When a DS question asks about the value of some variable, then the statement is sufficient ONLY if you can get the single numerical value of this variable. Now, our original question is asking about the value, thus the statement is sufficient ONLY if you can get the single numerical value of this variable. . Hope this helps. P.S. Please rad carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to the rules 3 and 7. Thank you.

uwengdori · Answer

Easy stuff obviously. we substitute and we get y = 2, and y = -1, which gives us x = 4, and x = -8

My question is I thought the answer would be 'C', but the answer says E. yes there are two x solutions, but from a quadratic equation pt of view, we did find definite solid answers for x, which are the two values we found above. So the way my brain thinks is we did answer the question of 'what the x is'. It is a singular 'is' in the question but still.

Of course, there are many scenarios of DS, but when solving DS questions, should I assume that there is absolutely and should only be one single answer in such cases as this?

Bunuel · Answer

When a DS question asks about the value of some variable, then the statement is sufficient ONLY if you can get the   single numerical value   of this variable.

Since you get TWO possible values of x, the statements are not sufficient.

Hope it's clear.

EMPOWERgmatRichC · Answer

Hi sytabish,

When you divided both sides by (Y+1), you 'removed' a potential solution. Here's a slightly different way to look at the algebra involved:

X = 4Y - 4
XY = 8

We can substitute in the value for X, giving us....

(4Y-4)(Y) = 8
4Y^2 - 4Y - 8 = 0

This is a Quadratic that can be factored into 2 pieces:

4Y^2 - 4Y - 8 = 0
(Y + 1)(4Y - 8) = 0

Y = -1 or +2

Since Y has 2 different solutions, you can plug those options into the second equation to prove that X has 2 different solutions:

IF...
Y = -1
XY = 8
X = -8

IF...
Y = 2
XY = 8
X = 4
Combined, INSUFFICIENT

Final Answer:  E

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

BrentGMATPrepNow · Answer

Target question :    What is the value of x?

Statement 1 : x = 4y − 4   
1 equation with 2 variables means there are infinitely many possible values for x. 
If we're uncertain, we can TEST some values.
There are several values of x and y that satisfy statement 1. Here are two: 
Case a: x = 0 and y = 1. in this case  x = 0 
Case b: x = 4 and y = 2. in this case  x = 4 
Since we cannot answer the  target question  with certainty, statement 1 is NOT SUFFICIENT

Statement 2 : xy = 8 
1 equation with 2 variables means there are infinitely many possible values for x. 
If we're uncertain, we can TEST some values.
There are several values of x and y that satisfy statement 2. Here are two: 
Case a: x = 1 and y = 8. in this case  x = 1 
Case b: x = 4 and y = 2. 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 1 tells us that x = 4y − 4 
Statement 2 tells us that xy = 8

Take x = 4y − 4, and solve for y. 
So, add 4 to both sides to get: x + 4 = 4y
Divide both sides by 4 to get:  (x + 4)/4 = y

Now take xy = 8 and replace y with  (x + 4)/4  to get...
(x) (x + 4)/4  = 8
Multiply both sides by 4 to get: (x)(x + 4) = 32
Expand: x² + 4x = 32
Set equal to zero to get: x² + 4x - 32 = 0
Factor: (x + 8)(x - 4) = 0
So, EITHER  x = -8  OR  x = 4 
Since we cannot answer the  target question  with certainty, the combined statements are NOT SUFFICIENT

Answer: E

GMATinsight · Answer

Statement 1: x = 4y - 4 
SInce x is dependent on y and y too is unknown hence x can NOT be calculated

NOT SUFFICIENT

Statement 2: xy = 8 
SInce x is dependent on y and y too is unknown hence x can NOT be calculated

NOT SUFFICIENT

COmbining the statement

x = 4y - 4 and xy = 8

o.e. x = 8/y

i.e. 8/y = 4y - 4

i.e. 4y^2 - 4y - 8 = 0

i.e. y^2 - y - 2 = 0

i.e. y^2 - 2y + y - 2 = 0

i.e. (y+1) (y - 2) = 0
i.e. y = -1 or 2
i.e. x = -8 or 4 respectively

Two vakues of x hence

NOT SUFFICIENT

Answer: Option E

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What is x? (1) x = 4y - 4 (2) xy = 8

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